Spel idag kräver en enorm mängd arbetstimmar för att skapas, därför behövs alltid sätt att spara tid och automatisera processer. Algoritmer för polygoniseringen av skalärfält, som Marching Cubes, har under de senaste åren blivit ett allt vanligare tillvägagångssätt för att automatiskt generera terräng. Scenkomplexiteten och kraven för visuell kvalitet i dagens spel ökar ständigt. Därmed kommer också kravet för prestandaeffektiva renderingsmetoder. Deferred rendering är en renderingsmetod som kan hantera scener med stora mängder ljuskällor och hög scenkomplexitet samtidigt. För att undersöka integreringen mellan procedurellt skapad terräng och en deferred rendering pipeline, skapades en applikation i DirectX 11 för att undersöka implementeringen och potentiella optimeringar av denna integration. / Detta projekt handlar om slumpmässig procedurell skapning av digital terräng för bruk inom datorspel, och hur man i denna kontext kan ta nytta av en grafikmotor som använder renderingstekniken deferred rendering. / Carl Engström can be reached at: Phone: 076-102 86 00 Mail: Lemmibl@gmail.com Felix Nawrin Oxing can be reached at: Mail: felix@nawrin-oxing.se

Particle simulations in real-time become reality only a few years before, when in computer science occured the idea of GPGPU. This new technology allows use the massive force of graphics card for general purposes. Today, the trend is to accelerate existing algorithms by rewriting into parallel form. On this priciple operate the particle systems too. An interesting area of particle systems are fluid simulations. The simulations are based on the theory of Navier-Stokes equations and their numerical solutions with SPH (Smoothed particle hydrodynamics). Liquids are part of everyday life, and therefore it is important to render them realistically. They are used in modern computer games and different visualizations that run in real time, therefore they must be quickly displayed.

The objective of this thesis is to design an algorithm used for localization of scalp electrodes in MRI structural data. The algorithm is based on fact that electrodes are visible on visualized head surface. The surface of a head is subdivided into smaller fragments, which are transformed from 3D space into 2D. The electrodes are then located in 2D space by use of registration techniques. The proposed algorithm is able to correctly locate up to 73% EEG electrodes, assuming that the subject has short hair. In case when a subject has long hair, the portion of correctly detected electrodes is 49%. The probability of false detection is 22% when the object is short-haired and 35% when long-haired. The algorithm should facilitate the process of EEG electrodes localization during examinations combining imaging modalities of type EEG and MRI.

This Thesis consists of four independent parts. In the first part I prove that the delooping, i.e.the classifying space, of a grouplike monoid is an $H$-space if and only if its multiplication is a homotopy homomorphism. This is an extension and clarification of a result of Sugawara. Furthermore I prove that the Moore loop space functor and the construction of the classifying space induce an adjunction on the corresponding homotopy categories. In the second part I extend a result of G. Dunn, by proving that the tensorproduct $C_{n_1}\otimes\dots \otimes C_{n_j}$ of little cube operads is a topologically equivalent suboperad of $C_{n_1 \dots n_j}$. In the third part I describe operads as algebras over a certain colored operad. By application of results of Boardman and Vogt I describe a model of the homotopy category of topological operads and algebras over them, as well as a notion of lax operads, i.e. operads whose axioms are weakened up to coherent homotopies. Here the W-construction, a functorial cofibrant replacement for a topological operad, plays a central role. As one application I construct a model for the homotopy category of topological categories. C. Berger claimed to have constructed an operad structure on the permutohedras, whose associated monad is exactly the Milgram-construction of the free two-fold loop space. In the fourth part I prove that this statement is not correct.

One main goal of this thesis is to show that for every K it is possible to find K consecutive natural numbers that cannot be written as sums of three nonnegative cubes. Since it is believed that approximately 10% of all natural numbers can be written in this way, this result indicates that the sums of three cubes distribute unevenly on the real line. These sums have been studied for almost a century, in relation with Waring's problem, but the existence of ``arbitrarily long gaps'' between them was not known. We will provide two proofs for this theorem. The first is relatively elementary and is based on the observation that the sums of three cubes have a positive bias towards being cubic residues modulo primes of the form p=1+3k. Thus, our first method to find consecutive non-sums of three cubes consists in searching them among the natural numbers that are non-cubic residues modulo ``many'' primes congruent to 1 modulo 3. Our second proof is more technical: it involves the computation of the Sato-Tate distribution of the underlying cubic Fermat variety {x^3+y^3+z^3=0}, via Jacobi sums of cubic characters and equidistribution theorems for Hecke L-functions of the Eisenstein quadratic number field Q(\sqrt{-3}). The advantage of the second approach is that it provides a nearly optimal quantitative estimate for the size of gaps: if N is large, there are >>\sqrt{log N}/(log log N)^4 consecutive non-sums of three cubes that are less than N. According to probabilistic models, an optimal estimate would be of the order of log N / log log N. In this thesis we also study other gap problems, e.g. between sums of four fourth powers, and we give an application to the arithmetic of cubic and biquadratic theta series. We also provide the following additional contributions to Number Theory and Combinatorics: a derivation of cubic identities from a parameterization of the pseudo-automorphisms of binary quadratic forms; a multiplicity estimate for multiprojective Chow forms, with applications to Transcendental Number Theory; a complete solution of a problem on planar graphs with everywhere positive combinatorial curvature.

This master thesis deals with modern technologies in graphic hardware and using their for general purpose computing. It is primary focused on architecture of unified processors and algorithm implementation via CUDA programming interface. Thesis base is to choose suited algorithm for GPU horsepower demonstration. Main aim of this work is implementation of multiplatform library offering algorithms for discrete volumetric data vectorization. For this purpose was chosen algorithm Marching cubes that is able to find surface of processed object. In created library will be contained algorithm runnable on graphic device and also one runnable on CPU. Finally we compare both variants and discuss their pros and cons.

Projektet utgår ifrån en frågeställning om hur skolbyggnaden i sig kan stimulera till lärande och nyfikenhet. Det finns flera sätt som detta kan utföras på, men det här projektet fokuserar på hur detta kan utföras genom utformning av rumsligheter. Inspirationen kommer huvudsakligen ifrån spelmiljödesign och från arkitekten Herman Hertzberger och hans bok "Space and Learning". Byggnaden består av ett program för en mellan- och högstadieskola, som är distribuerat på ett sätt som gör det utmanande att orientera sig. Rummen är utplacerade som kuber med helt eller delvis massiva väggar. De binds samman av en glasfasad, och mellanrummet som skapas blir en yta av öppen aktivitet och där intressanta rumsligheter skapas.  En annan metod för att stimulera och väcka nyfikenhet är att skapa siktlinjer. De är horisontella: genom glaspartier i väggarna, och vertikala: genom öppningar i bjälklaget.  Tanken är att eleverna allt eftersom de utforskar och lär känna sin skola också lär sig hitta, inte bara till sina klassrum eller toaletterna, utan också till spännande vrår och rumsligheter som skapas i mellanrummen. Det blir en kontrast mellan rummen; där aktiviteten är styrd av lärare och läroplanen, och ytorna i mellan där aktiviteten inte är styrd utan skapas av eleverna själva. / This project is grounded in a question about how a school building in itself can stimulate learning and curiousity. There are many ways of which this can be executed, but this project focuses on spatial design. Inspiration comes mostly from environmental design in games and from the architect Herman Hertzberger and his book "Space and Learning". The building consists of a program for middle school and junior high school, and is distributed in a way that makes orientation intentionally hard. The rooms are placed as cubes with massive or partly massive walls. They are connected by a glass facade, and the space between becomes place for interesting spatialities.  Another method for creating stimulation and curiousity is sightlines. They are horizontal: in the shape of glass walls, and vertical: by openings in the floor structure. The idea is that the students, by exploring and getting to know their school, also learns to find not only their classrooms or lavatories, but also those nooks and crannies that is formed in the in between space. There becomes a contrast between the rooms: where the activities are ruled by teachers and the curriculum, and the in between spaces: where the activity is free and formed by the students themselves.

This paper proposes an extension of Datalog devoted to data manipulations in On-Line Analytical Processing (OLAP) systems. This language provides a declarative and concise way to specify the basic standard restructuring and summarizing operations on multidimensional cubes used in these systems. We define its model-theoretic semantics and an equivalent fixpoint semantics that leads to a naive evaluation procedure. We also illustrate its applicability to specify usefull more complex data manipulations arising in OLAP systems.

Dans les nouveaux protocoles thérapeutiques par voie inhalée, le dosage des particules actives reste un problème complexe qui dépend de trois principaux facteurs : leur taille, la dynamique des flux et les variations de calibre bronchique. La solution nécessite de disposer d'un modèle de distribution des gaz et aérosols administrés dans les poumons. Ventilation pulmonaire et effets du cycle respiratoire sur la dynamique des fluides deviennent deux enjeux clés de la pratique clinique.<br /><br />Dans ce contexte, le projet RNTS RMOD a pour objectif de développer un simulateur morpho-fonctionnel des voies respiratoires pour l'aide au diagnostic, au geste médico-chirurgical et à l'administration de médicaments par inhalation.<br /><br />Contribuant au projet RMOD, la recherche développée dans cette thèse propose une modélisation in-silico de la structure des voies aériennes supérieures (VAS) et proximales (VAP) à partir d'examens tomodensitométriques (TDM). L'investigation morphologique et la simulation fonctionnelle bénéficient alors de géométries 3D réelles, adaptées au patient et spécifiques des pathologies rencontrées.<br /><br />La modélisation développée fait coopérer des méthodes originales de segmentation, de construction de surface maillée et d'analyse morpho-fonctionnelle.<br /><br />La segmentation des VAP est obtenue par un schéma diffusif et agrégatif gouverné par un modèle markovien, dont l'initialisation repose sur l'opérateur de coût de connexion sous contrainte topographique. De cette segmentation, l'axe central de l'arbre bronchique est extrait de manière robuste et précise en combinant information de distance, propagation de fronts, et partition conditionnelle locale. Cet axe central est représenté sous forme d'une structure hiérarchique multivaluée synthétisant caractéristiques topologiques et géométriques de l'arbre bronchique. Une surface maillée est ensuite construite en appliquant une procédure de Marching Cubes adaptative, les paramètres des différents filtres mis en jeu étant automatiquement ajustés aux caractéristiques locales du réseau bronchique conditionnellement aux attributs de l'axe central.<br /><br />La segmentation des VAS repose sur une propagation markovienne exploitant les variations locales de densité. L'initialisation combine morphologie mathématique et information de contour afin de garantir la robustesse à la topologie. Une procédure de type triangulation de Delaunay restreinte à une surface fournit ensuite la représentation maillée des VAS. Il est établi que la topologie et la géométrie des structures complexes composant les VAS sont effectivement préservées.<br /><br />Pour permettre aux médecins de valider les modèles maillés ainsi construits, un environnement virtuel 3D convivial et interactif a été réalisé. En outre, la morphologie des voies aériennes exo- et endo-luminale est analysée de façon automatique à partir de simulations d'écoulement pour des géométries réelles.<br /><br />Enfin, une modélisation unifiée des VAP et VAS est obtenue pour la première fois. Elle démontre la pertinence des approches développées. Elle ouvre la voie à la construction de modèles in-silico complets de l'appareil respiratoire ainsi qu'aux études fonctionnelles prenant en compte les paramètres morphologiques susceptibles d'influer localement ou globalement sur la dynamique des écoulements.

Este trabalho consiste no estudo de cubos de dados das regiões centrais de quatro galáxias com mesmo tipo morfológico da Via Láctea: NGC 1566, NGC 6744, NGC 613 e NGC 134. As observações foram feitas no período de 2013 a 2015 com o Integral Field Unit do Gemini Multi-Object Spectrograph do telescópio Gemini Sul. Foram utilizadas técnicas de análise de dados como Tomografia PCA, síntese espectral e Penalized Pixel Fitting. Além disso, para todos objetos, foram calculadas razões de linhas de emissão dos espectros das regiões centrais, imagens da emissão de [SII] 6716, 6731 das nuvens de alta e baixa densidades foram feitas e, em dois casos (NGC 1566 e NGC 613), analisaram-se imagens do Hubble Space Telescope para melhor entendimento do ambiente circumnuclear. Foram encontrados 6 espectros com emissão compatível com a de AGNs na amostra, sendo que, em duas galáxias, existe a possibilidade de AGNs duplos: NGC 6744 e NGC 613. No geral, todas as galáxias apresentaram populações estelares de idades variadas em suas regiões centrais, porém, predominantemente, com metalicidades altas (0.02 e 0.05). Todas as galáxias apresentaram cinemática estelar compatível com discos de rotação em torno do núcleo e, em duas galáxias (NGC 1566 e NGC 6744), foi observado um decréscimo da dispersão de velocidades estelar em direção ao núcleo, possivelmente devido à presença de estrelas jovens massivas. A emissão do featureless continuum do núcleo da galáxia de Seyfert NGC 1566 foi, pela primeira vez, isolada e estudada, sendo que foi encontrado um índice espectral igual 1.7. Uma amostra de quatro galáxias não é estatisticamente conclusiva e será necessário ampliar a amostra para um melhor entendimento global dos núcleos de galáxias de mesmo tipo morfológico da Via Láctea. / This work involved the analysis of data cubes of four nuclear regions of galaxies that have the same morphological type of the Milky Way: NGC 1566, NGC 6744, NGC 613 and NGC 134. The observations were taken in the period of 2013 to 2015 with the Integral Field Unit of Gemini Multi-object Spectrograph on the Gemini South telescope. The data were analyzed using techniques like PCA Tomography, spectral synthesis and the Penalized Pixel Fitting process. Besides that, for all the objects, emission-line ratios of the central regions were calculated, images of the emission-lines [SII]6716, 6731 of clouds of high and low densities were made and, in two cases (NGC 1566 and NGC 6744), their Hubble Space Telescope images were analyzed for better understanding of their circumnuclear regions. 6 spectra of the sample had emission compatible with that of AGNs, in two galaxies, there is a possibility of double AGN: NGC 613 and NGC 6744. In general, all the galaxies presented stellar populations with varying ages in their central regions, however mainly with high metallicities (0.02 and 0.05). All the galaxies presented stellar kinematics compatible with rotation disks around the central source and, in two galaxies (NGC 1566 and NGC 6744), there was a stellar dispersion velocity decrease toward the nuclei, possibly due to the presence of massive young stars. The featureless continuum emission of the Seyfert galaxy NGC 1566 was, for the rst time, isolated and studied. It was found that its spectral index is equal to 1.7. A sample of four galaxies is not conclusive and it is necessary to enlarge this sample to a better global understanding of the nuclei of galaxies with the same morphological type of the Milky Way.