The presented doctoral thesis aims at development a new efficient tool for optimization of uniformity of point samples. One of use-cases of these point sets is the usage as optimized sets of integration points in statistical analyses of computer models using Monte Carlo type integration. It is well known that the pursuit of uniformly distributed sets of integration points is the only possible way of decreasing the error of estimation of an integral over an unknown function. The tasks of the work concern a survey of currently used criteria for evaluation and/or optimization of uniformity of point sets. A critical evaluation of their properties is presented, leading to suggestions towards improvements in spatial and statistical uniformity of resulting samples. A refined variant of the general formulation of the phi optimization criterion has been derived by incorporating the periodically repeated design domain along with a scale-independent behavior of the criterion. Based on a notion of a physical analogy between a set of sampling points and a dynamical system of mutually repelling particles, a hyper-dimensional N-body system has been selected to be the driver of the developed optimization tool. Because the simulation of such a dynamical system is known to be a computationally intensive task, an efficient solution using the massively parallel GPGPU platform Nvidia CUDA has been developed. An intensive study of properties of this complex architecture turned out as necessary to fully exploit the possible solution speedup.

Denna rapport ar resultatet av ett examensarbete som har utforts vid institutionen for informationsoch kommunikationsteknik, Kungliga Tekniska Hogskolan (KTH), och omfattar 15 hp. Rapporten presenterar ett arbete dar examensarbetarna har utvecklat en terrang med hojdskillnader och ljussattning, partikeleffekter (CPU-GPU implementering) som liknar ett fyrverkeri, partikeleffekter (GPU implementering) som visar olika monster samt en kamera for att kunna observera spelvarlden fran alla mojliga olika vinklar i 3D med API:et Lightweight Java Game Library (LWJGL). LWJGL ar ett lagniva-API som riktar sig mot nyborjare och professionella spelutvecklare i programspraket Java. Flera tekniker exponeras istallet for att mappa lagniva-funktioner i objektorienterad programmeringsparadigm som manga javautvecklare ar vana vid. LWJGL hanterar sin egen grafik, ljud och styrkontroller enbart for att fa en solid grund for moderna spel och en battre anvandarupplevelse. Den grafiska renderingen skots med OpenGL. Syftet med det har examensarbetet var att utvardera LWJGL om den ar kompetent nog att anvandas i samband med spelutveckling. Det ar kant att Java Standard Edition (Java SE) har valdigt daligt stod for grafikintensiva och komplexa applikationer dar prestandan ar valdigt viktig. Darfor utvecklade vi en storre grafiskt kravande applikation, for att kunna gora en samlad bedomning om hur det ar att arbeta med LWJGL och vad det erbjuder en spelutvecklare. Arbetet delades upp i tre olika faser. Den forsta fasen borjade med att skapa en kravspecifikation for den produkt som skulle utvecklas, den lag till grund for hela arbetet. Nasta steg var datainsamling med syfte att erhalla forstaelse for olika tekniker och att identifiera problem. Den tredje fasen var sjalva utforandet dar vi designade, implementerade, testade och analyserade losningarna iterativt. Rapporten ger lasaren en oversikt over de krav som stallts pa prototypen, den projektmetod som anvants, tekniker som har tillampats, alla losningar som har tagits fram och varfor LWJGL blev utvald bland manga andra. Enligt de tester som utforts sa ar partikelsystem A (CPU-GPU implementering) bra mycket langsammare an partikelsystem B (GPU implementering) rent prestandamassigt. Nar 1,5 miljoner partiklar renderades sa fick partikelsystem A 5 bilder per sekund och partikelsystem B 110 bilder per sekund. Ingenjorsmassiga metoder och standarder har anvants under hela arbetets forlopp som forvarvats under civilingenjorsutbildningen informationsteknik pa KTH med inriktning datalogi. Det innefattar agil systemutveckling, programmering och problemlosning. Goda kunskaper i Java, matematik och allman IT-teknisk bakgrund forutsatts for att hanga med i alla resonemang i denna rapport. / This report is the result of a thesis work done at the Department of Information and Communication Technology, Royal Institute of Technology (Swedish: Kungliga Tekniska hogskolan, abbreviated KTH), and includes 15 credits. The report presents a work in which graduate students have developed a terrain with elevation changes and lighting, particle effects (CPU-GPU implementation) displaying fireworks, particle effects (GPU implementation) which displays different patterns as well as a camera in order to observe the game world from all sorts of different angles in 3D utilizing the API Lightweight Java Game Library (LWJGL). LWJGL is a low-level API that targets beginners and professional game developers alike in the Java programming language. Several technologies are exposed instead of mapping low-level features of object-oriented programming paradigm, which many Java developers are used to. LWJGL handles its own graphics, sound and controllers just to get a solid foundation for the modern game and an improved user experience. The graphical rendering is handled using OpenGL. The aim of this thesis was to evaluate LWJGL if it is competent enough to be used in conjunction with game development. It is known that the Java Standard Edition (Java SE) has very poor support for graphics-intensive and complex applications where performance is very important. Therefore, we developed a more graphically demanding application, in order to make an overall assessment of how it is to work with LWJGL and what it offers game developers. The work was divided into three different phases. The first phase began with creating a specification for the product to be developed which became the basis of the whole work. The next step was data collection with the objective to obtain an understand the different technologies and identify problems. The third phase was the actual execution where we designed, implemented, tested and analyzed solutions iteratively. The report provides the reader with an overview of the requirements imposed on the prototype, the project methodology, technologies that have been applied, all the solutions that have been developed and why LWJGL was chosen among many others. According to the tests conducted, particle system A (CPU-GPU implementation) is much slower than particle system B (GPU implementation) purely performance-wise. When 1,5 million particles were rendered, particle system A got 5 Frames per second (FPS) and particle system B 110 FPS. Engineering methods and standards were used throughout the work process acquired during the Information Technology Engineering degree at KTH majoring in computer science. It includes agile systems development, programming and problem solving. Good knowledge of Java, mathematics and a general IT technical background is required to keep up with all the information in this report.

Um conjunto de modelos compostos de redes de filas em grades finitas servindo como ambientes aleatorios para um ou mais passeios aleatorios, que por sua vez podem afetar o comportamento das filas, e desenvolvido. Duas formas de interacao entre os passeios aleatorios sao consideradas. Para cada modelo, e provado que o processo Markoviano correspondente e recorrente positivo e reversivel. As equacoes de balanceamento detalhado sao analisadas para obter a forma funcional da medida invariante de cada modelo. Em todos os modelos analisados neste trabalho, a medida invariante em uma grade finita tem forma produto. Modelos de redes de filas como ambientes para multiplos passeios aleatorios sao estendidos a grades infinitas. Para cada modelo estendido, sao especificadas as condicoes para a existencia do processo estocastico na grade infinita. Alem disso, e provado que existe uma unica medida invariante na rede infinita cuja projecao em uma subgrade finita e dada pela medida correspondente de uma rede finita. Finalmente, e provado que essa medida invariante na rede infinita e reversivel. / A set of models composed of queueing networks serving as random environments for one or more random walks, which themselves can affect the behavior of the queues, is developed. Two forms of interaction between the random walkers are considered. For each model, it is proved that the corresponding Markov process is positive recurrent and reversible. The detailed balance equa- tions are analyzed to obtain the functional form of the invariant measure of each model. In all the models analyzed in the present work, the invariant measure on a finite lattice has product form. Models of queueing networks as environments for multiple random walks are extended to infinite lattices. For each model extended, the conditions for the existence of the stochastic process on the infinite lattice are specified. In addition, it is proved that there exists a unique invariant measure on the infinite network whose projection on a finite sublattice is given by the corresponding finite- network measure. Finally, it is proved that that invariant measure on the infinite lattice is reversible.

Um conjunto de modelos compostos de redes de filas em grades finitas servindo como ambientes aleatorios para um ou mais passeios aleatorios, que por sua vez podem afetar o comportamento das filas, e desenvolvido. Duas formas de interacao entre os passeios aleatorios sao consideradas. Para cada modelo, e provado que o processo Markoviano correspondente e recorrente positivo e reversivel. As equacoes de balanceamento detalhado sao analisadas para obter a forma funcional da medida invariante de cada modelo. Em todos os modelos analisados neste trabalho, a medida invariante em uma grade finita tem forma produto. Modelos de redes de filas como ambientes para multiplos passeios aleatorios sao estendidos a grades infinitas. Para cada modelo estendido, sao especificadas as condicoes para a existencia do processo estocastico na grade infinita. Alem disso, e provado que existe uma unica medida invariante na rede infinita cuja projecao em uma subgrade finita e dada pela medida correspondente de uma rede finita. Finalmente, e provado que essa medida invariante na rede infinita e reversivel. / A set of models composed of queueing networks serving as random environments for one or more random walks, which themselves can affect the behavior of the queues, is developed. Two forms of interaction between the random walkers are considered. For each model, it is proved that the corresponding Markov process is positive recurrent and reversible. The detailed balance equa- tions are analyzed to obtain the functional form of the invariant measure of each model. In all the models analyzed in the present work, the invariant measure on a finite lattice has product form. Models of queueing networks as environments for multiple random walks are extended to infinite lattices. For each model extended, the conditions for the existence of the stochastic process on the infinite lattice are specified. In addition, it is proved that there exists a unique invariant measure on the infinite network whose projection on a finite sublattice is given by the corresponding finite- network measure. Finally, it is proved that that invariant measure on the infinite lattice is reversible.

Nous nous intéressons dans cette thèse à la théorie cinétique et aux systèmes de particules dans le cadre des équations de Boltzmann et Landau. Premièrement, nous étudions la dérivation des équations cinétiques comme des limites de champ moyen des systèmes de particules, en utilisant le concept de propagation du chaos. Plus précisément, nous étudions les probabilités chaotiques sur l'espace de phase de ces systèmes de particules : la sphère de Boltzmann, qui correspond à l'espace de phase d'un système de particules qui évolue conservant le moment et l'énergie ; et la sphère de Kac, correspondant à un système de particules qui conserve seulement l'énergie. Ensuite, nous nous intéressons à la propagation du chaos, avec des estimations quantitatives et uniforme en temps, pour les équations de Boltzmann et Landau. Deuxièmement, nous étudions le comportement asymptotique en temps grand des solutions de l'équation de Landau. / This thesis is concerned with kinetic theory and many-particle systems in the setting of Boltzmann and Landau equations. Firstly, we study the derivation of kinetic equation as mean field limits of many-particle systems, using the concept of propagation of chaos. More precisely, we study chaotic probabilities on the phase space of such particle systems : the Boltzmann's sphere, which corresponds to the phase space of a many-particle system undergoing a dynamics that conserves momentum and energy ; and the Kac's sphere, which corresponds to the energy conservation only. Then we are concerned with the propagation of chaos, with quantitative and uniform in time estimates, for Boltzmann and Landau equations. Secondly, we study the long-time behaviour of solutions to the Landau equation.

This thesis deals with the creation of the intro with limited size. This work describes methods for reducing the size of the final application. The main part describes methods for generating graphic content and methods for its animation. It deals with creation of textures and geometry. Another part is aimed on the physical simulation of particle and elastic systems.