Este trabalho trata do desenvolvimento de um material didático, sob a forma de cadernos (presentemente, em forma de capítulos), acompanhado de protótipo de circuito simples para testes experimentais, a ser utilizado no ensino de nível médio. O conteúdo reunido nos cadernos abrange o desenvolvimento analítico de tópicos pertinentes à física-matemática, esquema para a construção do protótipo e exemplos utilizando recursos computacionais. Mais especificamente, buscou-se enfatizar o ensino dos tópicos de equações e sistemas lineares, motivados por fenômenos físicos. Pretendeu-se explorar o aspecto experimental (com a construção e o uso de protótipo de circuitos simples), o analítico (com a resolução de equações e sistemas lineares, e com uma introdução à programação linear) e o computacional (com uso da planilha eletrônica). Em todos os conteúdos desenvolvidos, é dada especial ênfase à interpretação, à análise e à validação dos resultados. Com este material, procura-se oferecer ao professor um conjunto de atividades didático-pedagógicas, que possam estimular a sua atuação crítica e criativa. E que, também, propiciem a reflexão e a análise na identificação e resolução de problemas, a fim de desencadear processos cognitivos que levem o aluno a compreender as interrelações entre a física e a matemática. / This paper is about the development of a didatic material, under the way of notebooks (here, in chapters), accompained by the prototype of simple circuit for experimental tests, to be used in high school teaching. The issue brought in the notebooks comprehends the analytic development of the topics that belong to the physics- mathematics, scheme for the building of the prototype and examples with the use of computer resources. More specifically, applied to the teaching of the topics of equations and linear systems, motivated by physics phenomena. It was intended to explore the experimental aspect (with the building of simple circuit prototype), the analytic (with the resolution of equations and linear systems, with an introduction to the linear programming) and the computer (with the use of electronic chart). In all the topics developed, a special emphasis is given to the interpretation, analysis and validating of the results. With this material, it was intended to offer the teacher a set of didatic- pedagogical activities that can stimulate the critical and creative acting. And that can also provide the thinking and analysis in the identification and resolution of problems, with the aim of triggering cognitive processes that lead the student to understand the inter-relations between physics and mathematics.

Este trabalho trata do desenvolvimento de um material didático, sob a forma de cadernos (presentemente, em forma de capítulos), acompanhado de protótipo de circuito simples para testes experimentais, a ser utilizado no ensino de nível médio. O conteúdo reunido nos cadernos abrange o desenvolvimento analítico de tópicos pertinentes à física-matemática, esquema para a construção do protótipo e exemplos utilizando recursos computacionais. Mais especificamente, buscou-se enfatizar o ensino dos tópicos de equações e sistemas lineares, motivados por fenômenos físicos. Pretendeu-se explorar o aspecto experimental (com a construção e o uso de protótipo de circuitos simples), o analítico (com a resolução de equações e sistemas lineares, e com uma introdução à programação linear) e o computacional (com uso da planilha eletrônica). Em todos os conteúdos desenvolvidos, é dada especial ênfase à interpretação, à análise e à validação dos resultados. Com este material, procura-se oferecer ao professor um conjunto de atividades didático-pedagógicas, que possam estimular a sua atuação crítica e criativa. E que, também, propiciem a reflexão e a análise na identificação e resolução de problemas, a fim de desencadear processos cognitivos que levem o aluno a compreender as interrelações entre a física e a matemática. / This paper is about the development of a didatic material, under the way of notebooks (here, in chapters), accompained by the prototype of simple circuit for experimental tests, to be used in high school teaching. The issue brought in the notebooks comprehends the analytic development of the topics that belong to the physics- mathematics, scheme for the building of the prototype and examples with the use of computer resources. More specifically, applied to the teaching of the topics of equations and linear systems, motivated by physics phenomena. It was intended to explore the experimental aspect (with the building of simple circuit prototype), the analytic (with the resolution of equations and linear systems, with an introduction to the linear programming) and the computer (with the use of electronic chart). In all the topics developed, a special emphasis is given to the interpretation, analysis and validating of the results. With this material, it was intended to offer the teacher a set of didatic- pedagogical activities that can stimulate the critical and creative acting. And that can also provide the thinking and analysis in the identification and resolution of problems, with the aim of triggering cognitive processes that lead the student to understand the inter-relations between physics and mathematics.

Game theory has become very powerful tool for modelling decision-making situations of rational players. However, practical applications are strongly limited by the size of particular game, which is connected to the computational power of computers nowadays. Aim of this master's thesis is to design and implement a library, which would be able to find correlated equilibria in as complex non-cooperative games as possible.

L'hybridation des méthodes numériques est l'une des nombreuses pistes dans la recherche de la rapidité et de l'efficacité et de la précision d'une modélisation électromagnétique des structures complexes associant des parties de formes régulières de grandes dimensions électriques et des parties de formes complexes de dimensions plus modestes. Au lieu d'une seule formulation globale, on cherche à appliquer l'hybridation de plusieurs méthodes numériques notamment la méthode variationnelle multimodale (MVM), la méthode des éléments finis (FEM) et les réseaux de neurones artificiels. Un nouveau schéma hybride original qui combine la MVM et la FEM a été proposé pour caractériser une discontinuité complexe dans un guide d'onde rectangulaire. Les résultats obtenus tout en étant conformes aux résultats fournis par les simulateurs commerciaux et les résultats expérimentaux, apportent une amélioration sensible quant au temps de calcul. Le schéma hybride a été étendu pour la caractérisation des discontinuités complexes en cascade et appliqué à la conception de filtres micro-onde présentant des discontinuités complexes permettant ainsi un gain de temps très important. L'hybridation des réseaux de neurones artificiels et les méthodes modales a amélioré le temps de calcul pour l'analyse des discontinuités simples dans les guides d'onde rectangulaires ce qui a permis d'améliorer l'optimisation des filtres à guides d'ondes nervurés. / Hybridization of numerical methods is one inventive way in the research of the rapidity, the efficiency and the precision of the electromagnetic modeling of complex structures joining straight and large elements with complex and small ones. Instead of a global and unique formulation, we hybridize many numerical methods which are the modal methods, the finite element methods and the artificial neural networks. A novel computer- ided design (CAD) tool of complex passive microwave devices in rectangular waveguide technology is suggested. The multimodal variational method is applied to the full-wave description in the rectangular waveguides while the finite element analysis characterizes waves in the arbitrarily shaped discontinuities. The suggested hybrid approach is successfully applied to the full-wave analysis of complex discontinuities with great practical interest, thus improving CPU time and memory storage against several full-wave finite element method (FEM) based CAD tools. The proposed hybrid CAD tool is successfully extended to the design of filters with cascaded complex discontinuities. The hybridization of modal methods and the artificial neural networks improved the CPU time in the analysis of simple waveguide discontinuities which enhanced the optimization of rectangular ridged waveguide filters.

Σκοπός της παρούσας Διπλωματικής Εργασίας είναι η ανάπτυξη συγκεκριμένης μεθοδολογίας και αλγορίθμων ψηφιακής επεξεργασίας εικόνων για την αυτόματη εκτίμηση των διαμέτρων αγγείων σε οφθαλμολογικές εικόνες. Η συγκεκριμένη μέτρηση της διαμέτρου των αγγείων διαδραματίζει σημαντικό ρόλο στην έγκαιρη διάγνωση παθήσεων καθώς έχει αποδειχθεί ότι υπάρχει συσχετισμός μεταξύ των μεταβολών των τιμών των εν λόγω διαμέτρων και της εμφάνισης αλλοιώσεων στον αμφιβληστροειδή. Στα πλαίσια της εργασίας, υλοποιήθηκαν δύο μεθοδολογίες για τον υπολογισμό των διαμέτρων αγγείων οφθαλμολογικών εικόνων, οι οποίες συλλέγονται με χρήση κάμερας πυθμένα (fundus camera). Η πρώτη μεθοδολογία στηρίζεται στην εύρεση των σημείων που αποτελούν τους κεντρικούς άξονες των υπό εξέταση αγγείων με χρήση διαφορικού λογισμού. Ακολούθως, σε κάθε σημείο που ανήκει σε κεντρικό άξονα αγγείου, υπολογίζονται οι παράμετροι μιας συνάρτησης. Η εν λόγω συνάρτηση περιγράφει βέλτιστα τα επίπεδα φωτεινότητας της εικόνας κατά μήκος του ευθύγραμμου τμήματος που διέρχεται από το σημείο και είναι κάθετο στο αγγείο. H εύρεση των παραμέτρων της συνάρτησης πραγματοποιείται με χρήση τεχνικών βελτιστοποίησης. Το τελικό βήμα της μεθοδολογίας είναι η εκτίμηση της διαμέτρου των αγγείων από τις τιμές των παραμέτρων που έχουν υπολογιστεί. Η δεύτερη μεθοδολογία στηρίζεται στον αλγόριθμο που προτείνει ο P.H. Gregson. Αρχικά, πραγματοποιείται κατάτμηση της εικόνας με κατωφλίωση και εφαρμόζονται μορφολογικοί τελεστές συστολής και διαστολής στην εικόνα. Στη συνέχεια, εφαρμόζεται ο αλγόριθμος λέπτυνσης (thinning algorithm) με σκοπό την εύρεση των κεντρικών αξόνων των αγγείων και τέλος εκτιμάται η διάμετρος σε κάθε σημείο του κεντρικού άξονα με χρήση των επιπέδων του γκρίζου των εικονοστοιχείων που κείνται στην ευθεία που είναι κάθετη στο αγγείο σε κάθε σημείο του. / The scope of this Thesis is the development of a methodology and advance image processing techniques in order to automatically estimate vessel diameters in ophthalmological images. Motivation for the thesis is the fact that the measurement of vessel diameter plays significant role in the seasonable diagnosis of vascular disorders, as it is believed to be a relation between the variation in diameters and the detection of retinal disorders. In this thesis, two methodologies are developed in order to be applied in ophthalmological images that are collected by using a fundus camera. The first methodology is based on the detection of the pixels that constitute the centerlines of vessels, by using differential calculus. Specifically, at each pixel that belongs to a centerline of vessel, the parameters of a specific function are calculated. This function describes as accurately as possible the intensity levels along the segment that passes through the specific pixel and is perpendicular to the vessel. The parameters of this function are estimated using optimization techniques. The final step of the methodology is the assessment of the diameters of vessels using the values of the parameters. The second methodology is based on the algorithm that P.H.Gregson has proposed. At first, the vessels are detected by tresholding and a morphological closing algorithm is applied. Then, a thinning algorithm is used in order to detect the pixels that constitute the centerlines of the vessels and ultimately the diameter at each pixel of the centerlines is assessed using the gray levels of the pixels that constitute the segment that is perpendicular to the vessel at each specific pixel.

This Master Thesis deals with image restoration using deconvolution. The terms introducing into deconvolution theory like two-dimensional signal, distortion model, noise and convolution are explained in the first part of thesis. The second part deals with deconvolution methods via utilization of the Bayes approach which is based on the probability principle. The third part is focused on the Alternating Minimization Algorithm for Multichannel Blind Deconvolution. At the end this algorithm is written in Matlab with utilization of the NAG C Library. Then comparison of different optimization methods follows (simplex, steepest descent, quasi-Newton), regularization forms (Tichonov, Total Variation) and other parameters used by this deconvolution algorithm.