Les grilles de calcul et les grille de PC sur Internet offrent des alternatives intéressantes pour le calcul scientifique à grande échelle, qui demande des ressources de calcul importantes. Toutefois, l’adaptation des applications pour ces systèmes est difficile à cause des facteurs nombreux tels que l'interface complexe de programmation. L'objectif de cette thèse est de trouver une solution pour faciliter le calcul scientifique à grande échelle. Pour ce faire, j’ai travaillé sur l’algorithme de Gauss Jordan et une nouvelle version d’un schéma de parallélisme. Ce schéma peut exploiter le maximum de parallélisme entre des opérations. Comme un exemple excellent, l'algorithme de Gauss Jordan est également utilisé pour évaluer des environnements expérimentaux et des outils différents. Les expérimentations avec YML, OmniRPC et XtremWeb sur les grilles et les grilles de PC montrent que YML peut être une bonne solution pour que les utilisateurs fassent du calcul scientifique à grande échelle, à cause des bonnes caractéristiques comme « l’interface d'abstraction de haut niveau», « les composants réutilisables » et «le surcoût acceptable». Pour obtenir les meilleures performances de cette plate-forme, les questions concernées, telles que la granularité des tâches, la persistance des données et le mécanisme d’ordonnancement, sont également abordés dans cette thèse. Selon les analyses faites ci-dessus et les caractéristiques communes des nuages informatiques ciblés, YML-PC, une architecture de référence basée sur les workflows pour les constructions de nuages informatiques privés scientifique est proposée. YML-PC hérite les bonnes caractéristiques présentées ci-dessus et des autres technologies clefs telles que « la persistance des données », « La prévision du temps disponible »  et « l'évaluation sur des nœuds de calcul hétérogènes » pour YML-PC, qui sont également abordées dans cette thèse. Les évaluations sur l'algorithme de Gauss Jordan sont réalisées sur les grilles, les grilles de PC et les nuages informatiques privés qui sont implantés sur la plate-forme Grid5000, la plateforme de calcul de Polytech Lille en France et la plateforme de calcul de Hohai, en Chine. / Grid computing and Desktop Grid computing provide interesting alternatives for large scale scientific computing which needs very large scale computing resources. However gridification is hard to develop because of series of factors such as complex programming interface. The aim of this dissertation is to find a solution to make large scientific computing in an easy way. To do that, research on Gauss Jordan algorithm is made and a new parallel programming version is presented. The parallel version can achieve maximum degree parallelism between operations. Also the Gauss Jordan algorithm as an excellent example is used to evaluate different experimental environments and tools. Experiments with YML, OmniRPC and XtremWeb on Grid and Desktop Grid environments testify YML can be a good solution for end users to make large scale scientific computing for its series of good features such as higher level interface, component reuse and acceptable overhead. To get better performance of platform, related issues such as task granularity, data persistence and schedule mechanism are also discussed in this dissertation. According to analysis made above and the common features of Clouds possessed, YML-PC a reference architecture based on workflow for building scientific Private Clouds is proposed. YML-PC inherits those good features presented above and some other key technologies such as “data persistence”, “available time prediction” and “evaluation on heterogeneous computing nodes” for YML-PC are also discussed in this dissertation. Evaluations are made based on Gauss Jordan algorithm on Grids, Desktop Grids and Private Clouds which build on Grid5000, Polytech Lille platform, France and Hohai platform, China.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-02-22T12:19:46Z No. of bitstreams: 1 luizfernandonascimentovasconcellos.pdf: 592098 bytes, checksum: e48a1cd338b2f3a798491febc67e2897 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-02-26T14:00:18Z (GMT) No. of bitstreams: 1 luizfernandonascimentovasconcellos.pdf: 592098 bytes, checksum: e48a1cd338b2f3a798491febc67e2897 (MD5) / Made available in DSpace on 2016-02-26T14:00:18Z (GMT). No. of bitstreams: 1 luizfernandonascimentovasconcellos.pdf: 592098 bytes, checksum: e48a1cd338b2f3a798491febc67e2897 (MD5) Previous issue date: 2014-03-18 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho é voltado para professores e alunos do Ensino Médio. Tem como objetivo mostrar a utilização do Método da Eliminação de Gauss-Jordan para a resolução de sistemas de equações lineares, cálculo de matrizes inversas e cálculo de determinantes. A motivação para a escolha desse tema é que, cada vez mais, o estudo das matrizes, dos determinantes e, consequentemente, dos sistemas de equações lineares vem sendo deixado de lado no Ensino Médio. Inicialmente, é feito um pequeno apanhado sobre o que são matrizes equivalentes e operações elementares, além de se falar sobre cofator de um elemento de uma matriz e sobre matriz adjunta, necessária para o cálculo da inversa utilizando-se determinantes. Apresenta-se um pouco da história de Gauss e de Jordan e, logo em seguida, o método propriamente dito. Também é visto o que acontece com o método quando as matrizes não são invertíveis, os sistemas são possíveis e indeterminados ou os sistemas são impossíveis. Quanto aos determinantes, são apresentadas suas propriedades e mostrada a eficácia do método para determinantes de ordem n 3 e, além disso, é mostrada a aplicação dos determinantes no cálculo de inversas e na resolução de sistemas de equações pela Regra de Cramer. Finalmente, são apresentadas sugestões de exercícios com uma breve resolução. / This work is oriented to teachers and students in the high school. It aims to show the usage of Gauss-Jordan’s Elimination Method to solve systems of linear equations, calculation of inverse matrices and determinants. The motivation behind the selection of this topic is that, more and more, the study of matrices, determinants, and consequently, systems of linear equations has been ignored in the high school. Firstly, an abridgement is done on what equivalent matrices and elementary operations are. Secondly, it explains about the cofactor of an element of a matrix and about adjoint matrices, needed for the calculation of the inverse matrix using determinants. A little introduction of Gauss and Jordan’s histories is made, and then, the method itself. It is also shown what happens with the method when the matrices are not invertible, the systems are possible but undetermined, or, the systems are not possible. Concerning determinants, their properties are presented and the method’s efficacy for determinants of order n 3 is shown and furthermore, it is shown the application of the determinants in the calculation of inverse matrices and resolutions of systems using Cramer’s Rule. Finally, some suggestions for exercises are presented with brief resolutions.

This paper presents a study of the computer game ”Minesweeper”. The aim of the game is to search through a rectangular area of mined squares without hitting any mines. By using a strategy based on making every operation as safe as possible, series of the game have been simulated. The size of the playground is four times four squares. The si- mulations indicate how often the game will succeed and which square is the best one to start at. The strategy demands advanced mathematical calculations. The account of these is the ma- jor part of my work. My investigation shows that if there are three hidden mines the game will succeed about two times out of three. It also shows that the best startingpoint is a corner.

Numerical solutions of mathematical modelizations of heat and mass transfer in cubical and cylindrical reactors of solar adsorption refrigeration systems are studied. For the resolution of the equations describing the coupling between heat and mass transfer, Bubnov-Galerkin method is used. An exact solution for time dependent heat transfer in cylindrical multilayered annulus is presented. Separation of variables method has been used to investigate the temperature behavior. An analytical double series relation is proposed as a solution for the temperature distribution, and Fourier coefficients in each layer are obtained by solving some set of equations related to thermal boundary conditions at inside and outside of the cylinder.

Time synchronization is a process of ensuring all the time difference between the clocks of network components(like base stations, boundary clocks, grandmasters, etc.) in the mobile network is zero or negligible. It is one of the important factors responsible for ensuring effective communication between two user-equipments in a mobile network. Nevertheless, the presence of asymmetries can lead to faults, making the detection of these errors indispensable, especially in technologies demanding ultra-low latency, such as 5G technology. Developing methods to ensure time-synchronized mobile networks, would not only improve the network performance, and contribute towards cost-effective telecommunication infrastructure. A rulebased simulator to simulate the mobile network was built, using the rules provided by the domain experts, in order to generate more data for further studies. The possibility of using Reinforcement Learning to perform fault detection in the mobile network was explored. In addition to the simulator dataset, an unlabelled customer dataset, which consists of time error differences between the base stations, and additional features for each of its network components was provided. Classification algorithms to label the customer dataset were designed, and a comparative analysis of each of them has been presented. Mathematical algorithm and Graph Neural Network models were built to detect error, for both the simulator and customer dataset, for the faulty node detection task. The approach of using a Mathematical algorithm and Graph Neural Network architectures provided an accuracy of 95% for potential fault node detection. The feature importance of the additional features of the network components was analyzed using the best Graph Neural Network model which was used to train for the node classification task (to classify the base stations as faulty and non-faulty). Additionally, an attempt was made to predict the individual time error value for each of the links using Graph Neural Network, however, it failed potentially due to the presence of fewer features to train from. / Tidssynkronisering är en process för att säkerställa att all tidsskillnad mellan klockorna för nätverkskomponenter (som basstationer, gränsklockor, stormästare, etc.) i mobilnätet är noll eller försumbar. Det är en av de viktiga faktorerna som är ansvariga för att säkerställa effektiv kommunikation mellan två användarutrustningar i ett mobilnät. Icke desto mindre kan närvaron av asymmetrier leda till fel, vilket gör upptäckten av dessa fel oumbärlig, särskilt i tekniker som kräver ultralåg latens, som 5G-teknik. En regelbaserad simulator för att simulera mobilnätet byggdes, med hjälp av reglerna från domänexperterna, för att generera mer data för vidare studier. Möjligheten att använda RL för att utföra feldetektering i mobilnätet undersöktes. Utöver simulatordataset tillhandahölls en omärkt kunddatauppsättning, som består av tidsfelsskillnader mellan basstationerna och ytterligare funktioner för var och en av dess nätverkskomponenter. Klassificeringsalgoritmer för att märka kunddataset utformades, och en jämförande analys av var och en av dem har presenterats. Matematisk algoritm och GNN-modeller byggdes för att upptäcka fel, för både simulatorn och kunddatauppsättningen, för uppgiften att detektera felaktig nod. Metoden att använda en matematisk algoritm och GNN-arkitekturer gav en noggrannhet på 95% för potentiell felnoddetektering. Funktionens betydelse för de ytterligare funktionerna hos nätverkskomponenterna analyserades med den bästa GNN-modellen som användes för att träna för nodklassificeringsuppgiften (för att klassificera basstationerna som felaktiga och icke-felaktiga). Dessutom gjordes ett försök att förutsäga det individuella tidsfelsvärdet för var och en av länkarna med GNN, men det misslyckades potentiellt på grund av närvaron av färre funktioner att träna från.