Tesi sul tema "Geometry priors"

Geometry is an a priori science. However, its apriority is saddled with problems. The aim of this paper will be to show 1) how Kant understands that the contents of geometry are synthetic a priori judgments in the Critique of Pure Reason, and 2) if it’s still relevant to study Kant’s theory of geometry after the challenges posed by non-Euclidian theories of space. With respect to point 1: Kant understands geometry as the discipline that objectifies the pure intuition of space. Every geometric concept is built upon the pure intuition of space through a synthetic ostensive process. Furthermore, the pure intuition of space is the form of external experiences. Thus, geometry and external phenomena share a common ground – pure space. This common ground is what provides an answer to the question of the possibility of mathematics as a universal and a priori science. With respect to point 2: the relevance of studying Kant’s theory of geometry lies not only in the fact that geometry can serve as an example to philosophy based on the fact that it establishes its propositions a priori, but also because the object-study of geometry – the pure intuition of space– forces the reader to review Kant’s thoughts about sensibility and its relation to space. The analysis of Kant’s theory of geometry then amounts to studying Kant’s theory of sensibility.
Para Kant la geometría es una disciplina matemática que contiene proposiciones y juicios sintéticos a priori. Sin embargo, esta afirmación no se encuentra libre de problemas. La intención del artículo será mostrar 1) cómo entiende Kant la apodicticidad, universalidad y sinteticidad de la geometría en la Crítica de la razón pura; y 2) qué relevancia tiene hoy en día estudiar la teoría kantiana de la geometría luego de la superación de la teoría euclidiana del espacio. Con respecto a (1): Kant entiende a la geometría como la ciencia que objetiva la intuición pura del espacio. Todo concepto geométrico se construye en la intuición del espacio mediante un proceso sintético que exhibe la figura geométrica. Además, la intuición pura del espacio es la forma del sentido externo. Por tanto, los objetos geométricos y los fenómenos externos comparten un territorio común: el espacio como intuición pura. Este aspecto común garantiza la universidad de la geometría. Con respecto a (2): la importancia de estudiar la teoría kantiana de la geometría no solo radica en que esta disciplina determina a priori su objeto y por tanto sirve de ejemplo a la filosofía, sino que la comprensión del objeto de la geometría, el espacio como intuición pura, nos obliga a pasar revista a lo qué entiende Kant por sensibilidad y su relación con el espacio. El estudio de la sensibilidad obliga a Kant a repensar qué se entiende por espacio y, con ello, qué se entiende por geometría. El análisis de la teoría kantiana de la geometría, entonces, equivale al estudio de la teoría kantiana de la sensibilidad.

Comprendre les images est d’une importance cruciale pour une pléthore de tâches, de la composition numérique au ré-éclairage d’une image, en passant par la reconstruction 3D d’objets. Ces tâches permettent aux artistes visuels de réaliser des chef-d’oeuvres ou d’aider des opérateurs à prendre des décisions de façon sécuritaire en fonction de stimulis visuels. Pour beaucoup de ces tâches, les modèles physiques et géométriques que la communauté scientifique a développés donnent lieu à des problèmes mal posés possédant plusieurs solutions, dont généralement une seule est raisonnable. Pour résoudre ces indéterminations, le raisonnement sur le contexte visuel et sémantique d’une scène est habituellement relayé à un artiste ou un expert qui emploie son expérience pour réaliser son travail. Ceci est dû au fait qu’il est généralement nécessaire de raisonner sur la scène de façon globale afin d’obtenir des résultats plausibles et appréciables. Serait-il possible de modéliser l’expérience à partir de données visuelles et d’automatiser en partie ou en totalité ces tâches ? Le sujet de cette thèse est celui-ci : la modélisation d’a priori par apprentissage automatique profond pour permettre la résolution de problèmes typiquement mal posés. Plus spécifiquement, nous couvrirons trois axes de recherche, soient : 1) la reconstruction de surface par photométrie, 2) l’estimation d’illumination extérieure à partir d’une seule image et 3) l’estimation de calibration de caméra à partir d’une seule image avec un contenu générique. Ces trois sujets seront abordés avec une perspective axée sur les données. Chacun de ces axes comporte des analyses de performance approfondies et, malgré la réputation d’opacité des algorithmes d’apprentissage machine profonds, nous proposons des études sur les indices visuels captés par nos méthodes.
Understanding images is needed for a plethora of tasks, from compositing to image relighting, including 3D object reconstruction. These tasks allow artists to realize masterpieces or help operators to safely make decisions based on visual stimuli. For many of these tasks, the physical and geometric models that the scientific community has developed give rise to ill-posed problems with several solutions, only one of which is generally reasonable. To resolve these indeterminations, the reasoning about the visual and semantic context of a scene is usually relayed to an artist or an expert who uses his experience to carry out his work. This is because humans are able to reason globally on the scene in order to obtain plausible and appreciable results. Would it be possible to model this experience from visual data and partly or totally automate tasks? This is the topic of this thesis: modeling priors using deep machine learning to solve typically ill-posed problems. More specifically, we will cover three research axes: 1) surface reconstruction using photometric cues, 2) outdoor illumination estimation from a single image and 3) camera calibration estimation from a single image with generic content. These three topics will be addressed from a data-driven perspective. Each of these axes includes in-depth performance analyses and, despite the reputation of opacity of deep machine learning algorithms, we offer studies on the visual cues captured by our methods.

La thèse porte sur l’amélioration de la qualité des modèles numériques d'élévation (MNE) à partir d’imagerie aérienne et satellitaire. Notre démarche repose sur l’appariement dense d’images combinant la mesure de ressemblance et la régularisation semi-globale. Cependant, elle prévoit des corrélateurs neuronaux à la place des mesures de ressemblance classiques. Malgré les efforts de recherche considérables entrepris au cours des vingt dernières années, les mesures de ressemblance classiques (NCC, Census, etc...) sont généralement limitées surtout face aux zones d’images homogènes, proches des occlusions, ombragées et en présence de surfaces ayant des propriétés de réflectance non lambertienne. Alors que ces approches, fortement dépendantes de la notion de voisinage local, perdent de distinctivité en élargissant le contexte et face à ces scénarios difficiles, les architectures de réseaux neuronaux profonds offrent des capacités d’apprentissage étendues et peuvent appréhender des notions de similarité plus complexes capables ainsi de résoudre ces scénarios d’appariement complexes. Ce travail présente des architectures neuronales et des méthodes basées sur l’apprentissage profond pour l’appariement multi-images en photogrammétrie aérienne et satellitaire. Notre approche vise à apprendre des similarités transférables à l’ensemble des géométries de reconstruction (épipolaire, native et terrain) en œuvrant en accord avec l’a priori de nature géométrique des images. Tout d’abord, la fonction de similarité est apprise sur des paires d’images épipolaires. Ensuite, les similarités apprises sont transformées pour résoudre le problème de correspondance multi-vues sur la base de recalages épipolaires ou homographiques adaptés.Notre approche se démarque du paradigme de correspondance classique qui compense les imperfections des appariements par voisinage local avec des contraintes de surface semi-globales. Plus précisément, nos réseaux neuronaux apprennent de manière contrastive des scores de similarité globaux, expressifs et pixellaires par le biais d’architectures à large champ récepteur. Notre pipeline multi-vues ne nécessite pas de réapprentissage supplémentaire sur des jeux de données dédiés et exploite des géométries de transfert comme moyens pour calculer des descripteurs orientés robustes en géométrie native. Ces derniers sont ré-échantillonnés à chaque plan hypothétique pour évaluer les similarités le long de l’intervalle de profondeur. Contrairement à la fusion a posteriori des cartes de profondeur, notre stratégie multi-vues adopte un schéma de fusion a priori pondérant les similarités apprises par paires pour remplir puis régulariser la structure de coût. Nous établissons un équilibre de performances entre l’apprentissage profond de la similarité et la régression de bout en bout pour la mise en correspondance épipolaire et démontrons que nos modèles produisent des descripteurs généralisables pour la reconstruction de surfaces 3D multi-vues omni-scènes. En tirant parti des pipelines de correspondance multi-résolution hiérarchiques, nos corrélateurs neuronaux peuvent être facilement combinés avec des mesures de similarité classiques pour améliorer la précision des MNE. Les pipelines proposés sont implémentés dans MicMac, un logiciel photogrammétrique gratuit et open source
Dense image matching is a long standing ill-posed problem. Despite the extensive research efforts undertaken in the last twenty years, the state-of-the-art handcrafted algorithms perform poorly on featureless areas, in presence of occlusions, shadows and on non-lambertian surfaces. This is due to lack of distinctiveness of the handcrafted similarity metrics in such challenging scenarios. On the other hand, deep learning based approaches to image matching are able to learn highly non-linear similarity functions thus provide an interesting path to addressing such complex matching scenarios.In this research, we present deep learning based architectures and methods for stereo and multi-view dense image matching tailored to aerial and satellite photogrammetry. The proposed approach is driven by two key ideas. First, our goal is to develop a matching network that is as generic as possible to different sensors and acquisition scenarios. Secondly, we argue that known geometrical relationships between images can alleviate the learning phase and should be leveraged in the process. As a result, our matching pipeline follows the known two step pipeline where we first compute deep similarities between pixel correspondences, followed by depth regularization. This separation ensures “generality” or “transferability” to different scenes and acquisitions. Furthermore, our similarity functions are learnt on epipolar rectified image pairs, and to exploit the learnt embeddings in a general n-view matching problem, geometry priors are mobilized. In other words, we transform embeddings learnt on pairs of images to multi-view embeddings through a priori knowledge about the relative camera poses. This allows us to capitalize on the vast stereo matching benchmarks existing in the literature while extending the approach to multi-view scenarios. Finally, we tackle the insufficient distinctiveness of the state-of-the-art patch-based features/similarities by feeding the network with large images thus adding more context, and by proposing an adapted sample mining scheme. We establish a middle-ground between state-of-the-art similarity learning and end-to-end regression models for stereo matching and demonstrate that our models yield generalizable representations in multiple view 3D surface reconstruction from aerial and satellite acquisitions. The proposed pipelines are implemented in MicMac, a free, open-source photogrammetric software

TEIXEIRA, D. N. Uma técnica de decomposição a priori para geração paralela de malhas bidimensionais. 2014. 95 f. Dissertação (Mestrado em Ciência da Computação) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014.
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This work describes a technique of two-dimensional domain decomposition for parallel mesh generation. This technique works for both distributed and shared memory and has the freedom to use any data structure that manages rectangular regions parallel to the axes to decompose the domain given as input, such as a quaternary tree (quadtree) or a binary space decomposition (bsp), for example. Any process of mesh generation that respects the prerequisites established can be used in the subdomains created, for instance, Delaunay or Advancing Front, among others. This technique is called a priori because the mesh on the interface of the subdomains is generated prior to the their internal meshes. The load estimation for each sub-domain in this work is performed with the aid of a refined quadtree, whose level of refinement guides the creation of edges that are defined from the bounderies of only inner cells. This way of estimate load produces results that accurately represent the number of elements to be generated in each subdomain. That contributes to a good partitioning of the domain, making the mesh generation in parallel be significantly faster than the serial generation. Furthermore, the quality of the generated mesh in parallel is qualitatively equivalent to that generated serially within acceptable limits.
Este trabalho descreve uma técnica de decomposição de domínios bidimensionais para geração em paralelo de malhas. Esta técnica funciona tanto para memória distribuída quanto compartilhada, além de permitir que se utilize qualquer estrutura de dados que gere regiões quadrangulares paralelas aos eixos para decompor o domínio dado como entrada. Pode se utilizar por exemplo, uma árvore quaternária (quadtree) ou uma partição binária do espaço (bsp). Além disso, qualquer processo de geração de malha que respeite os pré-requisitos estabelecidos pode ser empregado nos subdomínios criados, como as técnicas de Delaunay ou Avanço de Fronteira, dentre outras. A técnica proposta é dita a priori porque a malha de interface entre os subdomínios é gerada antes das suas malhas internas. A estimativa de carga de processamento associada a cada subdomínio é feita nesse trabalho com a ajuda de uma quadtree refinada, cujo nível de refinamento orienta a criação das arestas que são definidas a partir da discretização das fronteiras das células internas. Essa maneira de estimar carga produz resultados que representam, com boa precisão, o número de elementos a serem gerados em cada subdomínio. Isso contribui para um bom particionamento do domínio, fazendo com que a geração de malha em paralelo seja significativamente mais rápida do que a geração serial. Além disso, a qualidade da malha gerada em paralelo é qualitativamente equivalente àquela gerada serialmente, dentro de limites aceitáveis.

CoordenaÃÃo de AperfeiÃoamento de NÃvel Superior
Este trabalho descreve uma tÃcnica de decomposiÃÃo de domÃnios bidimensionais para geraÃÃo em paralelo de malhas. Esta tÃcnica funciona tanto para memÃria distribuÃda quanto compartilhada, alÃm de permitir que se utilize qualquer estrutura de dados que gere regiÃes quadrangulares paralelas aos eixos para decompor o domÃnio dado como entrada. Pode se utilizar por exemplo, uma Ãrvore quaternÃria (quadtree) ou uma partiÃÃo binÃria do espaÃo (bsp). AlÃm disso, qualquer processo de geraÃÃo de malha que respeite os prÃ-requisitos estabelecidos pode ser empregado nos subdomÃnios criados, como as tÃcnicas de Delaunay ou AvanÃo de Fronteira, dentre outras. A tÃcnica proposta à dita a priori porque a malha de interface entre os subdomÃnios à gerada antes das suas malhas internas. A estimativa de carga de processamento associada a cada subdomÃnio à feita nesse trabalho com a ajuda de uma quadtree refinada, cujo nÃvel de refinamento orienta a criaÃÃo das arestas que sÃo definidas a partir da discretizaÃÃo das fronteiras das cÃlulas internas. Essa maneira de estimar carga produz resultados que representam, com boa precisÃo, o nÃmero de elementos a serem gerados em cada subdomÃnio. Isso contribui para um bom particionamento do domÃnio, fazendo com que a geraÃÃo de malha em paralelo seja significativamente mais rÃpida do que a geraÃÃo serial. AlÃm disso, a qualidade da malha gerada em paralelo à qualitativamente equivalente Ãquela gerada serialmente, dentro de limites aceitÃveis.
This work describes a technique of two-dimensional domain decomposition for parallel mesh generation. This technique works for both distributed and shared memory and has the freedom to use any data structure that manages rectangular regions parallel to the axes to decompose the domain given as input, such as a quaternary tree (quadtree) or a binary space decomposition (bsp), for example. Any process of mesh generation that respects the prerequisites established can be used in the subdomains created, for instance, Delaunay or Advancing Front, among others. This technique is called a priori because the mesh on the interface of the subdomains is generated prior to the their internal meshes. The load estimation for each sub-domain in this work is performed with the aid of a refined quadtree, whose level of refinement guides the creation of edges that are defined from the bounderies of only inner cells. This way of estimate load produces results that accurately represent the number of elements to be generated in each subdomain. That contributes to a good partitioning of the domain, making the mesh generation in parallel be significantly faster than the serial generation. Furthermore, the quality of the generated mesh in parallel is qualitatively equivalent to that generated serially within acceptable limits.

L'imagerie médicale est une ressource de données principale pour différents types d'applications. Bien que les images concrétisent beaucoup d'informations sur le cas étudié, toutes les connaissances a priori du médecin restent implicites. Elles jouent cependant un rôle très important dans l'interprétation et l'utilisation des images médicales. Dans cette thèse, des connaissances anatomiques a priori sont intégrées dans deux applications médicales. Nous proposons d'abord une chaîne de traitement automatique qui détecte, quantifie et localise des anévrismes dans un arbre vasculaire segmenté. Des lignes de centre des vaisseaux sont extraites et permettent la détection et la quantification automatique des anévrismes. Pour les localiser, une mise en correspondance est faite entre l'arbre vasculaire du patient et un arbre vasculaire sain. Les connaissances a priori sont fournies sous la forme d'un graphe. Dans le contexte de l'identification des sous-parties d'un organe représenté sous forme de maillage, nous proposons l'utilisation d'une ontologie anatomique, que nous enrichissons avec toutes les informations nécessaires pour accomplir la tâche de segmentation de maillages. Nous proposons ensuite un nouvel algorithme pour cette tâche, qui profite de toutes les connaissances a priori disponibles dans l'ontologie.

Educational Psychology
Ph.D.
Mathematics remains a subject many students fail to become competent in by the time they graduate from high school. Most students often require one on one, individualized tutoring to help them reach competence. That remains a challenge since most classrooms are understaffed and underfunded, frequently having only one teacher in a overpopulated classroom. One strategy that has been used to alleviate some of this over reliance on the teacher has been faded worked examples, or fading. Fading is the successive removal of the last steps in a series of problems until the student is solving problems completely on their own. The current study aimed to determine whether fading improves learning, and for whom. The goal was to compare fading with business as usual (control), worked examples with self-explanations, and fading with self-explanations. Specifically, I was interested in the following research questions: (1) Do the three experimental conditions differ in promoting posttest scores on surface area and volume? (2) Do the three experimental conditions differ in promoting conceptual knowledge and procedural knowledge of surface area and volume at posttest? and (3) When interaction terms are created between student profiles and conditions within regression analyses, which profiles explain significant variance in posttest scores? Repeated measures analysis of variance, principle axis factor analysis, and simple linear regressions were used to examine the differences between conditions at posttest, to create propensity scores, and to determine whether there were any interactions between propensity scores and conditions. Results indicated a significant effect of fading on posttest scores. A regression with propensity factors indicated that the fading conditions appeared to benefit low propensity students moreso than high propensity students. Findings are discussed in terms of educational implications and future research that can complement these findings to contribute to future research.
Temple University--Theses

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The present work is a study of Teodoro spiral, for the geometric aspects of the curve. At rst, the construction of Teodoro spiral in two and three dimensions is made. And through the softwares, GeoGebra and wxMaxima were developed respectively, the geometric constructions and the necessary calculations. With the possession of the spiral of concatenation, observe the pattern of behavior of growth and position, the collared peccary in the n - th triangle. Going through measurements of Teodoro spiral with other spirals such as the Archimedean, we come to denote behavior patterns in expanding spiral. The following is an arithmetic study on the spiral obtained by the length of the branches of the same, both perfect and imperfect hits with square also spaced apart relationship between them allows us to observe numbers as the . The distribution of prime numbers is seen as the nal part of this study, where you see speculatively allowing the formation of new curves on the spiral, as parabolas.
O presente trabalho faz um estudo da espiral de Teodoro, no tocante aos aspectos geométricos da curva. De início, é feita a construção da espiral de Teodoro em duas e três dimensões. E por meio dos softwares, GeoGebra e wxMaxima, foram desenvolvidas respectivamente, as construções geométricas e os cálculos necessários. Com a posse da concatenação da espiral, observa-se o comportamento do padrão de crescimento e posição, do cateto no enésimo triângulo. Passando por aferições da espiral de Teodoro com outras espirais, como por exemplo a arquimediana, chega-se a denotar padrões de comportamento na expansão da espiral. A seguir, é mostrado um estudo aritmético na espiral, obtido através do comprimento dos ramos da mesma, que tanto atinge quadrados perfeitos e imperfeitos como também a relação de afastamento entre eles nos permite observar números como o . A distribuição dos números primos é vista como parte fi nal desse estudo, onde se vê de forma especulativa, possibilitando a formação de novas curvas sobre a espiral, como parábolas.

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Financiadora de Estudos e Projetos
This paper presents a didactic proposal for Spatial Geometry classes in High School. We were taken to create this proposal from our experience as a teacher, when we observed that the study of this content requires experimentation and contextualization activities. The study of the Spatial Geometry is of great importance in High School. It contributes to the development of the capacity of abstraction, solving practical problems of everyday life and helps to acquire skills to estimate and compare results, recognize properties of geometric shapes, calculate areas, volume and working with different units of measure. Our work uses as motivation the problem of constructing a silo for grain storage, for this it is necessary to compare the volumes of the prisms with triangular, square and hexagonal base and of the cylinder without the cover, height and total area of the fixed surface to choose the format representing the highest volume. Our work is not intended to define or obtain formulas to calculate areas and volumes. The main focus of this work is to develop the ability to manipulate these formulas and other knowledge, such as solving quadratic equation, using the Pythagorean theorem, and correctly use the calculator to solve a practical problem. This activity has been applied to three classes of Second Grade High School students in a State School of São Paulo in Agudos town. For this purpose two classes of 100 minutes were used. The pupils enjoyed the activity that was carried out in groups of three and the lesson was without complications. This is a didactic sequence that does not require many resources and may be useful for teachers who want to work the theme in context. Our proposal adopts suggestions from the National Curricular Parameters (NCP) and we believe that can be used by fellow teachers, to which our product is available.
Este trabalho apresenta uma proposta didática para aulas de Geometria Espacial no Ensino Médio. Fomos levados a criar essa proposta a partir de nossa experiência como professor, quando observamos que o estudo desse conteúdo necessita de atividades de experimentação e contextualização. O estudo da Geometria Espacial é de grande importância no Ensino Médio. Contribui para o desenvolvimento da capacidade de abstração, resolução de problemas práticos do quotidiano, e ajuda a adquirir habilidades como estimar e comparar resultados, reconhecer propriedades das formas geométricas, calcular áreas, volumes e trabalhar com diferentes unidades de medida. Nosso trabalho usa como motivação o problema de construir um silo para armazenamento de grãos, para isso é preciso comparar os volumes dos prismas de base triangular, quadrada, hexagonal e do cilindro, sem a tampa, altura e área total da superfície fixa para escolher o formato que apresente o maior volume. Nosso trabalho não tem o objetivo de definir ou obter fórmulas para calcular áreas e volumes. O foco principal deste trabalho é desenvolver a capacidade de manipular tais fórmulas e outros conhecimentos, como por exemplo, resolver equações do segundo grau, utilizar o teorema de Pitágoras e utilizar corretamente a calculadora para resolver um problema prático. Esta atividade foi aplicada em três turmas da segunda série do Ensino Médio de uma escola da Rede Estadual de Ensino de São Paulo em Agudos. Para isso foram utilizadas duas aulas de 100 minutos. Os alunos gostaram da atividade que foi realizada em grupos de três e a aula transcorreu sem complicações. Trata-se de uma sequência didática que não requer muitos recursos e pode ser útil para os professores que pretendam trabalhar o tema de maneira contextualizada. Nossa proposta adota sugestões dos Parâmetros Curriculares Nacionais (PCN) e acreditamos que pode ser utilizada por colegas professores, aos quais nosso produto está disponível.

The financial market is a stochastic and complex system that is challenging to model. It is crucial for investors to be able to model the probability of possible outcomes of financial investments and financing decisions in order to produce fruitful and productive investments. This study investigates how Monte Carlo simulations of random walks can be used to model the probability of future stock returns and how the simulations can be improved in order to provide better accuracy. The implemented method uses a mathematical model called Geometric Brownian Motion (GBM) in order to simulate stock prices. Ten Swedish large-cap stocks were used as a data set for the simulations, which in turn were conducted in time periods of 1 month, 3 months, 6 months, 9 months and 12 months. The two main parameters which determine the outcome of the simulations are the mean return of a stock and the standard deviation of historical returns. When these parameters were calculated without weights the method proved to be of no statistical significance. The method improved and thereby proved to be statistically significant for predictions for a 1 month time period when the parameters instead were weighted. By varying the assumptions regarding price distribution with respect to the size of the current time period and using other weights, the method could possibly prove to be more accurate than what this study suggests. Monte Carlo simulations seem to have the potential to become a powerful tool that can expand our abilities to predict and model stock prices.
Den finansiella marknaden är ett stokastiskt och komplext system som är svårt att modellera. Det är angeläget för investerare att kunna modellera sannolikheten för möjliga utfall av finansiella investeringar och beslut för att kunna producera fruktfulla och produktiva investeringar. Den här studien undersöker hur Monte Carlo-simuleringar av så kallade random walks kan användas för att modellera sannolikheten för framtida aktieavkastningar, och hur simuleringarna kan förbättras för att ge bättre precision. Den implementerade metoden använder den matematiska modellen Geometric Brownian Motion (GBM) för att simulera aktiepriser. Tio svenska large-cap aktier valdes ut som data för simuleringarna, som sedan gjordes för tidsperioderna 1 månad, 3 månader, 6 månader, 9 månader och 12 månader. Huvudparametrarna som bestämmer utfallet av simuleringarna är medelvärdet av avkastningarna för en aktie samt standardavvikelsen av de historiska avkastningarna. När dessa parametrar beräknades utan viktning gav metoden ingen statistisk signifikans. Metoden förbättrades och gav då statistisk signifikans på en 1 månadsperiod när parametrarna istället var viktade. Metoden skulle kunna visa sig ha högre precision än vad den här studien föreslår. Det är möjligt att till exempel variera antagandena angående prisernas fördelning med avseende på storleken av den nuvarande tidsperioden, och genom att använda andra vikter. Monte Carlo-simuleringar har därför potentialen att utvecklas till ett kraftfullt verktyg som kan öka vår förmåga att modellera och förutse aktiekurser.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
The aim of this work is to present results about the existence of non-trivial solutions for some classes of resonant and superlinear eliptic systems employing topological methods. More specifcally, we use a-priori bounds on the eventual solutions of this problems and topological degree theory.
Neste trabalho apresentamos a existência de soluções não triviais para classes de sistemas elípticos ressonantes e superlineares. Tais sistemas são tratados via métodos topológicos. Encontramos estimativas a priori para possíveis soluções destes sistemas e utilizamos estas estimativas juntamente com a teoria do grau topológico para garantir a existência de soluções.

We define formal vector bundles with marked sections on Hilbert modular schemes and we show how to use them to construct modular sheaves with an integrable meromorphic connection and a filtration which, in degree 0, gives to us a p-adic interpolation of the usual Hodge filtration. We define an U_p-operator on this sheaf and relate it with the sheaf of overconvergent Hilbert modular forms.

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
As vantagens de incluir a flexibilidade gerencial e a analogia às opções financeiras nos critérios de avaliação de projetos têm sido alvo de discussões teóricas no ramo das finanças. Diversos autores criticam os métodos de análise de investimentos utilizados correntemente, que têm como principal representante o fluxo de caixa descontado (FCD), apoiando-se na noção de que os gerentes ao tomarem decisões devem utilizar técnicas que reflitam as flexibilidades disponíveis. Nesse sentido, a presente dissertação tem por finalidade validar as vantagens sugeridas na utilização da teoria de Opções Reais através de um back-testing, que tem como objeto campos de petróleo com características representativas da indústria petrolífera brasileira. Estes testes serão realizados para o período de 1970 a 1990, sendo contemplada a incerteza econômica e excluindo-se as incertezas técnicas. O modelo desenvolvido em Excel e VBA (Visual Basic for Applications) para decisões de investimento considera as opções de espera de até dois anos e de escolha entre três intensidades de produção. O Movimento Geométrico Browniano foi assumido como o processo estocástico para representar a evolução dos preços reais do petróleo em dólares americanos ao longo do tempo, e sua volatilidade foi variada a título de análise de sensibilidade. Por fim, cabe ressaltar que os resultados obtidos não devem ser aceitos como definitivos, e sim como base de futuros trabalhos na linha de estudos empíricos para verificar e validar as vantagens teóricas das Opções Reais em relação aos demais critérios utilizados na prática.
Financial researchers have discussed a lot about the theoretical advantages of including the managerial flexibility and the financial options analogy in projects valuation criteria. Plenty of authors criticize the currently used investment analysis methods, mainly represented by the discounted cash flow, supported by the notion that the managers should use techniques that better reflect the available flexibility to take their decisions. In this sense, the present dissertation has the objective of validating the suggested advantages of using the Real Options theory through a back-testing focused on oil fields with Brazilian oil industry representative characteristics. Those tests will be carried out for the 1970-1990 period, considering the economic uncertainty and excluding the technical uncertainties. The investment decisions model developed in Excel and VBA (Visual Basic for Applications) contemplates the options of waiting till two years and of choosing among three exploitation intensities. The Geometric Brownian Motion was assumed as the stochastic process to represent the real oil prices time evolution, and its volatility was varied to generate a sensibility analysis. Finally it is worthy to state that the results shall not be accepted as definitive, and just as a foundation to future studies on the empirical research line of verifying and validating the theoretical advantages of the Real Options with regard to others currently used criteria.

In this thesis we consider two great challenges in computer simulations of partial differential equations: multiscale data, varying over multiple scales in space and time, and data uncertainty, due to lack of or inexact measurements. We develop a multiscale method based on a coarse scale correction, using localized fine scale computations. We prove that the error in the solution produced by the multiscale method decays independently of the fine scale variation in the data or the computational domain. We consider the following aspects of multiscale methods: continuous and discontinuous underlying numerical methods, adaptivity, convection-diffusion problems, Petrov-Galerkin formulation, and complex geometries. For uncertainty quantification problems we consider the estimation of p-quantiles and failure probability. We use spatial a posteriori error estimates to develop and improve variance reduction techniques for Monte Carlo methods. We improve standard Monte Carlo methods for computing p-quantiles and multilevel Monte Carlo methods for computing failure probability.

Sur une variété kählérienne compacte connexe de dimension 2m, ! étant la forme de Kähler, ­ une forme volume donnée dans [!]m et k un entier 1 < k < m, on cherche à résoudre de façon unique dans [!] l'équation ˜ !k ^!m−k = ­ en utilisant une notion de k-positivité pour ˜ ! 2 [!] (les cas extrêmes sont résolus : k = m par Yau, k = 1 trivialement). Nous résolvons par la méthode de continuité l'équation hessienne d'ordre k complexe elliptique correspondante sous l'hypothèse que la variété est à courbure bisectionelle holomorphe non-négative, ici requise seulement pour établir un pincement a priori de valeurs propres.

This thesis comprises of a body of work that investigates the use of deeply learned priors for dense geometric reconstruction of scenes. A typical image captured by a 2D camera sensor is a lossy two-dimensional (2D) projection of our three-dimensional (3D) world. Geometric reconstruction approaches usually recreate the lost structural information by taking in multiple images observing a scene from different views and solving a problem known as Structure from Motion (SfM) or Simultaneous Localization and Mapping (SLAM). Remarkably, by establishing correspondences across images and use of geometric models, these methods (under reasonable conditions) can reconstruct a scene's 3D structure as well as precisely localise the observed views relative to the scene. The success of dense every-pixel multi-view reconstruction is however limited by matching ambiguities that commonly arise due to uniform texture, occlusion, and appearance distortion, among several other factors. The standard approach to deal with matching ambiguities is to handcraft priors based on assumptions like piecewise smoothness or planarity in the 3D map, in order to "fill in" map regions supported by little or ambiguous matching evidence. In this thesis we propose learned priors that in comparison more closely model the true structure of the scene and are based on geometric information predicted from the images. The motivation stems from recent advancements in deep learning algorithms and availability of massive datasets, that have allowed Convolutional Neural Networks (CNNs) to predict geometric properties of a scene such as point-wise surface normals and depths, from just a single image, more reliably than what was possible using previous machine learning-based or hand-crafted methods. In particular, we first explore how single image-based surface normals from a CNN trained on massive amount of indoor data can benefit the accuracy of dense reconstruction given input images from a moving monocular camera. Here we propose a novel surface normal based inverse depth regularizer and compare its performance against the inverse depth smoothness prior that is typically used to regularize regions in the reconstruction that are textureless. We also propose the first real-time CNN-based framework for live dense monocular reconstruction using our learned normal prior. Next, we look at how we can use deep learning to learn features in order to improve the pixel matching process itself, which is at the heart of multi-view geometric reconstruction. We propose a self-supervised feature learning scheme using RGB-D data from a 3D sensor (that does not require any manual labelling) and a multi-scale CNN architecture for feature extraction that is fast and eficient to run inside our proposed real-time monocular reconstruction framework. We extensively analyze the combined benefits of using learned normals and deep features that are good-for-matching in the context of dense reconstruction, both quantitatively and qualitatively on large real world datasets. Lastly, we explore how learned depths, also predicted on a per-pixel basis from a single image using a CNN, can be used to inpaint sparse 3D maps obtained from monocular SLAM or a 3D sensor. We propose a novel model that uses predicted depths and confidences from CNNs as priors to inpaint maps with arbitrary scale and sparsity. We obtain more reliable reconstructions than those of traditional depth inpainting methods such as the cross-bilateral filter that in comparison offer few learnable parameters. Here we advocate the idea of "just-in-time reconstruction" where a higher level of scene understanding reliably inpaints the corresponding portion of a sparse map on-demand and in real-time.
Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 2018

Vascular diseases are among the leading causes of death in Canada and around the globe. A major underlying cause of most such medical conditions is atherosclerosis, a gradual accumulation of plaque on the walls of blood vessels. Particularly vulnerable to atherosclerosis is the carotid artery, which carries blood to the brain. Dangerous narrowing of the carotid artery can lead to embolism, a dislodgement of plaque fragments which travel to the brain and are the cause of most strokes. If this pathology can be detected early, such a deadly scenario can be potentially prevented through treatment or surgery. This not only improves the patient's prognosis, but also dramatically lowers the overall cost of their treatment. Medical imaging is an indispensable tool for early detection of atherosclerosis, in particular since the exact location and shape of the plaque need to be known for accurate diagnosis. This can be achieved by locating the plaque inside the artery and measuring its volume or texture, a process which is greatly aided by image segmentation. In particular, the use of ultrasound imaging is desirable because it is a cost-effective and safe modality. However, ultrasonic images depict sound-reflecting properties of tissue, and thus suffer from a number of unique artifacts not present in other medical images, such as acoustic shadowing, speckle noise and discontinuous tissue boundaries. A robust ultrasound image segmentation technique must take these properties into account. Prior to segmentation, an important pre-processing step is the extraction of a series of features from the image via application of various transforms and non-linear filters. A number of such features are explored and evaluated, many of them resulting in piecewise smooth images. It is also proposed to decompose the ultrasound image into several statistically distinct components. These components can be then used as features directly, or other features can be obtained from them instead of the original image. The decomposition scheme is derived using Maximum-a-Posteriori estimation framework and is efficiently computable. Furthermore, this work presents and evaluates an algorithm for segmenting the carotid artery in 3D ultrasound images from other tissues. The algorithm incorporates information from different sources using an energy minimization framework. Using the ultrasound image itself, statistical differences between the region of interest and its background are exploited, and maximal overlap with strong image edges encouraged. In order to aid the convergence to anatomically accurate shapes, as well as to deal with the above-mentioned artifacts, prior knowledge is incorporated into the algorithm by using weak geometric priors. The performance of the algorithm is tested on a number of available 3D images, and encouraging results are obtained and discussed.

Jerry L. Prince and Alan S. Willsky.
Caption title. "October 26, 1988."
Includes bibliographical references.
This research is partially supported by the U.S. Army Research Office, contract DAAL03-86-K-0171 Research is partially supported by the National Science Foundation grant ECS-87-00903

abstract: Monte Carlo simulations are traditionally carried out for the determination of the amplification of forced vibration response of turbomachine/jet engine blades to mistuning. However, this effort can be computationally time consuming even when using the various reduced order modeling techniques. Accordingly, some investigations in the past have focused on obtaining simple approximate estimates for this amplification. In particular, two of these have proposed the use of harmonic patterns of the blade properties around the disk as an approximate alternative to the many random patterns of Monte Carlo analyses. These investigations, while quite encouraging, have relied solely on single degree of freedom per sector models of the rotor. In this light, the overall focus of the present effort is a revisit of harmonic mistuning of rotors focusing first the confirmation of the previously obtained findings with a more detailed model of the blisk in both conditions of an isolated blade-dominated resonance and of a veering between blade and disk dominated modes. The latter condition cannot be simulated by a single degree of freedom per sector model. Further, the analysis will consider the distinct cases of mistuning due to variations of material properties (Young's modulus) and geometric properties (geometric mistuning). In the single degree of freedom model, both mistuning types are equivalent but they are not, as demonstrated here, in more realistic models. The difference arises because changes in geometry induce not only changes in natural frequencies of the blades alone but of their modes and the importance of these two sources of variability is discussed with both Monte Carlo simulation and harmonic mistuning results. The present investigation focuses also on the possible extension of the harmonic mistuning concept and of its quantitative information that can be derived from such analyses. From it, a novel measure of blade-disk coupling is introduced and assessed in comparison with the coupling index introduced in the past. In conclusions, the low cost of harmonic mistuning computations in comparison with full Monte Carlo simulations is demonstrated to be worthwhile to elucidate the basic behavior of the mistuned rotor in a random setting.
Dissertation/Thesis
Masters Thesis Mechanical Engineering 2014

碩士
南臺科技大學
教育領導與評鑑研究所
106
This research was based on the mathematics teaching materials of the Project for the Implementation of Remedial Instruction supported by the Ministry of Education. A set of mathematics teaching materials of the Project for the Implementation of Remedial Instruction had been developed to integrate with the teaching materials for 5th grade geometry curriculum at elementary schools, and tests were conducted for the investigation of its teaching effectiveness. After the design of the lesson plan had been finished, it was actually applied to the elementary school where the researcher worked as a teacher. It was examined whether the implementation of the lesson plan could improve the mathematics ability and interest in learning of the 5th grade students. The research subjects consisted of 26 5th grade students at a public elementary school in Tainan City. The research period was one month and was composed of 18 classes of teaching activities. 　　The Unit 3, "Fan Shapes" lesson plan together with its pre-test paper and post-test paper, the "Cubes and Cuboids" lesson plan together with its pre-test paper and post-test paper, "Teaching Reflections" and "Mathematics Learning Interest Scale" in the integration of the Project for the Implementation of Remedial Instruction supported by the Ministry of Education and the Vol. 10 of the mathematics textbooks of Nan-I version were adopted as the research tools. After the teaching of each unit, the analysis and comparison of the dependent sample t-test results of the differences in scores of the pre-test and post-test. It was found that the students' learning interest and learning effectiveness after the application of the above-mentioned mathematics teaching materials, and the teaching competence of the teachers was also improved.

This thesis examines option pricing for a Long Range Dependent (LRD) stochastic process with student marginal distributions called Fractal Activity Time Geometric Brownian Motion (FATGBM), introduced in Heyde (1999). We address four separate problems involving the pricing of options under FATGBM and other LRD stochastic processes. Following an introduction into the mechanics of derivative pricing, the thesis begins by addressing the problem of derivative pricing under FATGBM. We first develop the properties of FATGBM and show that the market is arbitrage-free but incomplete under this model. We then prove that there is no replicating strategy for this model except under special circumstances. We show that those special circumstances lead to the hedging of a Timer Option where interest rates are zero and we conclude by discussing the issue of completing the market by calibrating FATGBM to liquid risky assets such as European Options, as discussed in Carr et al. (2001). We then describe how to price path dependent options under FATGBM. We first propose a non-recombining tree that is used to then construct a recombining tree to price path dependent options. Further, we prove that our discrete time model converges to the continuous time one, resulting in a discrete approximation scheme for path dependent options. We then prove that the discrete approximation scheme results in an upper bound for the price of an American put. The next chapter addresses the problem of sampling from the distribution of FATGBM conditional on price history. Given that FATGBM is a LRD process, it is imperative to be able to simulate future price paths given a price path history. We propose a Markov Chain Monte Carlo (MCMC) approach to develop two algorithms for two different LRD processes, one FATGBM and one similar to FATGBM that we call FATGBM 2. We prove that the algorithms result in a Markov chain with a stationary distribution identical to the conditional distribution from which we wish to sample. We then discuss the implementation of both algorithms and compare the mixing times and features of the resultant conditional distribution. The final chapter combines the themes and results of the preceding chapters by using the MCMC algorithm in conjunction with the recombining tree developed in Chapter 2. The result is an analysis of the effect of long range dependence on option prices, the most compelling finding being that LRD has more of an impact on the option price than the impact of heavy tails alone, a phenomenon that has thus far been overlooked by the literature on option pricing. We conclude with an analysis of the implied volatility surface arising from FATGBM and discuss the implications of our research in the context of the existing literature.