Finding an optimal solution for the logic circuit design problem is challenging and time-consuming especially for complex logic circuits. As the number of logic gates increases the task of designing optimal logic circuits extends beyond human capability. A number of evolutionary algorithms have been invented to tackle a range of optimisation problems, including logic circuit design. This dissertation explores two of these evolutionary algorithms i.e. Gene Expression Programming (GEP) and Multi Expression Programming (MEP) with the aim of integrating their strengths into a new Genetic Programming (GP) algorithm. GEP was invented by Candida Ferreira in 1999 and published in 2001 [8]. The GEP algorithm inherits the advantages of the Genetic Algorithm (GA) and GP, and it uses a simple encoding method to solve complex problems [6, 32]. While GEP emerged as powerful due to its simplicity in implementation and exibility in genetic operations, it is not without weaknesses. Some of these inherent weaknesses are discussed in [1, 6, 21]. Like GEP, MEP is a GP-variant that uses linear chromosomes of xed length [23]. A unique feature of MEP is its ability to store multiple solutions of a problem in a single chromosome. MEP also has an ability to implement code-reuse which is achieved through its representation which allow multiple references to a single sub-structure. This dissertation proposes a new GP algorithm, Improved Gene Expression Programming (IGEP) which im- proves the performance of the traditional GEP by combining the code-reuse capability and simplicity of gene encoding method from MEP and GEP, respectively. The results obtained using the IGEP and the traditional GEP show that the two algorithms are comparable in terms of the success rate when applied on simple problems such as basic logic functions. However, for complex problems such as one-bit Full Adder (FA) and AND-OR Arithmetic Logic Unit (ALU) the IGEP performs better than the traditional GEP due to the code-reuse in IGEP / Mathematical Sciences / M. Sc. (Applied Mathematics)

Le travail présenté dans cette thèse concerne la modélisation et la commande robuste en force de robots manipulateurs industriels à articulations flexibles utilisés pour le procédé FSW. Afin de réduire les temps de calcul et l'occupation de la mémoire, une approche basée sur la méthode par intervalle est proposée en vue de la simplification des modèles dynamiques des robots industriels, et contribue à identifier les paramètres d'inertie qui sont négligeables. Des études de cas sur trois types de trajectoires de test et l’analyse des couples moteurs ont démontré l'efficacité et les bonnes performances de la méthode de simplification. Ensuite, la modélisation dynamique et l'identification des paramètres du procédé FSW ont été effectuées. Les paramètres des modèles linéaires et non-linéaires de forces axiales sont identifiés. Sur la base de la modélisation du procédé FSW qui considère simultanément la cinématique du système complet, le modèle de déplacement du robot rigide, les flexibilités des articulations et le modèle dynamique de la force axiale, un contrôleur robuste en force est obtenu par la méthode de réglage fréquentielle. En outre, un simulateur du procédé FSW robotique est développé et les résultats de simulation montrent les bonnes performances du contrôleur en force. L'oscillation de la force axiale dans le procédé FSW peut être simulée en utilisant un modèle de perturbation de la position verticale de référence. / The work presented in this thesis focuses on the modeling and robust force control of flexible joints industrial robot manipulators used for FSW process. In order to reduce computation time and memory occupation, a novel interval-based approach for dynamic model simplification of industrial robots is proposed, which applies to arbitrary trajectories of whole robot workspace and contributes to obtaining negligible inertia parameters. Cases studies have been carried out on three kinds of test trajectories and torques analysis of robot dynamic equation, demonstrating the effectiveness and good performance of the simplification method. Then, the dynamic modeling and identification of robotic FSW process is performed, and the parameters of linear and nonlinear dynamic axial force process models are identified by using the plunge depth and its derivative. On the basis of the modeling of robotic FSW process which simultaneously considers the complete kinematics, the rigid robot displacement model, the joint flexibility and the dynamic axial force process model, a robust force controller can be obtained by using the frequency response approach. Besides, a simulator of robotic FSW process is developed and simulation results show good performance of the force controller. The oscillation of axial force in FSW process can be simulated when a disturbance model of initial vertical reference position is proposed and used in the simulation.

Cette thèse porte sur une méthode cartésienne parallèle pour résoudre des problèmes elliptiques avec interfaces complexes et sur son application aux problèmes elliptiques en domaine irrégulier dans le cadre d'un modèle de croissance tumorale.La méthode est basée sur un schéma aux différences finies et sa précision est d’ordre deux sur tout le domaine. L'originalité de la méthode consiste en l'utilisation d'inconnues additionnelles situées sur l'interface et qui permettent d’exprimer les conditions de transmission à l'interface. La méthode est décrite et les détails sur la parallélisation, réalisé avec la bibliothèque PETSc, sont donnés. La méthode est validée et les résultats sont comparés avec ceux d'autres méthodes du même type disponibles dans la littérature. Une étude numérique de la méthode parallélisée est fournie.La méthode est appliquée aux problèmes elliptiques dans un domaine irrégulier apparaissant dans un modèle continue et tridimensionnel de croissance tumorale, le modèle à deux espèces du type Darcy . L'approche utilisée dans cette application est basée sur la pénalisation des conditions de transmission à l'interface, afin de imposer des conditions de Neumann homogènes sur le border d'un domaine irrégulier. Les simulations du modèle sont fournies et montrent la capacité de la méthode à imposer une bonne approximation de conditions au bord considérées. / This theses deals with a parallel Cartesian method to solve elliptic problems with complex interfaces and its application to elliptic irregular domain problems in the framework of a tumor growth model.This method is based on a finite differences scheme and is second order accurate in the whole domain. The originality of the method lies in the use of additional unknowns located on the interface, allowing to express the interface transmission conditions. The method is described and the details of its parallelization, performed with the PETSc library, are provided. Numerical validations of the method follow with comparisons to other related methods in literature. A numerical study of the parallelized method is also given.Then, the method is applied to solve elliptic irregular domain problems appearing in a three-dimensional continuous tumor growth model, the two-species Darcy model. The approach used in this application is based on the penalization of the interface transmission conditions, in order to impose homogeneous Neumann boundary conditions on the border of an irregular domain. The simulations of model are provided and they show the ability of the method to impose a good approximation of the considered boundary conditions. / Questa tesi introduce un metodo parallelo su griglia cartesiana per risolvere problemi ellittici con interfacce complesse e la sua applicazione ai problemi ellittici in dominio irregolare presenti in un modello di crescita tumorale.Il metodo è basato su uno schema alle differenze finite ed è accurato al secondo ordine su tutto il dominio di calcolo. L'originalità del metodo consiste nell'introduzione di nuove incognite sull'interfaccia, le quali permettono di esprimere le condizioni di trasmissione sull'interfaccia stessa. Il metodo viene descritto e i dettagli della sua parallelizzazione, realizzata con la libreria PETSc, sono forniti. Il metodo è validato e i risultati sono confrontati con quelli di metodi dello stesso tipo trovati in letteratura. Uno studio numerico del metodo parallelizzato è inoltre prodotto.Il metodo è applicato ai problemi ellittici in dominio irregolare che compaiono in un modello continuo e tridimensionale di crescita tumorale, il modello a due specie di tipo Darcy. L'approccio utilizzato è basato sulla penalizzazione delle condizioni di trasmissione sull'interfaccia, al fine di imporre condizioni di Neumann omogenee sul bordo di un dominio irregolare. Le simulazioni del modello sono presentate e mostrano la capacità del metodo di imporre una buona approssimazione delle condizioni al bordo considerate.

This dissertation supplies the methodology of the measure (area) in the Earth model adopted for Geodesy. This model is the ellipsoid of revolution, in which the system of Cartesian coordinates, the curvilinear coordinate system and the polar coordinate system are described. The coordinate nature in the development of the surface measure calculation is discussed. The following demonstrations are illustrated: the ellipse equation, the eccentricity of the ellipse, the meridian section curvature radius equation, the meridian transversal section curvature radius equation and elliptic integral. It define algebraic geodesic line and geometrically. The juridical basis are the article 3º of Brazilian Federal Law 10.267/2001, which modify article 176 of the Brazilian Federal Law 6.015/1973 (Public Record Law) and adds to this article the paragraphs 3º and 4º, the paragraph 3º of article 225 of the Brazilian Law 6.015/1973 and the article 971 of the Código de Processo Civil (CPC), which require the coordinates of the corners of the real property on the Brazilian Geodetic System (SGB). The partitioning of the regular ellipsoid quadrilateral and the partitioning of the irregular ellipsoid quadrilateral located in the real property Pó de Serra is presented. To become this partitioning, it was used surface of the Lambert azimuthal equal-area projection, i. e., the curvilinear geodetic coordinates in plane coordinates has been transformed. The surface partitioning was determined using the method area equation of the Gauss trapezes connected with the equation of the straight line. The direct problem of the Lambert azimuthal equal-area projection and the inverse problem supply the methodology that become feasible the juridical exigence (articles 176 and 225 of Brazilian Federal Law 6.015/1973 and article 971 of the CPC). The methodology to the geodetic coordinates system with the purpose to calculate the partitioned areas of surface on the ellipsoid can be applied. The calculation of surface measure supplies the effective practice of the mencioned juridical basis. / O propósito deste trabalho é fornecer os fundamentos de cálculo de medida de superfície (área) no modelo de Terra adotado pela Geodésia. Esse modelo é o elipsóide de revolução ao qual se vincula o sistema de coordenadas cartesianas, o sistema de coordenadas curvilíneas e o sistema de coordenadas polares. Discute a natureza das coordenadas no desenvolvimento do cálculo da medida de superfície. Efetuam-se as seguintes demonstrações: equação da elipse, equação da excentricidade da elipse, equação do raio de curvatura da seção meridiana, equação do raio de curvatura da seção transversal meridiana e integral elíptica. Define linha geodésica algébrica e geometricamente. Apresentam-se os instrumentos legais que são o artigo 3º da Lei 10.267/2001, o qual altera o artigo 176, inciso II da Lei 6.015/1973 (Lei de Registros Públicos) e acrescenta a este artigo os parágrafos 3º e 4º, o parágrafo 3º do artigo 225 da Lei 6.015/1973 e o artigo 971 do Código de Processo Civil (CPC), os quais vinculam as coordenadas dos vértices do imóvel ao Sistema Geodésico Brasileiro (SGB). Efetuam-se a divisão do quadrilátero elipsóidico regular e também do quadrilátero elipsóidico irregular localizado na gleba Pó de Serra. Para se fazer esta divisão, usou-se a superfície da projeção azimutal equivalente de Lambert, ou seja, as coordenadas elipsóidicas curvilíneas foram transformadas em coordenadas planas desse sistema de projeção. A divisão destas superfícies foi efetuada pelo método da equação da área dos trapézios de Gauss em conjunto com a equação da reta. Os problemas direto e inverso da projeção azimutal equivalente de Lambert fornecem a metodologia que tornam exeqüíveis os dispositivos legais (artigos 176 e 225 da Lei 6.015/1973 e artigo 971 do CPC). A metodologia de cálculo proposto pode ser aplicada ao sistema de coordenadas geodésicas com a finalidade de calcular as áreas de uma divisão de superfície no elipsóide. Os fundamentos do cálculo de medida de superfície instrumentalizam o efetivo cumprimento dos dispositivos legais retrocitados.

Cette thèse étudie le raffinement local de maillage à la fois en espace et en temps pour l’équation de l’elastodynamique du second ordre pour le calcul haute performance. L’objectif est de mettre en place des méthodes numériques pour traiter des hétérogénéités de petite taille ayant un impact important sur la propagation des ondes. Nous utilisons une approche par éléments finis de Galerkin discontinus avec pénalisation pour leur flexibilité et facilité de parallélisation. La formulation éléments finis que nous proposons a pour particularité d’être élasto-acoustique, pour pouvoir prendre en compte des hétérogénéités acoustiques de petite taille. Par ailleurs, nous proposons un terme de pénalisation optimisé qui est mieux adapté à l’équation de l’élastodynamique, conduisant en particulier à une meilleure condition CFL. Nous avons aussi amélioré une formulation PML du second ordre pour laquelle nous avons proposé une nouvelle discrétisation temporelle qui rend la formulation plus stable. En tirant parti de la p-adaptivité et des maillages non-conformes des méthodes de Galerkin discontinues combiné à une méthode de pas de temps local, nous avons grandement réduit le coût du raffinement local. Ces méthodes ont été implémentées en C++, en utilisant des techniques de template metaprogramming, au sein d’un code parallèle à mémoire distribuée (MPI) et partagée (OpenMP). Enfin, nous montrons le potentiel de notre approche sur des cas tests de validation et sur des cas plus réalistes avec des milieux présentant des hydrofractures. / This thesis studies local mesh refinement both in time and space for the second order elastodynamic equation in a high performance computing context. The objective is to develop numerical methods to treat small heterogeneities that have global impact on wave propagation. We use an internal penalty discontinuous Galerkin finite element approach for its flexibity and parallelization capabilities. The elasto-acoustic finite element formulation we discuss is elasto-acoustic in order to handle local acoustic heterogeneities. We also propose an optimized penalty term more suited to the elastodynamic equation that results in better CFL condition. We improve a second order PML formulation with an original time discretization that results in a more stable formulation. Using the p-adaptivity and nonconforming mesh capabilities of discontinuous Galerkin methods combined with a local time stepping method, we greatly reduce the high computational cost of local refinements. These methods have been implemented in C++, using template metaprogramming, in a distributed memory (MPI) and shared memory (OpenMP) parallel code. Finally, we show the potential of our methods on validation test cases and on more realistic test cases with medium including hydrofractures.

In the thesis we discuss binary hyperstructures of linear differential operators of the second order both in general and (inspired by models of specific time processes) in a special case of the Jacobi form. We also study binary hyperstructures constructed from distributive lattices and suggest transfer of this construction to n-ary hyperstructures. We use these hyperstructures to construct multiautomata and quasi-multiautomata. The input sets of all these automata structures are constructed so that the transfer of information for certain specific modeling time functions is facilitated. For this reason we use smooth positive functions or vectors components of which are real numbers or smooth positive functions. The above hyperstructures are state-sets of these automata structures. Finally, we investigate various types of compositions of the above multiautomata and quasi-multiautomata. In order to this we have to generalize the classical definitions of Dörfler. While some of the concepts can be transferred to the hyperstructure context rather easily, in the case of Cartesian composition the attempt to generalize it leads to some interesting results.

The aim of the thesis is to verify synergy of genetic programming and neural networks. Solution is provided by set of experiments with implemented library built upon benchmark tasks. I've done experiments with directly and also indirectly encoded neural netwrok. I focused on finding robust solutions and the best calculation of configurations, overfitting detection and advanced stimulations of solution with fitness function. Generally better solutions were found using lower values of parameters n_c and n_r. These solutions tended less to be overfitted. I was able to evolve neurocontroller eliminating oscilations in pole balancing problem. In cancer detection problem, precision of provided solution was over 98%, which overcame compared techniques. I succeeded also in designing of maze model, where agent was able to perform multistep tasks.

Rembrandt's use of light in his self-portraits has received an abundance of scholarly attention throughout the centuries--and for good reason. His light delights the eye and captivates the mind with its textural quality and dramatic presence. At a time of scientific inquiry and religious reformation that was reshaping the way individuals understood themselves and their relationship to God, Rembrandt's light may carry more intellectual significance than has previously been thought. Looking at Rembrandt's oeuvre of self-portraits chronologically, it is apparent that something happened in his life or in his understanding that caused him to change how he used light. A distinct and consistent shift can be observed in the location and intensity of light to the crown of the forehead. This change indicates that light held particular significance for Rembrandt and that its connection to the head was a signifier with intentional meaning. This meaning could have developed as a result of Rembrandt's exposure to and interest in the contemporary theological and philosophical debates of the seventeenth-century Netherlands, particularly those relating to the physical and eternal nature of the soul stemming from the writings of René Descartes. The relative religious and intellectual freedom of the Dutch Republic provided a safe place for Descartes to publish and defend his metaphysical ideas relating to the nature of the soul and know-ability of God through personal intellectual inquiry. The widespread disturbance to established thought caused by his ideas and methods sped their dissemination into the early seventeenth-century discourse. Rembrandt's associations with the educated elite, particularly Constantijn Huygens and Jan Six, increases the probability that he knew of this new philosophy and had the opportunity to consider its relevance to his own quest for self-knowledge. With his particular emphasis on self-exploration and expression, demonstrated through his prolific oeuvre of self-portraits, and his inclination toward emotive, complex, and interdenominational religious works, it follows that Rembrandt would be eager to embrace Descartes' metaphysics and demonstrate his awareness through his self-portraits. Light on the forehead becomes a metaphor for enlightenment and is the key to reading Rembrandt's late self-portraits through the lens of Cartesian influence.

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This Master's thesis deals with question of the development of self-checking polymorphic circuits. It deals with a traditional way of creating reliable and self-checking circuits, presenting basic principles and methods. Also a method of Cartesian Genetic Programming for development of combinational circuits is explained. This thesis describes concepts of polymorphic gates and circuits and their benefits in practical use. Some existing self-checking polymorphic circuits are presented and their self-checking capabilities are analyzed. A proposal of realization of a design system for self-checking polymorphic circuits is given. A design system has been built based on presented specification and an application allowing simulations and analysis of system-proposed solutions has been created. Variety of experiments have been performed at created system and several interesting solutions have been acquired. At the end, conclusion is given and benefits of MSc. project are discussed.