Dissertations / Theses on the topic 'Circulant matrices'

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-30T14:02:41Z No. of bitstreams: 1 arquivototal.pdf: 1530287 bytes, checksum: bd20f7e7a563f1aa0ad40d276bc400f9 (MD5)
Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2017-08-30T14:19:18Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 1530287 bytes, checksum: bd20f7e7a563f1aa0ad40d276bc400f9 (MD5)
Made available in DSpace on 2017-08-30T14:19:18Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1530287 bytes, checksum: bd20f7e7a563f1aa0ad40d276bc400f9 (MD5) Previous issue date: 2015-07-10
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work we discuss the procedures for solving polynomials equations of degree n 4; n 2 N via circulant matrices, highlighting a new perspective to obtain the Cardano- Tartaglia formulae. This brings up a new look on connected subjects, including the elimination of the term of degree (n􀀀1) and the characterization of real polynomials with all real roots. The method is based on searching a circulant matrix whose characteristic polynomial is identical to the one with the same roots we desire to nd. This approach provides us a simple and uni ed method for all equations through degree four.
Neste trabalho abordamos via matrizes circulantes a resolução de equações polinomiais de grau n 4; n 2 N , destacando uma nova perspectiva para obtenção das fórmulas de Cardano-Tartaglia. Além disso, ele oportuniza uma nova maneira de olhar para questões conexas, incluindo a eliminação do termo de grau (n 􀀀 1) e a caracterização de equações reais com todas as raízes reais. O método é baseado na busca de uma matriz circulante cujo polinômio característico seja idêntico ao das raízes que queremos encontrar. Essa metodologia nos fornece um método simples e uni cado para todas equações até quarto grau.

Stationary reciprocal processes defined on a finite interval of the integer line can be seen as a special class of Markov random fields restricted to one dimension. This kind of processes are potentially useful for describing signals which naturally live in a finite region of the time (or space) line. Non-stationary reciprocal processes have been extensively studied in the past especially by Jamison, Krener, Levy and co-workers. The specialization of the non-stationary theory to the stationary case, however, does not seem to have been pursued in sufficient depth in the literature. Moreover, estimation and identification of reciprocal stochastic models starting from observed data seems still to be an open problem. This dissertation addresses these problems showing that maximum likelihood identification of stationary reciprocal processes on the discrete circle leads to a covariance extension problem for block-circulant covariance matrices. This generalizes the famous covariance band extension problem for stationary processes on the integer line. We show that the maximum entropy principle leads to a complete solution of the problem. An efficient algorithm for the computation of the maximum likelihood estimates is also provided.
Un processo reciproco su un intervallo finito può essere visto come la naturale riduzione al caso unidimensionale di un campo di Markov. Questo tipo di processi è potenzialmente utile per descrivere segnali che vivono su di un intervallo spaziale o temporale limitato (si pensi ad esempio alle immagini). I processi reciproci non stazionari sono stati studiati in letteratura da B. Jamison, A. J. Krener, B. C. Levy e coautori. La specializzazione di tale teoria al caso stazionario, tuttavia, non sembra essere stata oggetto di sufficiente approfondimento in letteratura. Inoltre i problemi di stima e identificazione per processi reciproci a partire da dati osservati sono tuttora aperti. Il presente lavoro di tesi si è concentrato su tali problematiche. In particolare è stato mostrato come il problema di stima a massima verosimiglianza per processi reciproci stazionari sia riconducibile a un problema di estensione di covarianza per matrici circolanti. Tale problema generalizza il ben noto problema di estensione di covarianza per processi stazionari definiti sull'asse degli interi e non sembra essere stato affrontato in letteratura. Nel corso del lavoro di tesi è stato mostrato come tale problema sia risolubile facendo ricorso a un principio di massimizzazione dell'entropia. Infine, è stato proposto un algoritmo efficiente per il calcolo della soluzione.

La thèse se compose de 6 articles. (1) Nous calculons les générateurs des SA₃(ℝ)-invariants pour les surfaces paraboliques. (2) Nous calculons les invariants rigides relatifs pour les hypersurfaces rigides 2-non-dégénérées de rang de Levi constant 1 dans ℂ³: V₀, I₀, Q₀ ayant 11, 52, 824 monômes au numérateur. (3) Nous organisons tous les modèles affinement homogènes non-dégénérés dans ℂ³ en branches inéquivalentes. (4) Pour un courant harmonique dirigé autour d'une singularité linéarisée non-hyperbolique qui ne charge pas les séparatrices triviales dont l'extension triviale à travers 0 est ddc-fermée, nous démontrons que le nombre de Lelong en 0 est : 4.1) strictement positif si λ>0 ; 4.2) nul si λ est rationnel et négatif ; 4.3) nul si λ est négatif et si T est invariant sous l'action d'un sous-groupe cofini du groupe de monodromie. (5) Nous construisons des fibrés holomorphes en droites en toute dimension n>=2 non-prolongeables au sens de Hartogs. (6) Nous montrons que les matrices circulantes ayant k entrées 1 et k+1 entrées 0 dans leur première rangée sont toujours non singulières lorsque 2k+1 est soit une puissance d'un nombre premier, soit un produit de deux nombres premiers distincts. Pour tout autre entier 2k+1, nous exhibons une matrice circulante singulière
The thesis consists of 6 papers. (1) We calculate the generators of SA₃(ℝ)-invariants for parabolic surfaces. (2) We calculate rigid relative invariants for rigid constant Levi-rank 1 and 2-non-degenerate hypersurfaces in ℂ³: V₀, I₀, Q₀ having 11, 52, 824 monomials in their numerators. (3) We organize all affinely homogeneous nondegenerate surfaces in ℂ³ in inequivalent branches. (4) For a directed harmonic current near a non-hyperbolic linearized singularity which does not give mass to any of the trivial separatrices and whose trivial extension across 0 is ddc-closed, we show that the Lelong number at 0 is: 4.1) strictly positive if the eigenvalue λ>0; 4.2) zero if λ is a negative rational number; 4.3) zero if λ<0 and if T is invariant under the action of some cofinite subgroup of the monodromy group. (5) We construct non-extendable, in the sense of Hartogs, holomorphic line bundles in any dimension n>=2. (6) We show that circulant matrices having k ones and k+1 zeros in the first row are always nonsingular when 2k+1 is either a power of a prime, or a product of two distinct primes. For any other integer 2k+1 we exhibit a singular circulant matrix

Dans la première partie de cette thèse, on formule deux méthodes pour le calcul d'une décomposition polyadique canonique avec facteurs matriciels linéairement structurés (tels que des facteurs de Toeplitz ou en bande): un algorithme de moindres carrés alternés contraint (CALS) et une solution algébrique dans le cas où tous les facteurs sont circulants. Des versions exacte et approchée de la première méthode sont étudiées. La deuxième méthode fait appel à la transformée de Fourier multidimensionnelle du tenseur considéré, ce qui conduit à la résolution d'un système d'équations monomiales homogènes. Nos simulations montrent que la combinaison de ces approches fournit un estimateur statistiquement efficace, ce qui reste vrai pour d'autres combinaisons de CALS dans des scénarios impliquant des facteurs non-circulants. La seconde partie de la thèse porte sur la récupération de tenseurs de rang faible et, en particulier, sur le problème de reconstruction tensorielle (TC). On propose un algorithme efficace, noté SeMPIHT, qui emploie des projections séquentiellement optimales par mode comme opérateur de seuillage dur. Une borne de performance est dérivée sous des conditions d'isométrie restreinte habituelles, ce qui fournit des bornes d'échantillonnage sous-optimales. Cependant, nos simulations suggèrent que SeMPIHT obéit à des bornes optimales pour des mesures Gaussiennes. Des heuristiques de sélection du pas et d'augmentation graduelle du rang sont aussi élaborées dans le but d'améliorer sa performance. On propose aussi un schéma d'imputation pour TC basé sur un seuillage doux du coeur du modèle de Tucker et son utilité est illustrée avec des données réelles de trafic routier
In the first part of this thesis, we formulate two methods for computing a canonical polyadic decomposition having linearly structured matrix factors (such as, e.g., Toeplitz or banded factors): a general constrained alternating least squares (CALS) algorithm and an algebraic solution for the case where all factors are circulant. Exact and approximate versions of the former method are studied. The latter method relies on a multidimensional discrete-time Fourier transform of the target tensor, which leads to a system of homogeneous monomial equations whose resolution provides the desired circulant factors. Our simulations show that combining these approaches yields a statistically efficient estimator, which is also true for other combinations of CALS in scenarios involving non-circulant factors. The second part of the thesis concerns low-rank tensor recovery (LRTR) and, in particular, the tensor completion (TC) problem. We propose an efficient algorithm, called SeMPIHT, employing sequentially optimal modal projections as its hard thresholding operator. Then, a performance bound is derived under usual restricted isometry conditions, which however yield suboptimal sampling bounds. Yet, our simulations suggest SeMPIHT obeys optimal sampling bounds for Gaussian measurements. Step size selection and gradual rank increase heuristics are also elaborated in order to improve performance. We also devise an imputation scheme for TC based on soft thresholding of a Tucker model core and illustrate its utility in completing real-world road traffic data acquired by an intelligent transportation

There is an ongoing need to improve the efficiency and error-correcting performance of error correcting codes, which are widely used to enhance accuracy when retrieving or communicating information. This research investigates several potential improvements to a high-performing class of error correcting codes known as low-density parity-check (LDPC) codes. The results presented here further the known literature surrounding a specific class of functions (Alltop functions). Additionally, this work demonstrates ways of manipulating existing LDPC code constructions using relaxed difference sets to provide constructions with far more flexible code parameters. These constructions have competitive performance when compared to relevant modern codes.

Submitted by Mario BC (mario@bc.ufrpe.br) on 2017-02-09T13:50:03Z No. of bitstreams: 1 Aliomar Santos Cavalcanti.pdf: 1166268 bytes, checksum: 226091faec44175c1bbd5a24a47d8ecd (MD5)
Made available in DSpace on 2017-02-09T13:50:03Z (GMT). No. of bitstreams: 1 Aliomar Santos Cavalcanti.pdf: 1166268 bytes, checksum: 226091faec44175c1bbd5a24a47d8ecd (MD5) Previous issue date: 2016-11-08
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Studies on many sorts of equations motivated and still motivate many mathematicians around the world. Most of the well-known mathematicians from the years 1400 to 1700 gave huge contributions to the study of algebraic equations. Solving equations was already a challenge since the beginning of the mathematical knowledge. In this paper, a technique is presented to solve polynomial equations up to fourth order, that use the circulating matrixes and basic knowledge of linear algebraic. Throughout this work we will collect the history of involved topics besides illustrating this entire dissertation with examples. Finally, a didactical sequence of our paper’s content will be presented, that we suggest to be developed in five days of classes within three hours of lessons a day, aiming at improving student’s preparation for the academic life.
Os estudos sobre vários tipos de equações motivaram e motivam muitos matemáticos em todo o mundo. Grande parte dos célebres matemáticos entre os anos de 1400 e 1700 deram grandes contribuições ao estudo das equações algébricas. Resolver uma equação já era um desafio desde o início do conhecimento matemático. Neste trabalho, apresentamos uma técnica para resolver equações polinomiais, de até o quarto grau, que utiliza as matrizes circulantes e conhecimentos básicos de álgebra linear. Ao longo do trabalho fazemos um apanhado histórico dos tópicos envolvidos, além de ilustrarmos toda a dissertação com exemplos. Por fim, apresentamos uma sequência didática com o conteúdo do nosso trabalho, que sugerimos ser desenvolvida em cinco dias de aulas com três horas de aula por dia, com o objetivo de melhor preparar os alunos para a vida universitária.

L’inversion consiste à reconstruire des objets d’intérêt à partir de données acquises au travers d’un système d’observation. Dans ces travaux, nous nous penchons sur la déconvolution d’image. Les données observées constituent une version dégradée de l’objet, altéré par le système (flou et bruit). A cause de la perte d’informations engendrée, le problème devient alors mal conditionné. Une solution est de régulariser dans un cadre bayésien : en se basant sur des modèles, on introduit de l’information a priori sur les inconnues. Se posent alors les questions suivantes : comment comparer les modèles candidats et choisir le meilleur ? Sur quel critère faut-il s’appuyer ? A quelles caractéristiques ou quantités doit-on se fier ? Ces travaux présentent une méthode de comparaison et de sélection automatique de modèles, fondée sur la théorie de la décision bayésienne. La démarche consiste à sélectionner le modèle qui maximise la probabilité a posteriori. Pour calculer ces dernières, on a besoin de connaître une quantité primordiale : l’évidence. Elle s’obtient en marginalisant la loi jointe par rapport aux inconnus : l’image et les hyperparamètres. Les dépendances complexes entre les variables et la grande dimension de l’image rendent le calcul analytique de l’intégrale impossible. On a donc recours à des méthodes numériques. Dans cette première étude, on s’intéresse au cas gaussien circulant. Cela permet, d’une part, d’avoir une expression analytique de l’intégrale sur l’image, et d’autre part, de faciliter la manipulation des matrices de covariances. Plusieurs méthodes sont mises en œuvre comme l’algorithme du Chib couplé à une chaîne de Gibbs, les power posteriors, ou encore la moyenne harmonique. Les méthodes sont ensuite comparées pour déterminer lesquelles sont les plus adéquates au problème dela restauration d’image
Inversing main goal is about reconstructing objects from data. Here, we focus on the special case of image restauration in convolution problems. The data are acquired through a altering observation system and additionnaly distorted by errors. The problem becomes ill-posed due to the loss of information. One way to tackle it is to exploit Bayesian approach in order to regularize the problem. Introducing prior information about the unknown quantities osset the loss, and it relies on stochastic models. We have to test all the candidate models, in order to select the best one. But some questions remain : how do you choose the best model? Which features or quantities should we rely on ? In this work, we propose a method to automatically compare and choose the model, based on Bayesion decision theory : objectively compare the models based on their posterior probabilities. These probabilities directly depend on the marginal likelihood or “evidence” of the models. The evidence comes from the marginalization of the jointe law according to the unknow image and the unknow hyperparameters. This a difficult integral calculation because of the complex dependancies between the quantities and the high dimension of the image. That way, we have to work with computationnal methods and approximations. There are several methods on the test stand as Harmonic Mean, Laplace method, discrete integration, Chib from Gibbs approximation or the power posteriors. Comparing is those methods is significative step to determine which ones are the most competent in image restauration. As a first lead of research, we focus on the family of Gaussian models with circulant covariance matrices to lower some difficulties

Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-02T18:31:29Z No. of bitstreams: 1 Arquivototal.pdf: 790723 bytes, checksum: 7e439258b05733c014dcd3e7de230c1f (MD5)
Made available in DSpace on 2018-05-02T18:31:29Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 790723 bytes, checksum: 7e439258b05733c014dcd3e7de230c1f (MD5) Previous issue date: 2017-08-31
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this present work, principles and theorems associated to integers are returned, as well as eigenvalues and eigenvectors problems, highlighting a Hermitian matrix. Then it is emphasized to the Circulating Matrices, through which it is found the association to two well-defined polynomials: the representative and the characteristic. Later a brief account about the history of polynomial equations is made, drafting the Cardano-Tartaglia Formulas associated to them. Afterwards a unification is made in the resolution process of the polynomial equations of smaller degrees than the equal to 4, by means of the circulating matrices. The work is completed by proving a Fermat theorem for n = 3, using the Cardano-Tartaglia Formulas.
No presente trabalho, princípios e teoremas associados aos números inteiros são retomados, bem como problemas de autovalores e autovetores, sendo ressaltada a matriz Hermitiana. Em seguida é dado ênfase às Matrizes Circulantes, através das quais verifica-se a associação a dois polinômios bem definidos: o representante e o característico. Posteriormente realiza-se um breve relato acerca da história das equações polinomiais, destacandose as Fórmulas de Cardano-Tartaglia associadas às mesmas. Logo após é feita uma unificação no processo de resolução das equações polinomiais de graus menores do que o igual a 4, por meio das matrizes circulantes. O trabalho é finalizado, sendo provado o Teorema de Fermat para n = 3, recorrendo-se às Fórmulas de Cardano-Tartaglia.

Submitted by camilla martins (camillasmmartins@gmail.com) on 2017-04-24T11:48:05Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_CorrecaoApagamentosRajadas.pdf: 12648601 bytes, checksum: 32c72b34186616144110cb119cba02b1 (MD5)
Approved for entry into archive by Edisangela Bastos (edisangela@ufpa.br) on 2017-04-24T16:57:51Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_CorrecaoApagamentosRajadas.pdf: 12648601 bytes, checksum: 32c72b34186616144110cb119cba02b1 (MD5)
Made available in DSpace on 2017-04-24T16:57:51Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_CorrecaoApagamentosRajadas.pdf: 12648601 bytes, checksum: 32c72b34186616144110cb119cba02b1 (MD5) Previous issue date: 2016-10-21
Nesta tese são propostos procedimentos para a construção de matrizes de verificação de paridade para codificação e decodificação de códigos LDPC (low-density paritycheck) na recuperação de bits apagados no canal com apagamentos em rajada. As matrizes de verificação de paridade são produzidas por concatenação das matrizes bases binárias justapostas por matrizes circulantes sendo de fácil implementação e de menor aleatoriedade. As matrizes bases são desenvolvidas a partir de fundamentos da álgebra e da geometria. Para demonstrar o potencial da técnica foi elaborado um conjunto de simulações que usa codificação de baixa complexidade, bem como o uso dos algoritmos soma e produto para recuperar os apagamentos. Foram gerados vários códigos LDPC, a partir das matrizes, e os resultados obtidos foram comparados com outros códigos LDPC obtidos da literatura. São ainda apresentados os resultados da simulação da recuperação de apagamentos resultantes da transmissão de uma imagem através de um canal ruidoso.partir das matrizes, e os resultados obtidos foram comparados com outros códigos LDPC obtidos da literatura. São ainda apresentados os resultados da simulação da recuperação de apagamentos resultantes da transmissão de uma imagem através de um canal ruidoso.
This thesis proposed procedures for the construction of parity check matrices for encoding and decoding of LDPC codes in the recovery of deleted bits in Burst Erasure Channel. The parity check matrices are produced by concatenation of binary bases matrices juxtaposed by circulating matrices are easy to implement and lower randomness. The base arrays are developed from the foundations of algebra and geometry. To demonstrate the potential of the technique, we developed a number of simulations using low complexity encoding as well as the sum-product algorithm. Several LDPC codes (matrices) were generated and the results were compared with other approaches. We also present the outcomes of erasure recovery simulations that result from the transmission of an image through a noisy channel.

The objective of this dissertation is the evaluation of the exploitability of corn cobs as natural additives for bio-based polymer matrices, in order to hone their properties while keeping the fundamental quality of being fully bio-derived. The first part of the project has the purpose of finding the best solvent and conditions to extract antioxidants and anti-degrading molecules from corn cobs, exploiting room and high-temperature processes, traditional and advanced extraction methods, as well as polar and nonpolar solvents. The extracts in their entirety are then analysed to evaluate their antioxidant content, in order to select the conditions able to maximise their anti-degrading properties. The second part of the project, instead, focuses on assessing chemical and physical properties of the best-behaving extract when inserted in a polymeric matrix. To achieve this, low-density polyethylene (LDPE) and poly (butylene succinate – co – adipate) (PBSA) are employed. These samples are obtained through extrusion and are subsequently characterised exploiting the DSC equipment and a sinusoidally oscillating rheometer. In addition, extruded polymeric matrices are subjected to thermal and photo ageing, in order to identify their behaviour after different forms of degradation and to assess their performances with respect to synthetically produced anti-degrading additives.

Cette thèse est basée sur un brevet réalisé chez XLIM Systèmes RF. La thèse précédente se concentre sur la partie théorique MARPEM et une certaine validation en polarisation linéaire. Dans cette thèse, nous avons visé à introduire le système MARPEM aux applications de polarisation circulaire en général et aux applications spatiales en particulier. Dans toute la thèse, MARPEM à polarité circulaire avec une architecture différente est réalisée avec la conception de circuits de polarisation et de diviseurs de puissance. On présente la formation de faisceau du motif Isoflux large avec le taux d'ellipticité, ainsi que des faisceaux de balayage sont réalisés pour grand azimut angles avec un bon taux d'ellipticité. Tous les résultats sont comparés à l'antenne réseau classique AESA. La fabrication de MARPEM à polarité circulaire et les circuits de polarisation et le diviseur de puissance sont effectués et les mesures correspondantes sont présentées. Ensuite, dans les perspectives, on s'attend à des défis différents dans un travail futur pour l'amélioration de système MARPEM
This thesis is based on a patent done at XLIM RF-Systems. Previous thesis focuses on the ARMA theoretical part and some validation in linear polarization. In this thesis we aimed to introduce the system ARMA to the circular polarization applications in general and to space applications especially. In the entire thesis circularly polarized ARMA with different architecture are achieved with the design of polarization circuits and power dividers. Beam forming of the wide Isoflux pattern with the axial ratio are presented, also scanning beams are achieved for far angles with good axial ratio. All the results are compared with the classical array antenna AESA. Manufacturing of circularly polarized ARMA and the polarization circuits and the power divider are done and the corresponding measurements are presented. Then in the perspectives different challenges are expected to be in a future work for enhancement of the whole ARMA system

Mesures des spectres d'absorption et des dichroismes lineaire et circulaire. Si les atomes presentent un fort couplage spin-orbite, ils ont, dans la matrice, des etats bien decrits par un modele d'atome libre. Par contre si la constante de couplage spin-orbite est faible, les atomes ont des etats electroniques fortement couples aux vibrations du reseau. Dans la premiere possibilite, c'est le cas du nickel et du fer, et dans la seconde c'est le cas du manganese

Les ADN circulants extracellulaires (ADNcf) sont considérés comme des biomarqueurs potentiels non invasifs de la progression tumorale. Ils présentent l'avantage d'être porteurs des altérations génétiques des tumeurs dont ils sont issus. Les connaissances sur les formes, les mécanismes de libération et les actions biologiques des ADNcf sont cependant encore peu caractérisées.Nous avons émis l'hypothèse que se focaliser sur l'étude de la structure et des origines des ADNcf issus des tumeurs permettrait d'ouvrir de nouvelles perspectives d'applications en génomique personnalisée.Nos travaux ont démontré à l'aide d'un animal modèle que les ADNcf issus des tumeurs de cancers colorectaux sont hautement fragmentés à des tailles inférieures à 145 bp. Cette observation a été confirmée sur plasma humain en réalisant par AFM la première image directe d'ADNcf issu de tumeurs. Nous avons déterminé que les proportions d'ADNcf mutés varient fortement dans la circulation sanguine, mais que près d'un tiers des individus présentaient des proportions d'ADNcf mutés supérieures à 25 % de tous les ADNcf retrouvés dans le sang. Ces découvertes nous ont permis de participer au développement d'une méthode d'analyse spécifique des ADNcf du plasma permettant de déterminer par Q-PCR la concentration en ADNcf, sa fragmentation ainsi que la présence des mutations KRAS et BRAF. Cette méthode a été validée cliniquement sur 79 échantillons de patients atteints de cancer colorectal métastatique en la comparant avec une concordance de 96 % à la technique de référence clinique utilisant l'ADN de tissu tumoral. L'utilisation des ADNcf en tant que « biopsie liquide » devrait être un biomarqueur central dans l'approche de génomique personnalisée des années à venir et les résultats de ces travaux de thèse participer au développement de cette nouvelle approche
Cell-free circulating DNA (cfDNA) are considered as potentials non invasive biomarkers of tumor progression. They present the advantage to exhibit the genetic alterations from their tumor of origin. Knowledge on the forms, mechanism of release, and biological effect of cfDNA are however still less characterized. We have hypothesized that focalizing on the study of cfDNA structure and origin will open new perspectives of application in personalized genomic. Our works demonstrated, with an animal model, that cfDNA from colorectal cancer tumor are highly fragmented at size lower than 145 bp. This observation was confirmed on human plasma with AFM by realizing the first direct picture of tumor-derived cfDNA. We have determined that cfDNA proportion highly varied in bloodstream, but more than a third of individual exhibit proportions larger than 25 % of blood total cfDNA.These discoveries let us participate to the development of a specific analysis method of plasma cfDNA owing to determinate by Q-PCR the cfDNA concentration, its fragmentation and the presence of KRAS and BRAF mutation. This method has been clinically validated on 79 samples of metastatic colorectal cancer patients by comparing it, with a concordance of 96 %, with the technique of reference using DNA from tumoral tissue.cfDNA could be used as « liquid biospy » and could be a central biomarker in the personalized genomic for the future years, and this thesis work participate to the development of this new approach

L'objectif principal de notre étude est de développer des algorithmes rapides pour une conception optimale et une implantation de très faible complexité des filtres numériques. Le critère d'optimisation choisi est celui de la minimisation de l'erreur quadratique moyenne. Ainsi, nous avons étudié et développé de nouveaux algorithmes de synthèse des filtres à réponse impulsionnelle finie (RIF) associés aux deux techniques de filtrage par blocs, overlap-save (OLS) et overlap-add (OLA). Ces deux techniques de filtrage RIF consistent à traiter le signal par blocs au moyen de la transformée de Fourier rapide (TFR) et permettent ainsi de réduire la complexité arithmétique des calculs de convolution. Les algorithmes que nous avons proposés sont basés sur le développement du modèle matriciel des structures OLS et OLA et sur l'utilisation des propriétés de l'algèbre linéaire, en particulier celles des matrices circulantes. Pour réduire davantage la complexité et la distorsion de filtrage, nous avons approfondi les bases mathématiques de la transformée en nombres de Fermat (FNT : Fermat Number Transform) qui est amenée à trouver des applications de plus en plus diverses en traitement du signal. Cette transformée, définie sur un corps de Galois d'ordre égal à un nombre de Fermat, est un cas particulier des transformées en nombres entiers (NTT : Number Theoretic Transform). Comparé à la TFR, la FNT permet un calcul sans erreur d'arrondi ainsi qu'une large réduction du nombre de multiplications nécessaires à la réalisation du produit de convolution. Pour mettre en évidence cette transformée, nous avons proposé et étudié une nouvelle conception des filtres blocs OLS et OLA mettant en oeuvre la FNT. Nous avons ensuite développé un algorithme de très faible complexité pour la synthèse du filtre optimal en utilisant les propriétés des matrices circulantes que nous avons développées dans le corps de Galois. Les résultats de l'implantation en virgule fixe du filtrage par blocs ont montré que l'utilisation de la FNT à la place de la TFR permettra de réduire la complexité et les erreurs de filtrage ainsi que le coût de synthèse du filtre optimal.

L’objectif principal de notre étude est de développer des algorithmes rapides pour une conception optimale et une implantation de très faible complexité des filtres numériques. Le critère d’optimisation choisi est celui de la minimisation de l’erreur quadratique moyenne. Ainsi, nous avons étudié et développé de nouveaux algorithmes de synthèse des filtrés à réponse impulsionnelle finie (RIF) associés aux deux techniques de filtrage par blocs, overlap-save (OLS) et overlap-add (OLA). Ces deux techniques de filtrage RIF consistent à traiter le signal par blocs au moyen de la transformée de Fourier rapide (TFR) et permettent ainsi de réduire la complexité arithmétique des calculs de convolution. Les algorithmes que nous avons proposés sont basés sur le développement du modèle matriciel des structures OLS et OLA et sur l’utilisation des propriétés de l’algèbre linéaire, en particulier celles des matrices circulantes. Pour réduire davantage la complexité et la distorsion de filtrage, nous avons approfondi les bases mathématiques de la transformée en nombres de Fermat (FNT Fermat Number Transform) qui est amenée à trouver des applications de plus en plus diverses en traitement du signal. Cette transformée, définie sur un corps de Galois d’ordre égal à un nombre de Fermat, est un cas particulier des transformées en nombres entiers (NTT Number Theoretic Transform). Comparé à la TFR, la FNT permet un calcul sans erreur d’arrondi ainsi qu’une large réduction du nombre de multiplications nécessaires à la réalisation du produit de convolution. Pour mettre en évidence cette transformée, nous avons proposé et étudié une nouvelle conception des filtres blocs OLS et OLA mettant en oeuvre la FNT. Nous avons ensuite développé un algorithme de très faible complexité pour la synthèse du filtre optimal en utilisant les propriétés des matrices circulantes que nous avons développées dans le corps de Galois. Les résultats de l’implantation en virgule fixe du filtrage par blocs ont montré que l’utilisation de la FNT à la place de la TFR permettra de réduire la complexité et les erreurs de filtrage ainsi que le coût de synthèse du filtre optimal
The main objective of our study is to develop fast algorithms for an optimal design and an implementation with low complexity of digital filters. The optimization criterion is the mean squared error at the filter output. Thus, we have studied and developed new algorithms for synthesis of finite impulse response (FIR) filters related to the two techniques of block filtering, overlap-save (OLS) and overlap-add (OLA). These two filtering techniques consist in processing the signal by blocks and use the fast Fourier transform (FFT) to reduce the complexity of the convolution calculation. Our algorithms, based on the matrix model development of the OLA and OLS structures, use the linear algebra properties, especially those of circulant matrices. To further reduce the complexity and the distortion, we have looked further into the mathematical foundations of the Fermat Number Transform (FNT). This transform is a particular case of the Number Theoretic Transforms (NTT) defined in the Galois field. Compared to the FFT, the FNT allows a calculation without rounding error and a large reduction of the number of multiplications necessary to carry out the convolution product. To highlight this transform, we have proposed and studied a new design of OLS and OLA filtering using the FNT. We have developed a low complexity algorithm for the optimal synthesis of filters using the properties of circulant matrices that we have developed in the Galois field. The simulation results of the block filtering with fixed-point implementation have shown that the use of the FNT instead of the FFT reduces the complexity and the filtering errors, as well as the cost of optimal filter synthesis

Cette thèse se concentre sur le sujet de la calibration de la camera interne et, en particulier, sur les aspects de haute précision. On suit et examine deux fils principaux: la correction d'une aberration chromatique de lentille et l'estimation des paramètres intrinsèques de la caméra. Pour la problème de l'aberration chromatique, on suit un chemin de post-traitement numérique de l'image, afin de se débarrasser des artefacts de couleur provoqués par le phénomène de dispersion du système d'objectif de la caméra, ce qui produit une désalignement perceptible des canaux couleur. Dans ce contexte, l'idée principale est de trouver un modèle de correction plus général pour réaligner les canaux de couleur que ce qui est couramment utilisé - différentes variantes du polynôme radial. Celui-ci ne peut pas être suffisamment général pour assurer la correction précise pour tous les types de caméras. En combinaison avec une détection précise des points clés, la correction la plus précise de l'aberration chromatique est obtenue en utilisant un modèle polynomial qui est capable de capter la nature physique du décalage des canaux couleur. Notre détection de points clés donne une précision allant jusqu'à 0,05 pixels, et nos expériences montrent sa grande résistance au bruit et au flou. Notre méthode de correction de l’aberration, par opposition aux logiciels existants, montre une géométrique résiduelle inférieure à 0,1 pixels, ce qui est la limite de la perception de la vision humaine. En ce qui concerne l'estimation des paramètres intrinsèques de la caméra, la question est de savoir comment éviter la compensation d'erreur résiduelle qui est inhérent aux méthodes globales d'étalonnage, dont le principe fondamental consiste à estimer tous les paramètres de la caméra ensemble - l'ajustement de faisceaux. Détacher les estimations de la distorsion de la caméra et des paramètres intrinsèques devient possible lorsque la distorsion est compensée séparément. Cela peut se faire au moyen de la harpe d'étalonnage, récemment développée, qui calcule le champ de distorsion en utilisant la mesure de la rectitude de cordes tendues dans différentes orientations. Une autre difficulté, étant donnée une image déjà corrigée de la distorsion, est de savoir comment éliminer un biais perspectif. Ce biais dû à la perspective est présent quand on utilise les centres de cibles circulaires comme points clés, et il s'amplifie avec l'augmentation de l'angle de vue. Afin d'éviter la modélisation de chaque cercle par une fonction conique, nous intégrons plutôt fonction de transformation affine conique dans la procédure de minimisation pour l'estimation de l'homographie. Nos expériences montrent que l'élimination séparée de la distorsion et la correction du biais perspectif sont efficaces et plus stables pour l'estimation des paramètres intrinsèques de la caméra que la méthode d'étalonnage globale
This dissertation focuses on internal camera calibration and, especially, on its high-precision aspects. Two main threads are followed and examined: lens chromatic aberration correction and estimation of camera intrinsic parameters. For the chromatic aberration problem, we follow a path of digital post-processing of the image in order to get rid from the color artefacts caused by dispersion phenomena of the camera lens system, leading to a noticeable color channels misalignment. In this context, the main idea is to search for a more general correction model to realign color channels than what is commonly used - different variations of radial polynomial. The latter may not be general enough to ensure stable correction for all types of cameras. Combined with an accurate detection of pattern keypoints, the most precise chromatic aberration correction is achieved by using a polynomial model, which is able to capture physical nature of color channels misalignment. Our keypoint detection yields an accuracy up to 0.05 pixels, and our experiments show its high resistance to noise and blur. Our aberration correction method, as opposed to existing software, demonstrates a final geometrical residual of less than 0.1 pixels, which is at the limit of perception by human vision. When referring to camera intrinsics calculation, the question is how to avoid residual error compensation which is inherent for global calibration methods, the main principle of which is to estimate all camera parameters simultaneously - the bundle adjustment. Detachment of the lens distortion from camera intrinsics becomes possible when the former is compensated separately, in advance. This can be done by means of the recently developed calibration harp, which captures distortion field by using the straightness measure of tightened strings in different orientations. Another difficulty, given a distortion-compensated calibration image, is how to eliminate a perspective bias. The perspective bias occurs when using centers of circular targets as keypoints, and it gets more amplified with increase of view angle. In order to avoid modelling each circle by a conic function, we rather incorporate conic affine transformation function into the minimization procedure for homography estimation. Our experiments show that separate elimination of distortion and perspective bias is effective and more stable for camera's intrinsics estimation than global calibration method

Dans ce travail de thèse, nous illustrons la pertinence de la technique de photoémission pour l'étude des propriétés électroniques des matériaux. Dans la première partie, nous détaillons le développement et la phase de tests d'un nouveau bâti expérimental composé d'une chambre d'épitaxie par jets moléculaires (MBE) ainsi que d'une chambre de photoémission résolue en angle et en spin (SR-ARPES), connecté au tube Daum à l'Institut Jean Lamour. Les hautes performances de ce nouveau dispositif sont d'une part évaluées par une série de mesures expérimentales sur un système connu de la littérature (état de Shockley à la surface de l'Au(111)), et d'autre part illustrées par l'analyse de matériaux originaux (isolants topologiques, effet Kondo moléculaire …). Les valeurs de résolution en énergie sont inférieures à 2 meV et 300 meV pour la photoémission utilisant les rayonnements UV (UPS) et X (XPS) respectivement. La résolution angulaire est quant à elle meilleure que 0,2° et la température minimale atteignable est de 8,7 K. Finalement, des premières mesures de SR-ARPES ont démontré la capacité de ce nouveau bâti à mesurer les détails les plus fins de la structure de bandes polarisée en spin, se rapprochant ainsi de l'état de l'art dans le domaine. Ce nouveau dispositif est donc pleinement opérationnel. La seconde partie est consacrée à l'étude d'un oxyde de silicium ultra-mince bidimensionnel (2D) à la surface d'un substrat monocristallin de Ru(0001). Nous étudions tous les stades de croissance en partant du substrat nu de Ru(0001) jusqu'à une bicouche cristalline de cet oxyde, par XPS haute résolution (rayonnement synchrotron) et photoémission résolue en angle (ARPES). Nous confirmons la structure atomique établie dans la littérature pour ce système à la monocouche, avec en particulier l'existence de deux types de liaisons inéquivalentes Si-O-Ru révélées par des mesures inédites d’XPS haute résolution au niveau de la raie de cœur de l'O1s. En outre, nos mesures ARPES mettent en évidence l'existence d'états dispersifs bidimensionnels propres à ce matériau 2D. Alors que la monocouche est fortement connectée au substrat de ruthénium (liaisons covalentes), la bicouche en est déconnectée (liaisons de van der Waals). Notre étude confirme l'existence d’une telle transition avec des signatures claires à la fois en XPS et en ARPES, démontrant notamment la disparition des liaisons Si-O-Ru. Nous démontrons également la robustesse de ce système, qui une fois cristallisé peut être remis à l'air sans modifications majeures de ses propriétés électroniques, lui donnant ainsi un fort potentiel de fonctionnalisation (par exemple au sein d'hétérostructures 2D complexes comme couche isolante). Finalement, dans une troisième partie nous nous intéressons aux aspects théoriques de la photoémission résolue en angle. Alors que la structure de bandes est périodique dans l'espace réciproque, ce n'est pas le cas de l'intensité de photoémission, qui peut présenter des variations complexes dépendant de nombreux paramètres. Ces aspects sont généralement mal compris par les expérimentateurs. Nous présentons ici un modèle simple récemment proposé qui s'inscrit dans une description en trois étapes du processus de photoémission, et qui permet d'évaluer les éléments de matrice à un électron. Ces éléments de matrice représentent l'ingrédient essentiel permettant de comprendre la répartition du poids spectral en photoémission. Nous démontrons que dans ce modèle ils sont proportionnels à la transformée de Fourier de l'état de Wannier du système considéré, ainsi qu'à un terme de polarisation contenant les effets géométriques inhérents à toute expérience de photoémission. Nous appliquons alors cette approche à des systèmes physiques comme le graphène, ou encore au cas de mesures de dichroïsme circulaire réalisées au niveau des états d et de l'état de Shockley d'un monocristal de Cu(111), mettant ainsi en évidence ses succès et ses limitations
In this work, we highlight the relevance of photoemission spectroscopy for investigating the electronic properties of materials. In the first part, we tackle the development and the test phase of a new experimental setup which is composed of a molecular beam epitaxy (MBE) and a spin and angle resolved photoemission (SR-ARPES) chambers, connected to the tube at the Institut Jean Lamour. The high performances of this new setup are evaluated. On one hand by measuring well known system from the litterature (Shockley state at the Au(111) surface) and on the other hand by studying materials with novel properties (topological insulators, molecular Kondo effect …). Energy resolution is better than 2 meV for UV photoemission (UPS) and 300 meV for X-ray photoemission (XPS). We also have an angular resolution better than 0.2° and a lowest sample temperature of 8.7 K. Finally, first SR-ARPES measurements demonstrate the ability of this new installation to measure finest details of the spin polarized band structure. In short, this new setup is fully operationnal. The second part is dedicated to the study of a two dimensionnal (2D) ultra thin silicon oxide at the surface of a cristalline Ru(0001) substrate. Both growth and electronic properties are studied by high resolution XPS and ARPES. We confirm the structural model accepted for the system in the litterature for the monolayer case. In particular we confirm the existence of two inequivalent Si-O-Ru bonds with unprecedented high resolution XPS measurements on the O1s core level. In addition, our ARPES measurements highlight new dispersives states with 2D character which are unambiguously attributed to this oxide. While the monolayer is strongly connected to the ruthenium substrate (covalent bonds), the bilayer is disconnected from this latter one (van der Waals). Our work confirms the existence of such a transition with unambiguous signatures both in XPS and ARPES, in particular with the breaking of Si-O-Ru bonds. We also demonstrate the robustness of this system which, after being cristallised, can go to atmosphere without fundamental modification of his electronic properties. That gives a lot of potential applications to this 2D cristalline oxide, which could play in the futur the role of a wide band gap insulator in 2D heterostructures. In the last part, we focus on the theoretical aspects of photoemission. While band structure is periodic in the reciprocal space, it is not the case of photoemission intensity which can depend on a lot of parameters. We are motivated by the fact that these considerations are generally not well understood by experimentalists. Here, we present a simple model recently proposed in the three step approach of the photoemission process. With this model we can evaluate the one-electron matrix elements which play a key role to understand the variations of spectral weight in photoemission. In this approach, one-electron matrix elements are proportionnal to both Fourier transform of the Wannier state of the system and to a polarization term. We apply this model to « real » systems, in particular to graphene and to circular dichroism measurements on Cu(111) sample, highlighting sucess and limitations of this model

[EN] The general goal of this thesis is the development of a basic tool for the analysis of passive microwave and millimetre-wave devices used in the new generation of communication systems. In particular, the work is focused on the development of a tool for an efficient and accurate modal characterization of passive devices composed of waveguides with arbitrary cross section. In order to achieve this goal, a method recently arisen and called BI-RME (Boundary Integral - Resonant Mode Expansion) is extended. This method has been revealed as one of the most appropriate, for its high computational efficiency, to characterize waveguides with arbitrary cross section. Regarding the original BI-RME method, this one will improve the precision and the efficiency of the modal solution in presence of circular and elliptic perturbations in the arbitrary waveguide contour. Then, the first work consists on extending the original BI-RME method theory to circular and elliptic geometries including the possibility to connect these two new types of segments (circular and elliptic) with the straight segments used until now in the practical implementation of the method. In order to validate the new developed theory, a set of parameters as the cut-off frequencies, the cut-off wavelengths or the electromagnetic fields of canonical waveguides and arbitrarily shaped waveguides of great practical interest, are calculated. These results are compared with analytical well-known solutions or results published in the literature. Once the electromagnetic modal chart of different arbitrarily shaped waveguides is obtained, the following step is the computation of the coupling integrals between these modes and the ones of the rectangular waveguide that completely surrounds the arbitrary contour. Such integrals are essential for the modal analysis of microwave passive structures involving waveguides with arbitrary cross section. For this purpose, the new extended BI-RME method is included into a software package tool based on the integral equation method, which allows to characterize efficiently waveguide discontinuities by means of inmitance matrices (admittance or impedance). This efficient full-wave analysis method requires the knowledge of the modal chart related to all the waveguides included in the devices under consideration, as well as the coupling integrals between the modes of the two waveguides composing the discontinuity. In the rectangular waveguides case this modal information can be easily obtained in an analytical way. However, when a waveguide or both have arbitrary cross section, the accurate and efficient modal analysis can be obtained by means of the BI-RME method. The use of the integral equation method based on admittance or impedance matrices to characterize devices composed of cascading waveguides is specially advantageous because it leads to a linear system of equations. The coefficients matrix of this linear system presents a banded structure that can be appropriately exploited to increase the computational efficiency associated to the resolution of the aforementioned system, and to reduce considerably the computational cost associated to the analysis of complex devices. Next step is the demonstration that in waveguides with arbitrary cross section and with one or two symmetry axes you can generate, also by means of the BI-RME method, the whole family of waveguide modes, so that they verify a certain fictitious boundary condition of electric or magnetic walls in the symmetry plane, and the advantages regarding the computation of the modes are discussed. Furthermore, those different symmetry families of waveguide modes propagate in an independent way along the structures constituted by a connection of uniform waveguides. This situation can also be exploited to increase in a remarkable way the efficiency of the Computer-Aided-Design (CAD) electromagnetic software packages. Once verified with success the efficiency and precision of the new CAD tool developed by means of the analysis of transitions published in the related technical bibliography, the analysis of really complex passive waveguide devices is performed. Some passive waveguide devices analyzed are for instance a filter with inductive coupling windows and tuning screws, a filter with rounded corners, dual mode filters in circular waveguide with elliptic irises or in elliptic waveguides, an evanescent filter, a low bandpass filter in coaxial waveguide, and finally a new 90º twist component for space applications. The simulated results are totally validated by means of comparison with other data published in the related technical bibliography, or by means of measurements of manufactured prototypes. Finally, the conclusions of this work are extracted and future research lines are outlined. Publications in journal and congress presentations in the framework of this thesis are also indicated.
[ES] El objetivo general de esta tesis es el desarrollo de una herramienta b´asica general para el an´alisis de dispositivos pasivos de microondas y ondas milim´etricas usados en la nueva generaci´on de sistemas de comunicaciones. En particular, el trabajo se centra en desarrollar una herramienta para una eficiente y precisa caracterizaci´on modal de dispositivos pasivos constituidos por gu´ıas de onda de secci´on transversal arbitraria. Para cumplir con este objetivo se propone extender un m´etodo surgido recientemente y llamado BI-RME (Boundary Integral - Resonant Mode Expansion, que en espa˜nol significa Integral de Contorno - Expansi´on Modal Resonante). Este m´etodo se ha revelado como uno de los m´as adecuados, por su tremenda eficiencia computacional, para caracterizar modalmente las gu´ıas de secci´on transversal arbitraria. Respecto al m´etodo BI-RME original se pretende mejorar la precisi´on y la eficiencia en presencia de perturbaciones circulares y el´ıpticas en el contorno de las gu´ıas a estudiar. El primer trabajo de la tesis consiste entonces en extender la teor´ıa del m´etodo BI-RME a geometr´ıas circulares y el´ıpticas incluyendo la posibilidad de conectar estos dos nuevos tipos de arcos (circulares y el´ıpticos) con los tramos rectos usados hasta ahora en la implementaci´on pr´actica del m´etodo. Con el objeto de validar la nueva teor´ıa desarrollada se calcula un conjunto de par´ametros, como las frecuencias de corte, la longitud de onda de corte o el campo electromagn´etico, que caracterizan gu´ıas can´onicas y gu´ıas arbitrarias de inter´es pr´actico, y se comparan los resultados obtenidos con las soluciones anal´ıticas conocidas o resultados publicados en la literatura. Una vez obtenida la carta modal de las diferentes gu´ıas de secci´on transversal arbitraria, el paso siguiente es calcular las integrales de acoplo entre estos modos y los modos de la gu´ıa rectangular que encierra completamente el contorno arbitrario. Tales integrales son fundamentales para el an´alisis modal de estructuras pasivas de microondas constituidas por transiciones planares entre gu´ıas de secci´on transversal distinta. Para estudiar estas estructuras pasivas, se integra la nueva y extendida t´ecnica BI-RME propuesta en una herramienta inform´atica basada en el m´etodo de la ecuaci´on integral, el cual permite caracterizar eficientemente transiciones planares mediante matrices de inmitancia (admitancia o impedancia). Este m´etodo de an´alisis electromagn´etico full-wave necesita el espectro modal de cada una de las gu´ıas que forman las transiciones, as´ı como las integrales de acoplo entre los modos de las dos gu´ıas adyacentes que constituyen la discontinuidad. En el caso de gu´ıas rectangulares, dicha informaci´on modal se puede obtener f´acilmente de forma anal´ıtica. Sin embargo cuando una gu´ıa o las dos tienen una secci´on transversal arbitraria, esta informaci´on se puede obtener de forma eficiente y precisa mediante el m´etodo BI-RME. El empleo del m´etodo de la ecuaci´on integral basado en matrices de admitancias o de impedancias para caracterizar dispositivos integrados por gu´ıas conectadas en cascada resulta especialmente ventajoso, pues conduce a un sistema de ecuaciones lineales a resolver cuya matriz de coeficientes presenta una estructura en banda, caracter´ıstica que puede explotarse adecuadamente para incrementar la eficiencia computacional asociada a la resoluci´on del citado sistema, y reducir considerablemente el coste asociado al an´alisis de dispositivos complejos. A continuaci´on se demuestra como en gu´ıas de secci´on transversal arbitraria con uno o dos ejes de simetr´ıa se puede generar, tambi´en mediante el m´etodo BI-RME, toda la familia de modos de dicha gu´ıa de manera que verifiquen una cierta condici´on de contorno ficticia de pared el´ectrica o pared magn´etica en el plano de simetr´ıa, y se discuten las ventajas computacionales respecto a calcular todos los modos simult´aneamente. Adem´as, las distintas familias de simetr´ıa se propagan de forma independiente a lo largo de estructuras constituidas por una conexi´on en cascada de gu´ıas uniformes que presentan la misma simetr´ıa. Dicha situaci´on se puede explotar para aumentar de forma notable la eficiencia del simulador electromagn´etico. Verificada con ´exito la eficiencia y precisi´on de la nueva herramienta inform´atica desarrollada mediante el an´alisis de transiciones publicadas en la bibliograf´ıa t´ecnica relacionada, se analizan dispositivos pasivos realmente complejos, tales como un filtro con ventanas de acoplo inductivas y tornillos de sinton´ıa, un filtro con esquinas redondeadas, filtros de modo dual en gu´ıa circular con iris el´ıpticos o en gu´ıa el´ıptica, un filtro de modo evanescente, un filtro paso bajo en gu´ıa coaxial, y finalmente un nuevo girador de polarizaci´on de 90o para aplicaciones espaciales. Los resultados son completamente validados mediante comparaci´on con otros publicados en la bibliograf´ıa t´ecnica relacionada, o bien mediante las medidas de las respuestas asociadas a unas implementaciones pr´acticas de las estructuras analizadas. Finalmente se extraen las conclusiones de la tesis y se indican posibles l´ıneas de investigaci´on futuras. Se indican tambi´en las publicaciones en revistas y las comunicaciones en congresos a que ha dado lugar el trabajo desarrollado en el marco de esta tesis.
[CAT] L’objectiu general d’esta tesi ´es el desenrotllament d’una ferramenta b`asica general per a l’an`alisi de dispositius passius de microones i ones mil·lim`etriques usats en la nova generaci´o de sistemes de comunicacions. En particular, el treball se centra en desenrotllar una ferramenta per a una eficient i precisa caracteritzaci´o modal de dispositius passius constitu¨ıts per guies d’ona de secci´o transversal arbitr`aria. Per a complir amb este objectiu es proposa estendre un m`etode sorgit recentment i anomenat BI-RME (Boundary Integral - Resonant Mode Expansion, que en valenci`a significa Integral de Contorn - Expansi´o Modal Ressonant). Este m`etode s’ha revelat com un dels mes adequats, per la seua tremenda efici`encia computacional, per a caracteritzar modalment les guies de secci´o transversal arbitr`aria. Respecte al m`etode BI-RME original es pret´en millorar la precisi´o i l’efici`encia en pres`encia de pertorbacions circulars i el·l´ıptiques en el contorn de les guies a estudiar. El primer treball de la tesi consistix aleshores a estendre la teoria del m`etode BI-RME a geometries circulars i el·l´ıptiques incloent la possibilitat de connectar estos dos nous tipus d’arcs (circulars i el·l´ıptics) amb els trams rectes usats fins ara en la implementaci´o pr`actica del m`etode. Amb l’objecte de validar la nova teoria desenrotllada es calcula un conjunt de par`ametres, com les freq¨ u`encies de tall, la longitud d’ona de tall o el camp electromagn`etic, que caracteritzen guies can`oniques i guies arbitr`aries d’inter´es pr`actic, i es comparen els resultats obtinguts amb les solucions anal´ıtiques conegudes o resultats publicats en la literatura. Una vegada obtinguda la carta modal de les diferents guies de secci´o transversal arbitr`aria, el pas seg¨uent ´es calcular les integrals d’acoblament entre estos modes i els modes de la guia rectangular que tanca completament el contorn arbitrari. Tals integrals s´on fonamentals per a l’an`alisi modal d’estructures passives de microones constitu¨ıdes per transicions planars entre guies de secci´o transversal distinta. Amb eixa finalitat, s’integra la nova i estesa t`ecnica BI-RME proposta en una ferramenta inform`atica basada en el m`etode de l’equaci´o integral, el qual permet caracteritzar eficientment transicions planars per mitj`a de matrius d’inmit`ancia (admit`ancia o imped`ancia). Este m`etode d’an`alisi electromagn`etica full-wave necessita l’espectre modal de cadascuna de les guies que formen les transicions, aix´ı com les integrals d’acoblament entre els modes de les dos guies adjacents que constitu¨ıxen la discontinu¨ıtat. En el cas de guies rectangulars, dita informaci´o modal es pot obtindre f`acilment de forma anal´ıtica. No obstant quan una guia o les dos tenen una secci´o transversal arbitr`aria, esta informaci´o es pot obtindre de forma eficient i precisa per mitj` a del m`etode BI-RME. L’us del m`etode de l’equaci´o integral basat en matrius d’admit`ancies o d’imped`ancias per a caracteritzar dispositius integrats per guies connectades en cascada resulta especialment avantatj´os, perqu`e condu¨ıx a un sistema d’equacions lineals a resoldre la matriu de coeficients del qual presenta una estructura en banda, caracter´ıstica que pot explotar-se adequadament per a incrementar l’efici`encia computacional associada a la resoluci´o del citat sistema, i reduir considerablement el cost associat a l’an`alisi de dispositius complexos. A continuaci´o es demostra com en guies de secci´o transversal arbitr`aria amb un o dos eixos de simetria es pot generar, tamb´e per mitj`a del m`etode BI-RME, tota la fam´ılia de modes de dita guia de manera que verifiquen una certa condici´o de contorn fict´ıcia de paret el`ectrica o paret magn`etica en el pla de simetria, i es discutix els avantatges computacionals respecte a calcular tots els modes simult`aniament. A m´es, les distintes fam´ılies de simetria es propaguen de forma independent al llarg d’estructures constitu¨ıdes per una connexi´o en trencada de guies uniformes que tenen les meteixes propietats de simetria. La dita situaci´o es pot explotar per a augmentar de forma notable l’efici`encia del simulador electromagn`etic. Verificada amb `exit l’efici`encia i precisi´o de la nova ferramenta inform`atica desenrotllada per mitj`a de l’an`alisi de transicions publicades en la bibliografia t`ecnica relacionada, s’analitzen dispositius passius realment complexos, tals com un filtre amb finestres d’acoblament inductives i tornels de sintonia, un filtre amb cantons arredonits, filtres de modo dual en guia circular amb iris el·l´ıptics o en guia el·l´ıptica, un filtre de modo evanescent, un filtre pas baix en guia coaxial, i finalment un nou girador de polaritzaci´o de 90o per a aplicacions espacials. Els resultats s´ on completament validats per mitjanc¸ant la comparaci´o amb altres publicats en la bibliografia t` ecnica relacionada, o b´e per mitj`a de les mesures de les respostes associades a unes implementacions pr`actiques de les estructures analitzades. Finalment s’extrauen les conclusions de la tesi i s’indiquen possibles l´ınies d’investigaci´o futures. S’indiquen tamb´e les publicacions en revistes i les comunicacions en congressos a qu`e ha donat lloc el treball desenrotllat en el marc d’esta tesi.
Marini, S. (2005). Análisis modal eficiente de dispositivos pasivos de microondas implementados con guías de sección transversal arbitraria [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/131737

by Tat-Ming Tso.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.
Includes bibliographical references (p. 43-45).
Chapter Chapter 1 --- INTRODUCTION --- p.1
Chapter §1.1 --- Introduction --- p.1
Chapter §1.2 --- Preconditioned Conjugate Gradient Method --- p.3
Chapter §1.3 --- Outline of Thesis --- p.3
Chapter Chapter 2 --- CIRCULANT AND NON-CIRCULANT PRECONDITIONERS --- p.5
Chapter §2.1 --- Circulant Matrix --- p.5
Chapter §2.2 --- Circulant Preconditioners --- p.6
Chapter §2.3 --- Circulant Preconditioners from Kernel Function --- p.8
Chapter §2.4 --- Non-circulant Band-Toeplitz Preconditioners --- p.9
Chapter Chapter 3 --- B-SPLINES --- p.11
Chapter §3.1 --- Introduction --- p.11
Chapter §3.2 --- New Version of B-splines --- p.15
Chapter Chapter 4 --- CIRCULANT PRECONDITIONERS CONSTRUCTED FROM B-SPLINES --- p.24
Chapter Chapter 5 --- NUMERICAL RESULTS AND CONCLUDING REMARKS --- p.28
Chapter Chapter 6 --- APPLICATIONS TO SIGNAL PROCESSING --- p.37
Chapter §6.1 --- Introduction --- p.37
Chapter §6.2 --- Preconditioned regularized least squares --- p.39
Chapter §6.3 --- Numerical Example --- p.40
REFERENCES --- p.43

Let F be a finite field with q elements where $q=p\sp{m}, p$ prime. Let ${\cal M}$ be the algebra of n x n circulant matrices over F. The set $O\sb{(n,q)}$ of orthogonal n x n circulant matrices is a subgroup of ${\cal M}\sp\times.$ The major purposes of the thesis are: (1) to explain K. A. Byrd and T. P. Vaughan's results stated in (8), about formulas for the orders, and algorithms for the construction, of the groups $O\sb{(n,q)};$ (2) to show new examples and develop programs to find the orders and to actually construct the group $O\sb{(n,q)}$ for any given n and q.

碩士
國立中山大學
應用數學研究所
85
To compute the eigenvalues of two special matrices, the symmetric circulant tridiagonal matrix and the symmetric quindiagonal matrix, in this thesis, we propose parallel algorithms based on the bisection method and the Sylvester's law of inertia on these two kinds matrices. The algorithm can be used for calculating some specified eigenvalues of the symmetric tridiagonal matrix. When we apply it on these two kinds matrices, we get a simpler method than the determination notation for the matrix eigenvalue problem.

Tese de doutoramento em Engenharia Electrotécnica e de Computadores, apresentada ao Departamento de Engenharia Electrotécnica e de Computadores da Universidade de Coimbra
Visual recognition systems are extremely data-hungry. To accurately recognize a new kind of object, a learning algorithm requires a massive dataset of example images, often augmented artificially by cropping different image regions. More examples seem to invariably raise the computational burden of learning. Is this an inescapable fact? In this thesis, we show that it is not true -- that the structure of these datasets hides important shortcuts. The key observation is that samples are not independent, since samples cropped from the same image share most pixels. Using an analytical model of image translation, the cyclic shift, we show that the resulting dataset contains circulant matrices. As a result, we can diagonalize it with the Discrete Fourier Transform (DFT), which reduces both storage and computation by orders of magnitude. The use of the DFT further reveals an interesting link to correlation filters from classical signal processing. We accelerate learning algorithms such as Ridge Regression and Support Vector Regression, addressing linear and non-linear kernel methods. We propose two trackers, the Dual and Kernelized Correlation Filters, which run at hundreds of frames-per-second, and yet perform better than more complex trackers on a 50 videos benchmark. For detection, we propose a decomposition that is several times faster than hard-negative mining, a staple of detector learning. We also generalize these results for other kinds of datasets, such as rotated images or non-rigidly deformed images, which accelerates the learning of pose estimators. The proposed solutions require only a few lines of code to implement, relying on the Fast Fourier Transform and optional off-the-shelf solvers for the bulk of the computations, which easily run in parallel. The software produced during this thesis is open-source.
Os sistemas de reconhecimento visual necessitam de vastas quantidades de dados. Para reconhecer um novo tipo de objecto, um algoritmo de aprendizagem requer uma grande base de dados de imagens-exemplo, muitas vezes aumentada artificialmente através da extracção de diferentes regiões dessas imagens. Intuitivamente, processar mais exemplos implica aumentar invariavelmente o custo computacional do processo de aprendizagem. Será que esta intuição corresponde à realidade? Esta tese demonstra que tal não é verdade -- que a estrutura destas bases de dados contém atalhos ainda inexplorados. A principal observação é que as amostras não são independentes, já que amostras extraídas da mesma imagem vão ter vários píxeis em comum. Com base num modelo analítico da translação de imagem, chamado "deslocação cíclica", é demonstrado que a base de dados resultante contém matrizes circulantes. Consequentemente, podemos diagonalizá-la com a Transformada de Fourier Discreta (TFD), o que reduz significativamente os requisitos de armazenamento e de computação. O uso da TFD revela uma ligação importante aos filtros de correlação estudados em processamento de sinal. Demonstra-se que é possível acelerar algoritmos de aprendizagem tais como o método dos mínimos quadrados com regularização, e regressão de vectores de suporte, abordando tanto métodos lineares como de kernel (núcleo). São propostos dois métodos de seguimento visual, o Filtro de Correlação Dual e o de Kernel, capazes de processar vídeo a centenas de imagens por segundo, e que demonstram maior precisão que outros métodos mais complexos numa base de dados de 50 vídeos. Para detecção de objectos, é proposta uma decomposição várias vezes mais rápida que a procura sistemática de exemplos negativos, o método mais comum de aprendizagem de detectores. Estes resultados são também generalizados para outros tipos de bases de dados, tais como imagens que sofreram rotação ou deformações não rígidas, o que permite ainda acelerar detectores de pose. As soluções propostas podem ser implementadas com poucas linhas de código, usando apenas a Transformada de Fourier Rápida, e opcionalmente algoritmos de aprendizagem externos, que podem ser executados em paralelo. O código-fonte relativo a esta tese é de acesso livre.

碩士
國立中央大學
數學系
103
For an $S_n$-matrix with a circular disc as its numerical range, we want to know whether its rank-$k$ numerical range is also a circular disc. We show that, for an $S_5$-matrix $A$ with real spectrum and circular numerical range, if its associated Blaschke product $B$ has a normalized decomposition $B=C\circ D$, with $C$ of degree 2 and $D$ of degree 3, then $\Lambda_2(A)$ is also a circular disk and $\Lambda_3(A)$ is singleton (cf. Theorem 3.3). For $A$ and $B$ be $2\times2$ matrices, we have $w(A+B)\le w(A)+w(B)$. We are interested in when it becomes equality. We obtain a necessary and sufficient condition for $w(A+B)= w(A)+w(B)$ to hold (cf. Proposition 4.3).

博士
國立交通大學
土木工程系所
97
A computer program is developed in the thesis for calculating torsional, vertical, horizontal, coupling and rocking impedances in frequency domain for axial-symmetric foundations embedded in layered medium. In this process of formulating the impedances, the soil medium is divided into interior and exterior domains. The analytical solutions are formed separately with unknown coefficients for both domains. In order to find the unknown coefficients for both domains, the variational principle is employed using the continuity conditions (both displacements and stresses) at the interfaces between interior and exterior domains, interior domain and foundation, and exterior domain and foundation to find impedance functions. To solve those problems, the analytic solution for the interior domain is the combination of a homogeneous solution and a particular solution, the exterior domain is described by a homogeneous solution only. To obtain the homogeneous solution, one has to solve the complex root of the transcendental equations. A numerical scheme has been proposed. The wave numbers of transcendental equations have been employed for finding impedance matrices. Some numerical results of torsional, vertical, horizontal, coupling and rocking impedances with different embedded depths will be presented in layered medium and comments on the numerical scheme will be given. The impedance matrices of axial-symmetric foundations embedded in an elastic half-space medium approximated using analytical solutions in layer. To approximate the situation of half-space medium, the thickness of one layer medium gradually increased to see if the impedance function is approaching those for the case of half-space medium. However, as the thickness increases the numerical instability problem will be arisen. To overcome this numerical problem, a new numerical technique will be developed. Some numerical results of torsional, vertical, horizontal, coupling and rocking impedances with different embedded depths will be presented in an elastic half-space medium and comments on the numerical scheme will be given.

It was conjectured in the early 1950¡¯s that the empirical spectral distribution (ESD) of an $n \times n$ matrix whose entries are independent and identically distributed with mean zero and variance one, normalized by a factor of $\frac{1}{\sqrt{n}}$, converges to the uniform distribution over the unit disk on the complex plane, which is called the circular law. The goal of this thesis is to prove the so called Replacement Principle introduced by Tao and Vu which is a crucial step in their recent proof of the circular law in full generality. It gives a general criterion for the difference of the ESDs of two normalised random matrices $\frac{1}{\sqrt{n}}A_n$, $\frac{1}{\sqrt{n}}B_n$ to converge to 0.
Thesis (Master, Mathematics & Statistics) -- Queen's University, 2009-07-11 14:57:44.225

No
In this paper the sensitivity of the decoupling matrix used for mutual coupling compensation in small size uniform circular arrays has been studied. The compensation matrix is calculated using the receiving mode technique for a 5-element uniform circular array and applied to two groups of direction finding algorithms, namely phase comparison-based (interferometry) and subspace-based algorithms. In the tracking application considered the receiver array is deployed on a car roof or aircraft, so the geometry of the platform influences the compensation results. In this work, the effect of different ground plane geometries in terms of the standard deviation of angular error for each estimation algorithm using simulation results is investigated. The results show that the calibration conditions used to determine the compensation matrix affect the AOA estimation accuracy.

Dissertação apresentada para a obtenção do grau de Mestre em Engenharia Mecânica na Especialidade de Sistemas de Produção, apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra
O presente trabalho centra-se na simulação numérica do ensaio de expansão biaxial, em matrizes circular e elíptica, sob pressão hidráulica, com recurso ao programa DD3IMP. São realizados diversos ensaios de modo a determinar a curva de encruamento de chapas metálicas, até valores elevados de deformação. A análise de resultados segue uma metodologia idêntica à utilizada experimentalmente, tendo como objectivo testá-la e simplificá-la. Neste contexto, foi realizado um estudo em chapas anisotrópicas, apresentando ou não anisotropia de propriedades no seu plano, com a finalidade de determinar a respectiva curva de encruamento, a partir de ensaios em matrizes circular e elíptica. Numa primeira fase, realizou-se um estudo sobre o ensaio de expansão em matriz circular para cada material, analisando as evoluções de pressão e do raio de curvatura com a altura do pólo da calote. Foi determinada a curva de encruamento e realizada uma análise de erro. Posteriormente, foi realizado o mesmo tipo de estudo, em alguns dos materiais analisados anteriormente, mas para o ensaio de expansão biaxial em matriz elíptica. Em ambos os casos, matriz circular e elíptica, foram testadas metodologias de análise que permitem simplificar o procedimento experimental habitualmente utilizado, nomeadamente no que diz respeito à determinação dos raios de curvatura no topo da calote, necessária à avaliação das tensões no plano da chapa e da tensão equivalente. Este estudo permitiu examinar a possibilidade de obtenção de uma curva única de evolução do raio de curvatura em função da altura no pólo para o caso de materiais anisotrópicos, ensaiados em matriz circular. A análise foi estendida ao caso da matriz elíptica.
Abstract This work focuses on the numerical simulation of the biaxial bulge test, with circular and elliptical dies, under hydraulic pressure, using the in-house code DD3IMP. Several tests are performed until high strain values in order to determine the work hardening law on metal sheets. The analysis of results follows a methodology similar to the one used experimentally, aiming to test and simplify it. In this context, a study was carried out in anisotropic metal sheets, presenting or not in-plane isotropy of properties, in order to determine their hardening curve from tests on circular and elliptical dies. In a first stage, a study was performed concerning the bulge testing in a circular die for each material, analyzing the evolution of the pressure and radius of curvature with the pole height. Then, the hardening curve was determined and an error analysis was performed. Complementarily, the same type of study was carried out on some of the previous used materials but for the bulge testing in an elliptical die. In both cases, elliptical and circular die, methodologies of analysis were tested that allow to simplify the experimental procedures commonly used, namely conceming the determination of the radii of curvature in the pole, necessary to the evaluation of the in-plane stresses of the metal sheet and the correspondent equivalent stress. This study allowed examining the possibility of obtaining a single curve for the evolution of the radius of curvature as a function of height in the pole for the case of anisotropic materials, tested in circular die. The analysis was extended to the case of elliptic die.