PINHEIRO, Neilha Márcia. Rigidez da esfera no espaço euclidiano. 2013. 41 f. Dissertação(Mestrado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Programa de Pós-Graduação em Matemática, Fortaleza, 2013. / Submitted by Erivan Almeida (eneiro@bol.com.br) on 2014-02-10T18:02:48Z No. of bitstreams: 1 2013_dis_nmpinheiro.pdf: 464377 bytes, checksum: bfe6fd9d9382d5993f7d0850c4acd7bd (MD5) / Approved for entry into archive by Rocilda Sales(rocilda@ufc.br) on 2014-02-11T13:21:07Z (GMT) No. of bitstreams: 1 2013_dis_nmpinheiro.pdf: 464377 bytes, checksum: bfe6fd9d9382d5993f7d0850c4acd7bd (MD5) / Made available in DSpace on 2014-02-11T13:21:07Z (GMT). No. of bitstreams: 1 2013_dis_nmpinheiro.pdf: 464377 bytes, checksum: bfe6fd9d9382d5993f7d0850c4acd7bd (MD5) Previous issue date: 2013 / In this work, we prove new rigidity results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable result for almost-umbilic hypersurfaces and new characterizations of geodesic spheres. / Neste trabalho, provamos novos resutados de rigidez para hipersuperfícies quase-Einsteins no espaço euclidiano, baseado-se nos resultados pinching do autovalor. Então, nós deduzimos alguns resultados análogos para hipersuperfícies quase-umbílicas e uma nova caracterização de esferas geodésicas.

The following abstract is for a thesis submitted to the University of Manchester for the degree of Doctor in Philosophy by Omar AbdelRehim AbdelKerim in 2015.Anti-personnel (AP) mines remain a global problem that affects communities around the world, with 110 million active landmines still present. Landmines are a particularly callous and indiscriminate type of weapon detonating irrespective of presence of an enemy soldier or a child. Their devastating effect on communities has led to their ban through the 1997 Mine Ban Treaty. Current detectors used for mine clearance operations have an impeding weakness that has prompted this research; metal detectors used in humanitarian demining suffer from a high False Alarm Rate (FAR) prompting regular excavation of metallic clutter. The research presented aims to develop a detector capable of discriminating between metallic clutter and mines through the use of the magnetic polarizability dyadic tensor to reduce FARs, increase demining efficiency and improve deminer’s safety. A measurement apparatus was designed and constructed to perform spectroscopic magnetic measurements of small symmetrical metallic objects and produce for the first time unscaled accurate tensor values. The tensors deduced from the measurements were validated against analytical and simulated results and were found to be within 5% of measured tensors. The tensors of minimum metal AP mine surrogates and metallic clutter of symmetrical shape were measured and formed part of a tensor library to be used later by future research. This is in addition to a set of un-circulated US coinage which could be used as a calibration metric and a comparison piece for future work in this area. A detailed description of the coil design and manufacturing process is presented to develop a coil array capable of inverting buried metallic object tensors. The selection criterion was poised to identify an array that was best suited to perform the correct measurements in order to invert to an accurate tensor. The manufactured coil exhibited strong mutual coupling between the receive coils deeming it unfit for the portable detector; however, the findings of the work presented and the selection criterion developed has aided the future design of a suitable coil array. Expected signal levels from minimum metal mine detection were calculated and helped aide in the design of future detectors to ensure suitable SNR performance is achieved. A portable detector has been developed using the sensor head presented within this thesis. Work still lies ahead to achieve the complete detector capable of performing target characterisation and clutter elimination; however, significant advances have been made and are presented throughout this thesis.

Se presentan algunos conceptos básicos tensoriales, junto con el desarrollo de una forma práctica del tensor de curvatura de Riemann-Christoffel, tensor que es de mucha utilidad en diferentes aplicaciones.

abstract: Multidimensional data have various representations. Thanks to their simplicity in modeling multidimensional data and the availability of various mathematical tools (such as tensor decompositions) that support multi-aspect analysis of such data, tensors are increasingly being used in many application domains including scientific data management, sensor data management, and social network data analysis. Relational model, on the other hand, enables semantic manipulation of data using relational operators, such as projection, selection, Cartesian-product, and set operators. For many multidimensional data applications, tensor operations as well as relational operations need to be supported throughout the data life cycle. In this thesis, we introduce a tensor-based relational data model (TRM), which enables both tensor- based data analysis and relational manipulations of multidimensional data, and define tensor-relational operations on this model. Then we introduce a tensor-relational data management system, so called, TensorDB. TensorDB is based on TRM, which brings together relational algebraic operations (for data manipulation and integration) and tensor algebraic operations (for data analysis). We develop optimization strategies for tensor-relational operations in both in-memory and in-database TensorDB. The goal of the TRM and TensorDB is to serve as a single environment that supports the entire life cycle of data; that is, data can be manipulated, integrated, processed, and analyzed. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2014

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / In this dissertation the problem of channel estimation in cooperative MIMO systems is investigated. More specifically, channel estimation techniques have been developed for a communication system assisted by relays with amplify-and-forward (AF) processing system in a three-hop scenario. The techniques developed use training sequences and enable, at the receiving node, the estimation of all the channels involved in the communication process. In an initial scenario, we consider a communication system with N transmit antennas and M receive antennas and between these nodes we have two relay groups with R1 and R2 antennas each. We propose protocols based on temporal multiplexing to coordinate the retransmission of the signals. At the end of the training phase, the receiving node estimates the channel matrices by combining the received data. By exploiting the multilinear (tensorial) structure of the sets of signals, we can model the received data through tensor models, such as PARAFAC and PARATUCK2 . This work proposes the combined use of these models and algebraic techniques to explore the spatial diversity. Secondly, we consider that the number of transmit and receive antennas at the relays may be different and that the data can travel in a bidirectional scheme (two-way). In order to validate the algorithms we use Monte-Carlo simulations in which we compare our proposed models with competing channel estimation algorithms, such as, the PARAFAC and Khatri-Rao factorization based algorithms in terms of NMSE and bit error rate. / Nesta dissertaÃÃo o problema de estimaÃÃo de canal em sistemas MIMO cooperativos à investigado. Mais especificamente, foram desenvolvidas tÃcnicas para estimaÃÃo de canal em um sistema de comunicaÃÃo assistida por relays com processamento do tipo amplifica-e-encaminha (do inglÃs, amplify-and-forward) em um cenÃrio de 3 saltos. As tÃcnicas desenvolvidas utilizam sequÃncia de treinamento e habilitam, no nà receptor, a estimaÃÃo de todos os canais envolvidos no processo de comunicaÃÃo. Em um cenÃrio inicial, consideramos um sistema de comunicaÃÃo com N antenas transmissoras e M antenas receptoras e entre esses nÃs temos dois grupos de relays com R1 e R2 antenas cada um. Foram desenvolvidos protocolos de transmissÃo baseado em multiplexaÃÃo temporal para coordenar as retransmissÃes dos sinais. Ao final da fase de treinamento, o nà receptor faz a estimaÃÃo das matrizes de canal atravÃs da combinaÃÃo dos dados recebidos. Explorando a estrutura multilinear (tensorial) dos diversos conjuntos de sinais, podemos modelar os dados recebidos atravÃs de modelos tensoriais, tais como: PARAFAC e PARATUCK2. Este trabalho propÃe a utilizaÃÃo combinada desses modelos e de tÃcnicas algÃbricas para explorar a diversidade espacial. Em um segundo momento, consideramos que o nÃmero de antenas transmissoras e receptoras dos relays podem ser diferentes e ainda que os dados podem trafegar em um esquema bidirecional (do inglÃs, two-way). Para fins de validaÃÃo dos algoritmos utilizamos simulaÃÃes de Monte-Carlo em que comparamos os modelos propostos com outros algoritmos de estimaÃÃo de canal, tais como os algoritmos baseados em PARAFAC e FatoraÃÃo de Khatri-Rao em termos de NMSE e taxa de erro de bit.

Doctorado en Ciencias, Mención Astronomía / This thesis describes the work that I performed to analyse the data from the Atacama B-mode Search (ABS) experiment. The ABS experiment observed the Cosmic Microwave Background (CMB) radiation for three years using polarisation sensitive detectors. The telescope is located at the Atacama desert in the north of Chile at an altitude of 5190 metres. The goal of the experiment is to detect the primordial gravitational waves which were supposed to have been generated during the initial phase of exponential expansion of the universe. These gravitational waves leave unique signatures on the polarised CMB called the tensor B-modes. Several experiments have been built over the last decade to observe them but the primordial tensor B-modes still remain undetected. If found, they will be a direct evidence for a process called Cosmic inflation which is responsible for the initial period of exponential expansion. The detection will also provide hints about the physics of inflation as the characterisation of tensor B-modes via the parameter called tensor-to-scalar ratio r is directly related to the energy scale of inflation O(10^16) GeV, comparable to the grand-unification-theory (GUT) energy scales. The ABS experiment was designed and led by the Physics department at Princeton University. The ABS observed the CMB at 145 GHz using polarisation sensitive transition-edge-sensor (TES) bolometers. There are two mirrors, 60 cms each arranged in a compact crossed-Dragone configuration. The ABS was the first ground-based CMB experiment to successfully implement the rapid polarisation modulation using a continuously rotating (warm) half-wave-plate (HWP). In this article, I present the observation strategy, data acquisition, instrument calibration, and the data selection techniques used to produce the CMB maps and power spectrum estimation. For completeness, I also briefly describe the work done by other members of the ABS project but clearly mention my contribution at the start of every chapter. The final power spectrum is not shown as the data selection techniques and the modelling of the galactic foregrounds are still being finalised. However, the results from detailed statistical assessment of the data using an exhaustive suite of null tests indicate that we are not affected by any significant systematic effects. The assessment of the ABS null tests will be the major result of this work. ### en español: Esta tesis describe el trabajo que he realizado para analizar los datos del experimento Atacama B-mode Search (ABS). Utilizando el telescopio de ABS, cuyos detectores son sensible a la polarización, durante un periodo de tres años se observa la radiación en microondas del fonda cósmico (CMB). El telescopio esta instalado en el desierto de Atacama, en el norte de Chile, a una altura de 5190 metros. El objetivo del experimento es detectar las ondas gravitationales primordiales supuestamente generadas durante la fase inicial de expansión exponencial del universo. Estas ondas gravitacionales dejan registros únicas en polarizacion del CMB llamados tensor B-modes. Durante la ultima decada se han realizado varios instrumentos para observar tensor B-modes, pero no se han detectado aun. Si se les detecta, serian una evidencia directa de un proceso llamado inflación cósmica que sera el período inicial de la expansión exponencial. La detección también proporcionará pistas sobre la física de la inflación como la caracterización de tensor B-modes vía el cuociente tensor-a-escalar llamado r, está directamente relacionada con la escala de energía de la inflación O(10^16) GeV, comparable a la gran unificación teoría (GUT) escalas de energía. El experimento ABS fue diseñado y dirigido por el departamento de Física de la Universidad de Princeton. El ABS observo la CMB en la frecuencia de 145 GHz utilizando bolometros sensibles a la polarizacio del tipo transition-edge-sensor (TES). Posee dos espejos, de 60 cms cada uno y dispuestos en una configuracion del tipo compact crossed-Dragone. El ABS fue el primer experimento de medicion de la CMB, situado en la Tierra, en implementar exitosamente la modulacion de polarizacion rápida mediante una placa de media-onda half-wave-plate (HWP) mantenida a temperatura ambiente y girando continuamente. En este reporte, presento la estrategia de observación, adquisición de datos, la calibración del instrumento, y las técnicas de selección de datos utilizados para producir los mapas de la CMB y estimación del Espectro de potencia de la CMB. Por completitud, también describo brevemente el trabajo realizado por otros miembros del proyecto ABS, pero menciono claramente mi contribución al comienzo de cada capítulo. El espectro de potencia final no se ha incluido debido a que tanto las técnicas de selección de datos y el modelado de la absorpcion debida a nuestra galaxia no están aun finalizadas. Sin embargo, los resultados de la evaluación estadística detallada de los datos utilizando un conjunto exhaustivo de pruebas de sesgo nulo (null tests) indican que nuestras medidas no estan afectadas significativamente por efectos sistemáticos. La evaluación de las pruebas de sesgo nulo de las observaciones llevadas a cabo con el telescopio ABS nulos, es el principal resultado de este trabajo. Este resultado posibilita una determinacion robusta del Espectro de Potencia de la CMB.

Magíster en Ciencias, Mención Geofísica / Obtener parámetros de la fuente sísmica a partir de datos sismológicos y/o geodésicos es de suma importancia en la caracterización de la fuente de terremotos, lo cual cobra especial relevancia en sistemas de monitoreo sísmico en tiempo real. Existen modelos y metodologías que permiten realizar estas inferencias asumiendo distintos niveles de complejidad en el modelo de la fuente sísmica. Sin embargo, la inversión simultánea del tensor de momento y función fuente temporal utilizando datos regionales y de campo cercano de terremotos es un tema poco estudiado. El obje- tivo principal de este trabajo es invertir la función fuente temporal y el tensor de momento sísmico utilizando datos sismológicos de campo cercano y regional. Para ello se planteó una metodología y se desarrolló una herramienta computacional propia, la cual se usó para estudiar parámetros de la fuente de sismos magnitud Mw > 6.0 ocurridos en la zona Norte de Chile. El código computacional se escribió en lenguaje de programación Python, el cual permite in- vertir el tensor de momento sísmico y la función fuente temporal usando registros de campo cer- cano. Para calcular las funciones de Green del medio se utilizaron los programas computacionales Computer Programs in Seismology (CPS). El programa de inversión lee las funciones de Green precalculadas y minimiza el error de ajuste entre los sismogramas sintéticos y observados usando el método de mínimos cuadrados para estimar las componentes del tensor de momento. La función fuente se parametrizó como la suma de funciones bases, donde las amplitudes de éstas son las in- cógnitas del problema. Para estimar la función fuente se aplicó la técnica de mínimos cuadrados no negativo con un término adicional de regularización que impone una condición de suavidad sobre la función fuente. El código realiza la búsqueda del mejor centroide espacial para el ajuste de los datos, para ello itera primero en latitud y longitud, fijando la profundidad, y una vez obtenidas las coordenadas óptimas realiza una segunda iteración esta vez en profundidad. La metodología se aplicó a eventos de la secuencia sísmica del terremoto de Pisagua del 2014, Mw 8.1, y a un evento ocurrido el 2011 a 130 km de profundidad en la zona de estudio. El análisis de las soluciones obtenidas de los eventos estudiados muestra que los resultados son confiables y robustos al compararlos con soluciones publicadas por agencias sismológicas, pudiéndose incluso obtener relaciones entre la función fuente y las características del evento tales como su magnitud o profundidad (superficial, en la zona de contacto o profundo). El método de inversión si bien posee algunas limitaciones que pueden ser mejoradas, logra recuperar el tensor de momento y la función fuente en forma robusta. Las diferencias observadas con otras soluciones se encuentran en el rango de error y se observa que la función fuente depende de la zona sismogénica en donde ocurre.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第17572号 / 工博第3731号 / 新制||工||1569(附属図書館) / 30338 / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 小林 哲生, 教授 土居 伸二, 教授 山川 宏 / 学位規則第4条第1項該当

Le rayonnement d'une source ultrasonore située sur l'une des interfaces d'une plaque anisotrope est étudié. Le calcul du tenseur de Green est effectué dans le cas général d'un problème 3D. Une décomposition en multiples réflexions /réfractions, constituant une série de rayons au sein de la plaque, est utilisée pour une comparaison théorie-expérience dans le cas d'un mono cristal de Cuivre. La vitesse de phase et la vitesse d'énergie sont mesurées en fonction de la fréquence ou de la direction d'observation, pour une plaque de carbone-époxy unidirectionnels, et comparées avec la théorie. / The ultrasonic radiation from a source located on one of the interfaces of an anisotropic plateis studied. The calculation of the Green tensor is performed in the general case of a 3Dproblem. Decomposition into multiple reflections /refractions, as a series of rays in the plate,is used for comparison between theory and experiment in the case of a single crystal of copper. The phase velocity and energy velocity are measured in terms of frequency ordirection of observation, for a plate of unidirectional carbon-epoxy, and compared withtheory.

Factor analysis and related models for probabilistic matrix factorisation are of central importance to the unsupervised analysis of data, with a colourful history more than a century long. Probabilistic models for matrix factorisation allow us to explore the underlying structure in data, and have relevance in a vast number of application areas including collaborative filtering, source separation, missing data imputation, gene expression analysis, information retrieval, computational finance and computer vision, amongst others. This thesis develops generalisations of matrix factorisation models that advance our understanding and enhance the applicability of this important class of models. The generalisation of models for matrix factorisation focuses on three concerns: widening the applicability of latent variable models to the diverse types of data that are currently available; considering alternative structural forms in the underlying representations that are inferred; and including higher order data structures into the matrix factorisation framework. These three issues reflect the reality of modern data analysis and we develop new models that allow for a principled exploration and use of data in these settings. We place emphasis on Bayesian approaches to learning and the advantages that come with the Bayesian methodology. Our port of departure is a generalisation of latent variable models to members of the exponential family of distributions. This generalisation allows for the analysis of data that may be real-valued, binary, counts, non-negative or a heterogeneous set of these data types. The model unifies various existing models and constructs for unsupervised settings, the complementary framework to the generalised linear models in regression. Moving to structural considerations, we develop Bayesian methods for learning sparse latent representations. We define ideas of weakly and strongly sparse vectors and investigate the classes of prior distributions that give rise to these forms of sparsity, namely the scale-mixture of Gaussians and the spike-and-slab distribution. Based on these sparsity favouring priors, we develop and compare methods for sparse matrix factorisation and present the first comparison of these sparse learning approaches. As a second structural consideration, we develop models with the ability to generate correlated binary vectors. Moment-matching is used to allow binary data with specified correlation to be generated, based on dichotomisation of the Gaussian distribution. We then develop a novel and simple method for binary PCA based on Gaussian dichotomisation. The third generalisation considers the extension of matrix factorisation models to multi-dimensional arrays of data that are increasingly prevalent. We develop the first Bayesian model for non-negative tensor factorisation and explore the relationship between this model and the previously described models for matrix factorisation.