Gauge fields, geometric phases, and quantum adiabatic pumps

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.

DNA Sequence Representation methods

DNA sequence representation methods are used to denote a gene structure effectively and help in similarities/dissimilarities analysis of coding sequences. Many different kinds of representations have been proposed in the literature. They can be broadly classified into Numerical, Graphical, Geometrical and Hybrid representation methods. DNA structure and function analysis are made easy with graphical and geometrical representation methods since it gives visual representation of a DNA structure. In numerical method, numerical values are assigned to a sequence and digital signal processing methods are used to analyze the sequence. Hybrid approaches are also reported in the literature to analyze DNA sequences. This paper reviews the latest developments in DNA Sequence representation methods. We also present a taxonomy of various methods. A comparison of these methods where ever possible is also done

Geometric polarimetry − part I: spinors and wave states

A new formal approach for representation of polarization states of coherent and partially coherent electromagnetic plane waves is presented. Its basis is a purely geometric construction for the normalised complex-analytic coherent wave as a generating line in the sphere of wave directions, and whose Stokes vector is determined by the intersection with the conjugate generating line. The Poincare sphere is now located in physical space, simply a coordination of the wave sphere, its axis aligned with the wave vector. Algebraically, the generators representing coherent states are represented by spinors, and this is made consistent with the spinor-tensor representation of electromagnetic theory by means of an explicit reference spinor we call the phase flag. As a faithful unified geometric representation, the new model provides improved formal tools for resolving many of the geometric difficulties and ambiguities that arise in the traditional formalism.

The paternity of the price-quality 'value map'

In the literature on firm strategy and product differentiation, consumer price-quality trade-offs are sometimes represented using consumer 'value maps'. These involve the geometric representation of indifferent price and quality combinations as points along curves that are concave to the 'quality' axis. In this paper, it is shown that the value map for price-quality tradeoffs may be derived from a Hicksian compensated demand curve for product quality. The paper provides the theoretical link between analytical methods employed in the existing literature on firm strategy and competitive advantage with the broader body of economic analysis.

Impact of using different radiation therapy techniques in breat cancer: contralateral breast dose

RESUMO: O cancro de mama e o mais frequente diagnoticado a indiv duos do sexo feminino. O conhecimento cientifico e a tecnologia tem permitido a cria ção de muitas e diferentes estrat egias para tratar esta patologia. A Radioterapia (RT) est a entre as diretrizes atuais para a maioria dos tratamentos de cancro de mama. No entanto, a radia ção e como uma arma de dois canos: apesar de tratar, pode ser indutora de neoplasias secund arias. A mama contralateral (CLB) e um orgão susceptivel de absorver doses com o tratamento da outra mama, potenciando o risco de desenvolver um tumor secund ario. Nos departamentos de radioterapia tem sido implementadas novas tecnicas relacionadas com a radia ção, com complexas estrat egias de administra ção da dose e resultados promissores. No entanto, algumas questões precisam de ser devidamente colocadas, tais como: E seguro avançar para tecnicas complexas para obter melhores indices de conformidade nos volumes alvo, em radioterapia de mama? O que acontece aos volumes alvo e aos tecidos saudaveis adjacentes? Quão exata e a administração de dose? Quais são as limitações e vantagens das técnicas e algoritmos atualmente usados? A resposta a estas questões e conseguida recorrendo a m etodos de Monte Carlo para modelar com precisão os diferentes componentes do equipamento produtor de radia ção(alvos, ltros, colimadores, etc), a m de obter uma descri cão apropriada dos campos de radia cão usados, bem como uma representa ção geometrica detalhada e a composição dos materiais que constituem os orgãos e os tecidos envolvidos. Este trabalho visa investigar o impacto de tratar cancro de mama esquerda usando diferentes tecnicas de radioterapia f-IMRT (intensidade modulada por planeamento direto), IMRT por planeamento inverso (IMRT2, usando 2 feixes; IMRT5, com 5 feixes) e DCART (arco conformacional dinamico) e os seus impactos em irradia ção da mama e na irradia ção indesejada dos tecidos saud aveis adjacentes. Dois algoritmos do sistema de planeamento iPlan da BrainLAB foram usados: Pencil Beam Convolution (PBC) e Monte Carlo comercial iMC. Foi ainda usado um modelo de Monte Carlo criado para o acelerador usado (Trilogy da VARIAN Medical Systems), no c odigo EGSnrc MC, para determinar as doses depositadas na mama contralateral. Para atingir este objetivo foi necess ario modelar o novo colimador multi-laminas High- De nition que nunca antes havia sido simulado. O modelo desenvolvido est a agora disponí vel no pacote do c odigo EGSnrc MC do National Research Council Canada (NRC). O acelerador simulado foi validado com medidas realizadas em agua e posteriormente com c alculos realizados no sistema de planeamento (TPS).As distribui ções de dose no volume alvo (PTV) e a dose nos orgãos de risco (OAR) foram comparadas atrav es da an alise de histogramas de dose-volume; an alise estati stica complementar foi realizadas usando o software IBM SPSS v20. Para o algoritmo PBC, todas as tecnicas proporcionaram uma cobertura adequada do PTV. No entanto, foram encontradas diferen cas estatisticamente significativas entre as t ecnicas, no PTV, nos OAR e ainda no padrão da distribui ção de dose pelos tecidos sãos. IMRT5 e DCART contribuem para maior dispersão de doses baixas pelos tecidos normais, mama direita, pulmão direito, cora cão e at e pelo pulmão esquerdo, quando comparados com as tecnicas tangenciais (f-IMRT e IMRT2). No entanto, os planos de IMRT5 melhoram a distribuição de dose no PTV apresentando melhor conformidade e homogeneidade no volume alvo e percentagens de dose mais baixas nos orgãos do mesmo lado. A t ecnica de DCART não apresenta vantagens comparativamente com as restantes t ecnicas investigadas. Foram tamb em identi cadas diferen cas entre os algoritmos de c alculos: em geral, o PBC estimou doses mais elevadas para o PTV, pulmão esquerdo e cora ção, do que os algoritmos de MC. Os algoritmos de MC, entre si, apresentaram resultados semelhantes (com dferen cas at e 2%). Considera-se que o PBC não e preciso na determina ção de dose em meios homog eneos e na região de build-up. Nesse sentido, atualmente na cl nica, a equipa da F sica realiza medi ções para adquirir dados para outro algoritmo de c alculo. Apesar de melhor homogeneidade e conformidade no PTV considera-se que h a um aumento de risco de cancro na mama contralateral quando se utilizam t ecnicas não-tangenciais. Os resultados globais dos estudos apresentados confirmam o excelente poder de previsão com precisão na determinação e c alculo das distribui ções de dose nos orgãos e tecidos das tecnicas de simulação de Monte Carlo usados.---------ABSTRACT:Breast cancer is the most frequent in women. Scienti c knowledge and technology have created many and di erent strategies to treat this pathology. Radiotherapy (RT) is in the actual standard guidelines for most of breast cancer treatments. However, radiation is a two-sword weapon: although it may heal cancer, it may also induce secondary cancer. The contralateral breast (CLB) is a susceptible organ to absorb doses with the treatment of the other breast, being at signi cant risk to develop a secondary tumor. New radiation related techniques, with more complex delivery strategies and promising results are being implemented and used in radiotherapy departments. However some questions have to be properly addressed, such as: Is it safe to move to complex techniques to achieve better conformation in the target volumes, in breast radiotherapy? What happens to the target volumes and surrounding healthy tissues? How accurate is dose delivery? What are the shortcomings and limitations of currently used treatment planning systems (TPS)? The answers to these questions largely rely in the use of Monte Carlo (MC) simulations using state-of-the-art computer programs to accurately model the di erent components of the equipment (target, lters, collimators, etc.) and obtain an adequate description of the radiation elds used, as well as the detailed geometric representation and material composition of organs and tissues. This work aims at investigating the impact of treating left breast cancer using di erent radiation therapy (RT) techniques f-IMRT (forwardly-planned intensity-modulated), inversely-planned IMRT (IMRT2, using 2 beams; IMRT5, using 5 beams) and dynamic conformal arc (DCART) RT and their e ects on the whole-breast irradiation and in the undesirable irradiation of the surrounding healthy tissues. Two algorithms of iPlan BrainLAB TPS were used: Pencil Beam Convolution (PBC)and commercial Monte Carlo (iMC). Furthermore, an accurate Monte Carlo (MC) model of the linear accelerator used (a Trilogy R VARIANR) was done with the EGSnrc MC code, to accurately determine the doses that reach the CLB. For this purpose it was necessary to model the new High De nition multileaf collimator that had never before been simulated. The model developed was then included on the EGSnrc MC package of National Research Council Canada (NRC). The linac was benchmarked with water measurements and later on validated against the TPS calculations. The dose distributions in the planning target volume (PTV) and the dose to the organs at risk (OAR) were compared analyzing dose-volume histograms; further statistical analysis was performed using IBM SPSS v20 software. For PBC, all the techniques provided adequate coverage of the PTV. However, statistically significant dose di erences were observed between the techniques, in the PTV, OAR and also in the pattern of dose distribution spreading into normal tissues. IMRT5 and DCART spread low doses into greater volumes of normal tissue, right breast, right lung, heart and even the left lung than tangential techniques (f-IMRT and IMRT2). However,IMRT5 plans improved distributions for the PTV, exhibiting better conformity and homogeneity in target and reduced high dose percentages in ipsilateral OAR. DCART did not present advantages over any of the techniques investigated. Di erences were also found comparing the calculation algorithms: PBC estimated higher doses for the PTV, ipsilateral lung and heart than the MC algorithms predicted. The MC algorithms presented similar results (within 2% di erences). The PBC algorithm was considered not accurate in determining the dose in heterogeneous media and in build-up regions. Therefore, a major e ort is being done at the clinic to acquire data to move from PBC to another calculation algorithm. Despite better PTV homogeneity and conformity there is an increased risk of CLB cancer development, when using non-tangential techniques. The overall results of the studies performed con rm the outstanding predictive power and accuracy in the assessment and calculation of dose distributions in organs and tissues rendered possible by the utilization and implementation of MC simulation techniques in RT TPS.

Harmonic active contours.

We propose a segmentation method based on the geometric representation of images as 2-D manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set function and the objective functional corresponds to the surface of the image manifold. In this geometric framework, both data-fidelity and regularity terms of the segmentation are represented by a single functional that intrinsically aligns the gradients of the level set function with the gradients of the image and results in a segmentation criterion that exploits the directional information of image gradients to overcome image inhomogeneities and fragmented contours. The proposed formulation combines this robust alignment of gradients with attractive properties of previous methods developed in the same geometric framework: 1) the natural coupling of image channels proposed for anisotropic diffusion and 2) the ability of subjective surfaces to detect weak edges and close fragmented boundaries. The potential of such a geometric approach lies in the general definition of Riemannian manifolds, which naturally generalizes existing segmentation methods (the geodesic active contours, the active contours without edges, and the robust edge integrator) to higher dimensional spaces, non-flat images, and feature spaces. Our experiments show that the proposed technique improves the segmentation of multi-channel images, images subject to inhomogeneities, and images characterized by geometric structures like ridges or valleys.

Optimization and validation of a new 3D-US imaging robot to detect, localize and quantify lower limb arterial stenoses

L’athérosclérose est une maladie qui cause, par l’accumulation de plaques lipidiques, le durcissement de la paroi des artères et le rétrécissement de la lumière. Ces lésions sont généralement localisées sur les segments artériels coronariens, carotidiens, aortiques, rénaux, digestifs et périphériques. En ce qui concerne l’atteinte périphérique, celle des membres inférieurs est particulièrement fréquente. En effet, la sévérité de ces lésions artérielles est souvent évaluée par le degré d’une sténose (réduction >50 % du diamètre de la lumière) en angiographie, imagerie par résonnance magnétique (IRM), tomodensitométrie ou échographie. Cependant, pour planifier une intervention chirurgicale, une représentation géométrique artérielle 3D est notamment préférable. Les méthodes d’imagerie par coupe (IRM et tomodensitométrie) sont très performantes pour générer une imagerie tridimensionnelle de bonne qualité mais leurs utilisations sont dispendieuses et invasives pour les patients. L’échographie 3D peut constituer une avenue très prometteuse en imagerie pour la localisation et la quantification des sténoses. Cette modalité d’imagerie offre des avantages distincts tels la commodité, des coûts peu élevés pour un diagnostic non invasif (sans irradiation ni agent de contraste néphrotoxique) et aussi l’option d’analyse en Doppler pour quantifier le flux sanguin. Étant donné que les robots médicaux ont déjà été utilisés avec succès en chirurgie et en orthopédie, notre équipe a conçu un nouveau système robotique d’échographie 3D pour détecter et quantifier les sténoses des membres inférieurs. Avec cette nouvelle technologie, un radiologue fait l’apprentissage manuel au robot d’un balayage échographique du vaisseau concerné. Par la suite, le robot répète à très haute précision la trajectoire apprise, contrôle simultanément le processus d’acquisition d’images échographiques à un pas d’échantillonnage constant et conserve de façon sécuritaire la force appliquée par la sonde sur la peau du patient. Par conséquent, la reconstruction d’une géométrie artérielle 3D des membres inférieurs à partir de ce système pourrait permettre une localisation et une quantification des sténoses à très grande fiabilité. L’objectif de ce projet de recherche consistait donc à valider et optimiser ce système robotisé d’imagerie échographique 3D. La fiabilité d’une géométrie reconstruite en 3D à partir d’un système référentiel robotique dépend beaucoup de la précision du positionnement et de la procédure de calibration. De ce fait, la précision pour le positionnement du bras robotique fut évaluée à travers son espace de travail avec un fantôme spécialement conçu pour simuler la configuration des artères des membres inférieurs (article 1 - chapitre 3). De plus, un fantôme de fils croisés en forme de Z a été conçu pour assurer une calibration précise du système robotique (article 2 - chapitre 4). Ces méthodes optimales ont été utilisées pour valider le système pour l’application clinique et trouver la transformation qui convertit les coordonnées de l’image échographique 2D dans le référentiel cartésien du bras robotisé. À partir de ces résultats, tout objet balayé par le système robotique peut être caractérisé pour une reconstruction 3D adéquate. Des fantômes vasculaires compatibles avec plusieurs modalités d’imagerie ont été utilisés pour simuler différentes représentations artérielles des membres inférieurs (article 2 - chapitre 4, article 3 - chapitre 5). La validation des géométries reconstruites a été effectuée à l`aide d`analyses comparatives. La précision pour localiser et quantifier les sténoses avec ce système robotisé d’imagerie échographique 3D a aussi été déterminée. Ces évaluations ont été réalisées in vivo pour percevoir le potentiel de l’utilisation d’un tel système en clinique (article 3- chapitre 5).

Modélisation procédurale par composants

Le réalisme des images en infographie exige de créer des objets (ou des scènes) de plus en plus complexes, ce qui entraîne des coûts considérables. La modélisation procédurale peut aider à automatiser le processus de création, à simplifier le processus de modification ou à générer de multiples variantes d'une instance d'objet. Cependant même si plusieurs méthodes procédurales existent, aucune méthode unique permet de créer tous les types d'objets complexes, dont en particulier un édifice complet. Les travaux réalisés dans le cadre de cette thèse proposent deux solutions au problème de la modélisation procédurale: une solution au niveau de la géométrie de base, et l’autre sous forme d'un système général adapté à la modélisation des objets complexes. Premièrement, nous présentons le bloc, une nouvelle primitive de modélisation simple et générale, basée sur une forme cubique généralisée. Les blocs sont disposés et connectés entre eux pour constituer la forme de base des objets, à partir de laquelle est extrait un maillage de contrôle pouvant produire des arêtes lisses et vives. La nature volumétrique des blocs permet une spécification simple de la topologie, ainsi que le support des opérations de CSG entre les blocs. La paramétrisation de la surface, héritée des faces des blocs, fournit un soutien pour les textures et les fonctions de déplacements afin d'appliquer des détails de surface. Une variété d'exemples illustrent la généralité des blocs dans des contextes de modélisation à la fois interactive et procédurale. Deuxièmement, nous présentons un nouveau système de modélisation procédurale qui unifie diverses techniques dans un cadre commun. Notre système repose sur le concept de composants pour définir spatialement et sémantiquement divers éléments. À travers une série de déclarations successives exécutées sur un sous-ensemble de composants obtenus à l'aide de requêtes, nous créons un arbre de composants définissant ultimement un objet dont la géométrie est générée à l'aide des blocs. Nous avons appliqué notre concept de modélisation par composants à la génération d'édifices complets, avec intérieurs et extérieurs cohérents. Ce nouveau système s'avère général et bien adapté pour le partionnement des espaces, l'insertion d'ouvertures (portes et fenêtres), l'intégration d'escaliers, la décoration de façades et de murs, l'agencement de meubles, et diverses autres opérations nécessaires lors de la construction d'un édifice complet.

A geometrical heuristic for drawing concept lattices

Concept lattices are used in formal concept analysis to represent data conceptually so that the original data are still recognizable. Their line diagrams should reflect the semantical relationships within the data. Up to now, no satisfactory automatic drawing programs for this task exist. The geometrical heuristic is the most successful tool for drawing concept lattices manually. It ueses a geometric representation as intermediate step between the list of upper covers and the line diagram of the lattice.

Um estudo sobre os conhecimentos geométricos adquiridos por alunos do ensino médio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Os Processos de visualização e de representação dos signos matemáticos no contexto didático-pedagógico

Pós-graduação em Educação Matemática - IGCE

Uma forma quadrática no corpo de condutor primo

Pós-graduação em Matemática - IBILCE

Cúbicas galoisianas

Pós-graduação em Matemática - IBILCE

Digital surface model, hillshade and Lambertian reflectance model of the rock glaciers Oelgrube and Aeusseres Hochebenkar (Oetztal Alps, Tyrol, Austria)

With full-waveform (FWF) lidar systems becoming increasingly available from different commercial manufacturers, the possibility for extracting physical parameters of the scanned surfaces in an area-wide sense, as addendum to their geometric representation, has risen as well. The mentioned FWF systems digitize the temporal profiles of the transmitted laser pulse and of its backscattered echoes, allowing for a reliable determination of the target distance to the instrument and of physical target quantities by means of radiometric calibration, one of such quantities being the diffuse Lambertian reflectance. The delineation of glaciers is a time-consuming task, commonly performed manually by experts and involving field trips as well as image interpretation of orthophotos, digital terrain models and shaded reliefs. In this study, the diffuse Lambertian reflectance was compared to the glacier outlines mapped by experts. We start the presentation with the workflow for analysis of FWF data, their direct georeferencing and the calculation of the diffuse Lambertian reflectance by radiometric calibration; this workflow is illustrated for a large FWF lidar campaign in the Ötztal Alps (Tyrol, Austria), operated with an Optech ALTM 3100 system. The geometric performance of the presented procedure was evaluated by means of a relative and an absolute accuracy assessment using strip differences and orthophotos, resp. The diffuse Lambertian reflectance was evaluated at two rock glaciers within the mentioned lidar campaign. This feature showed good performance for the delineation of the rock glacier boundaries, especially at their lower parts.

Advanced voxel-based CAD modelling for FSI simulations for automotive structures design

Additive Manufacturing (AM) is nowadays considered an important alternative to traditional manufacturing processes. AM technology shows several advantages in literature as design flexibility, and its use increases in automotive, aerospace and biomedical applications. As a systematic literature review suggests, AM is sometimes coupled with voxelization, mainly for representation and simulation purposes. Voxelization can be defined as a volumetric representation technique based on the model’s discretization with hexahedral elements, as occurs with pixels in the 2D image. Voxels are used to simplify geometric representation, store intricated details of the interior and speed-up geometric and algebraic manipulation. Compared to boundary representation used in common CAD software, voxel’s inherent advantages are magnified in specific applications such as lattice or topologically structures for visualization or simulation purposes. Those structures can only be manufactured with AM employment due to their complex topology. After an accurate review of the existent literature, this project aims to exploit the potential of the voxelization algorithm to develop optimized Design for Additive Manufacturing (DfAM) tools. The final aim is to manipulate and support mechanical simulations of lightweight and optimized structures that should be ready to be manufactured with AM with particular attention to automotive applications. A voxel-based methodology is developed for efficient structural simulation of lattice structures. Moreover, thanks to an optimized smoothing algorithm specific for voxel-based geometries, a topological optimized and voxelized structure can be transformed into a surface triangulated mesh file ready for the AM process. Moreover, a modified panel code is developed for simple CFD simulations using the voxels as a discretization unit to understand the fluid-dynamics performances of industrial components for preliminary aerodynamic performance evaluation. The developed design tools and methodologies perfectly fit the automotive industry’s needs to accelerate and increase the efficiency of the design workflow from the conceptual idea to the final product.