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.

Contribution to the Analysis, Design and Assessment of Compact Antenna Test Ranges At Millimeter Wavelengths - Contribución al Análisis, Diseño y Caracterización de Sistemas de Medida de Antenas en Rango Compacto para Frecuencias Milimétricas

This Doctoral Thesis entitled Contribution to the analysis, design and assessment of compact antenna test ranges at millimeter wavelengths aims to deepen the knowledge of a particular antenna measurement system: the compact range, operating in the frequency bands of millimeter wavelengths. The thesis has been developed at Radiation Group (GR), an antenna laboratory which belongs to the Signals, Systems and Radiocommunications department (SSR), from Technical University of Madrid (UPM). The Radiation Group owns an extensive experience on antenna measurements, running at present four facilities which operate in different configurations: Gregorian compact antenna test range, spherical near field, planar near field and semianechoic arch system. The research work performed in line with this thesis contributes the knowledge of the first measurement configuration at higher frequencies, beyond the microwaves region where Radiation Group features customer-level performance. To reach this high level purpose, a set of scientific tasks were sequentially carried out. Those are succinctly described in the subsequent paragraphs. A first step dealed with the State of Art review. The study of scientific literature dealed with the analysis of measurement practices in compact antenna test ranges in addition with the particularities of millimeter wavelength technologies. Joint study of both fields of knowledge converged, when this measurement facilities are of interest, in a series of technological challenges which become serious bottlenecks at different stages: analysis, design and assessment. Thirdly after the overview study, focus was set on Electromagnetic analysis algorithms. These formulations allow to approach certain electromagnetic features of interest, such as field distribution phase or stray signal analysis of particular structures when they interact with electromagnetic waves sources. Properly operated, a CATR facility features electromagnetic waves collimation optics which are large, in terms of wavelengths. Accordingly, the electromagnetic analysis tasks introduce an extense number of mathematic unknowns which grow with frequency, following different polynomic order laws depending on the used algorithmia. In particular, the optics configuration which was of our interest consisted on the reflection type serrated edge collimator. The analysis of these devices requires a flexible handling of almost arbitrary scattering geometries, becoming this flexibility the nucleus of the algorithmia’s ability to perform the subsequent design tasks. This thesis’ contribution to this field of knowledge consisted on reaching a formulation which was powerful at the same time when dealing with various analysis geometries and computationally speaking. Two algorithmia were developed. While based on the same principle of hybridization, they reached different order Physics performance at the cost of the computational efficiency. Inter-comparison of their CATR design capabilities was performed, reaching both qualitative as well as quantitative conclusions on their scope. In third place, interest was shifted from analysis - design tasks towards range assessment. Millimetre wavelengths imply strict mechanical tolerances and fine setup adjustment. In addition, the large number of unknowns issue already faced in the analysis stage appears as well in the on chamber field probing stage. Natural decrease of dynamic range available by semiconductor millimeter waves sources requires in addition larger integration times at each probing point. These peculiarities increase exponentially the difficulty of performing assessment processes in CATR facilities beyond microwaves. The bottleneck becomes so tight that it compromises the range characterization beyond a certain limit frequency which typically lies on the lowest segment of millimeter wavelength frequencies. However the value of range assessment moves, on the contrary, towards the highest segment. This thesis contributes this technological scenario developing quiet zone probing techniques which achieves substantial data reduction ratii. Collaterally, it increases the robustness of the results to noise, which is a virtual rise of the setup’s available dynamic range. In fourth place, the environmental sensitivity of millimeter wavelengths issue was approached. It is well known the drifts of electromagnetic experiments due to the dependance of the re sults with respect to the surrounding environment. This feature relegates many industrial practices of microwave frequencies to the experimental stage, at millimeter wavelengths. In particular, evolution of the atmosphere within acceptable conditioning bounds redounds in drift phenomena which completely mask the experimental results. The contribution of this thesis on this aspect consists on modeling electrically the indoor atmosphere existing in a CATR, as a function of environmental variables which affect the range’s performance. A simple model was developed, being able to handle high level phenomena, such as feed - probe phase drift as a function of low level magnitudes easy to be sampled: relative humidity and temperature. With this model, environmental compensation can be performed and chamber conditioning is automatically extended towards higher frequencies. Therefore, the purpose of this thesis is to go further into the knowledge of millimetre wavelengths involving compact antenna test ranges. This knowledge is dosified through the sequential stages of a CATR conception, form early low level electromagnetic analysis towards the assessment of an operative facility, stages for each one of which nowadays bottleneck phenomena exist and seriously compromise the antenna measurement practices at millimeter wavelengths.

A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established.

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

Neuromorphic Detection of Vowel Representation Spaces

In this paper a layered architecture to spot and characterize vowel segments in running speech is presented. The detection process is based on neuromorphic principles, as is the use of Hebbian units in layers to implement lateral inhibition, band probability estimation and mutual exclusion. Results are presented showing how the association between the acoustic set of patterns and the phonologic set of symbols may be created. Possible applications of this methodology are to be found in speech event spotting, in the study of pathological voice and in speaker biometric characterization, among others.

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.

A compact lightweight multipurpose ground-penetrating radar for glaciological applications

We describe a compact lightweight impulse radar for radio-echo sounding of subsurface structures designed specifically for glaciological applications. The radar operates at frequencies between 10 and 75 MHz. Its main advantages are that it has a high signal-to-noise ratio and a corresponding wide dynamic range of 132 dB due mainly to its ability to perform real-time stacking (up to 4096 traces) as well as to the high transmitted power (peak voltage 2800 V). The maximum recording time window, 40 ?s at 100 MHz sampling frequency, results in possible radar returns from as deep as 3300 m. It is a versatile radar, suitable for different geophysical measurements (common-offset profiling, common midpoint, transillumination, etc.) and for different profiling set-ups, such as a snowmobile and sledge convoy or carried in a backpack and operated by a single person. Its low power consumption (6.6 W for the transmitter and 7.5 W for the receiver) allows the system to operate under battery power for mayor que7 hours with a total weight of menor que9 kg for all equipment, antennas and batteries.

An Efficient Hybrid GO-PWS Algorithm to Analyze Conformal Serrated-Edge Reflectors for Millimeter-Wave Compact Range

A method to analyze parabolic reflectors with arbitrary piecewise rim is presented in this communication. This kind of reflectors, when operating as collimators in compact range facilities, needs to be large in terms of wavelength. Their analysis is very inefficient, when it is carried out with fullwave/MoM techniques, and it is not very appropriate for designing with PO techniques. Also, fast GO formulations do not offer enough accuracy to reach performance results. The proposed algorithm is based on a GO-PWS hybrid scheme, using analytical as well as non-analytical formulations. On one side, an analytical treatment of the polygonal rim reflectors is carried out. On the other side, non-analytical calculi are based on efficient operations, such as M2 order 2-dimensional FFT. A combination of these two techniques in the algorithm ensures real ad-hoc design capabilities, reached through analysis speedup. The purpose of the algorithm is to obtain an optimal conformal serrated-edge reflector design through the analysis of the field quality within the quiet zone that it is able to generate in its forward half space.

Spaces of the Past, Histories of the Present: An Interview with Stuart Elden and Derek Gregory

The ontologies of space and territory, our experience of them and the techniques we use to govern them, the very conception of the socio-spatial formations that we inhabit, are all historically specific: they depend on a genealogy of practices, knowledges, discourses, regulations, performances and representations articulated in a way that is extremely complex yet nevertheless legible over time. In this interview we look at the logic and the patterns that intertwine space and time — both as objects and tools of inquiry — though a cross-disciplinary dialogue. The discussion with Stuart Elden and Derek Gregory covers the place of history in socio-spatial theory and in their own work, old and new ways of thinking about the intersection between history and territory, space and time, the implications of geography and history for thinking about contemporary politics, and the challenges now faced by critical thought and academic work in the current neo-liberal attack on public universities and the welfare state

Planar compact array with parasitic elements for MIMO systems

A compact planar array with parasitic elements is studied to be used in MIMO systems. Classical compact arrays suffer from high coupling which makes correlation and matching efficiency to be worse. A proper matching network improves these lacks although its bandwidth is low and may increase the antenna size. The proposed antenna makes use of parasitic elements to improve both correlation and efficiency. A specific software based on MoM has been developed to analyze radiating structures with several feed points. The array is optimized through a Genetic Algorithm to determine parasitic elements position in order to fulfill different figures of merit. The proposed design provides the required correlation and matching efficiency to have a good performance over a significant bandwidth.

Design of a compact objective for SWIR applications

Lately the short-wave infrared (SWIR) has become very important due to the recent appearance on the market of the small detectors with a large focal plane array. Military applications for SWIR cameras include handheld and airborne systems with long range detection requirements, but where volume and weight restrictions must be considered. In this paper we present three different designs of telephoto objectives that have been designed according to three different methods. Firstly the conventional method where the starting point of the design is an existing design. Secondly we will face design starting from the design of an aplanatic system. And finally the simultaneous multiple surfaces (SMS) method, where the starting point is the input wavefronts that we choose. The designs are compared in terms of optical performance, volume, weight and manufacturability. Because the objectives have been designed for the SWIR waveband, the color correction has important implications in the choice of glass that will be discussed in detail

Ultra-compact SWIR telephoto lens design with SMS method

In this work, we propose two new optical structures, using the Simultaneous Multiple Surfaces (SMS) method, comprised of 2 reflecting surfaces and 2 refracting surfaces, 800mm focal length, f/8 (aperture diameter 100 mm) and 1.18 0 diagonal field of view in the SWIR band. The lens surfaces are rotational symmetric and calculated to have good control of non-paraxial rays. We have achieved designs with excellent performance, and with total system length of less than 60 mm.

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.

SMS-based optimization strategy for ultra-compact SWIR telephoto lens design: erratum

We report and correct an error in [Opt. Express 20, 9726–9735 (2012)]. The author list has been modified. All other contents are unchanged.