Les interactions non-Covalentes entre des protéines et des polysaccharides anioniques tels que les glycosaminoglycanes (GAGs) interviennent dans de nombreux processus physio-Pathologiques tels que la signalisation, la reconnaissance cellulaire, les infections bactériennes et virales ou lors de la progression des cancers. Une des difficultés pour comprendre les mécanismes moléculaires mis en jeu lors de ces interactions réside dans le déchiffrage des informations structurales contenues dans les GAGs. Cette tâche est délicate, surtout en raison du degré variable d'acétylations et de sulfatations de ces GAG's, constituant des limitations importantes pour l'avancée des recherches en glycobiologie. Pour contourner ces restrictions, des méthodes analytiques fines et innovantes, telles que la spectrométrie de masse (MS) offrent de nombreux avantages. Durant cette thèse, trois approches originales basées sur la MS ont été developpées. La première a consisté à synthétiser de nouvelles matrices ioniques liquides limitant la désulfatation et favorisant l'obtention de dépôt homogène pour l'analyse par UV-MALDI-TOF. La seconde a montré le potentiel d'une méthode d'ionisation douce récemment introduite, la désorption ionisation assistée par électronébulisation (DESI) permettant l'analyse directe et en conditions ambiantes d'oligosaccharides anioniques seuls ou sous forme de complexes avec une protéine. Enfin, la troisième a nécessité la fabrication de puces à protéines ou à saccharides pour lanalyse de complexes protéines/GAG en utilisant le couplage de la résonance plasmonique de surface avec la MS (SPR-MS). Ce couplage permet d'effectuer le suivi en temps réel de la formation de complexes entre des protéines et des GAGs, d'en déterminer les constantes de la dissociation, puis de détecter directement par UV-MALDI-TOF les ligands, qu'ils soient de nature protéique ou saccharidique. / The non-Covalent interactions between proteins and anionic polysaccharides such as glycosaminoglycans (GAGs) are involved in several physio-Pathological processes such as cell signalling and recognition, bacterial and viral infections or during cancer progression. One of the obstacles to get the molecular mechanisms involved during these interactions hold in the structural information deciphering within GAG's sequences. This task is delicate especially because of variable level of acetylations and sulfations, constituting important bottleneck in the research advances of the glycobiology field. To bypass these restrictions, accurate and innovative analytical methods such as mass spectrometry (MS) provide numerous advantages. During this Ph.D training, three original MS based approaches have been developed. The first dealt with the synthesis of new ionic liquid matrices, which both restrict desulfation process and favour the homogeneous deposits for UV-MALDI-TOF analysis. The second way used a soft recently introduced ionization method, desorption electrospray ionization (DESI) allowing direct analysis in ambient conditions of anionic oligosaccharides or under complexes with protein. Finally, the third involved the making of protein or saccharide chips for the analysis of protein / GAG complexes using the hyphenation of surpface plasmon resonance with MS (SPR-MS). Thos coupling allows real time monitoring protein / GAG complexes formation, their dissociation constant determination and the direct detection of protéic as wall as saccharidic ligands by UV-MALDI-TOF.

Sign pattern theory examines what can be said about a matrix if one knows the signs of all or some of its entries but not the exact values. Since all we know is the sign of each entry, we can write these sign patterns as matrices whose entries come from the set {+1, -1, 0, #}, where # is used for an unknown sign. Semirings satisfy all properties of rings with unity except the existence of additive inverses. The set {+1, -1, 0, #} can be viewed as a commutative semiring in natural way. In the thesis, we give a semiring version of the Cayley-Dickson construction which allows one to construct the sign pattern semiring from the Boolean semiring. We use tools from Boolean matrices to study sign nonsingular (SNS) matrices. We also investigate different notions of rank of matrices over semirings. For these rank functions we simplify proofs of classical inequalities for the sum and the product of matrices using the semiring versions of the Cauchy-Binet and Laplace theorems. For matrices over the sign pattern semiring, the minimum rank of the sign pattern is compared with the other versions of the rank. We also characterize irreducible powerful sign pattern matrices and investigate the period and base of an SNS matrix.

Our main aim in this thesis is to produce new T-matrices from the set of existing T-matrices. In Theorem 4.3 a multiplication method is introduced to generate new T-matrices of order st, provided that there are some specially structured T-matrices of orders s and t. A class of properly amicable and double disjoint T-matrices are introduced. A number of properly amicable T-matrices are constructed which includes 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 18, 22. To keep the new matrices disjoint an extra condition is imposed on one set of T-matrices and named double disjoint T-matrices. It is shown that there are some T-matrices that are both double disjoint and properly amicable. Using these matrices an infinite family of new T-matrices are constructed. We then turn our attention to the application of T-matrices to construct orthogonal designs and complex Hadamard matrices. Using T-matrices some orthogonal designs constructed from 16 circulant matrices are constructed. It is known that having T-matrices of order t and orthogonal designs constructible from 16 circulant matrices lead to an infinite family of orthogonal designs. Using amicable T-matrices some complex Hadamard matrices are shown to exist. / iii, 49 leaves ; 29 cm

Thesis (M. Phil.)--University of Hong Kong, 2008. / Includes bibliographical references (leaf 57-58) Also available in print.

This paper is the result of a study of the power method to find dominant eigenvalues of square matrices. It introduces ideas basic to the study and shows the development of the power method for the most well-behaved matrices possible, and it explores exactly which other types of matrices yield to the power method. The paper also discusses a type of matrix typically considered impossible for the power method, along with a modification of the power method which works for this type of matrix. It gives an overview of common extensions of the power method. The appendices contain BASIC versions of the power method and its modification.

This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.

Magíster en Ciencias de la Ingeniería, Mención Matemáticas Aplicadas. Ingeniera Civil Matemática / Las matrices aleatorias y su reciente teoría están jugando un papel fundamental como herramienta estadística en áreas tales como finanzas, meteorología y procesamiento de señales e imágenes. Algunas de las aplicaciones que han adquirido mayor desarrollo se encuentran en el sector financiero y en el área de las comunicaciones inalámbricas. El desafío planteado en este trabajo de tesis consiste en realizar un análisis estadístico basado en la teoría de matrices aleatorias referido a un modelo de factores. A través de la experimentación computacional, se pretende alcanzar dos metas. La primera de ellas consiste en contrastar dos versiones de un mismo test de hipótesis, las cuales se definen a partir de estadísticos provenientes de dos de las más conocidas familias gaussianas de matrices aleatorias: GUE y GOE. Esta comparación surge del hecho de que la familia GOE es menos estudiada en las aplicaciones de matrices aleatorias a considerar, de modo que se busca ampliar el conocimiento que de ella se tiene. Para hacer efectivo el contraste entre ambas versiones, estas se implementan para luego analizarlas en términos de sus comportamientos frente a errores y aciertos. Así, se logra probar empíricamente que no existe diferencia alguna entre ellas, por lo que la versión GOE del test es la que asume el protagonismo. Alcanzada la meta anterior, la segunda consiste en dar utilidad al test en su versión GOE, mediante el desarrollo de un procedimiento que lo aplica iteradas veces para estimar el número de factores de una muestra sujeta al modelo de factores. Posteriormente, el procedimiento es sometido a una serie de pruebas empíricas que buscan validarlo como método de estimación del número de factores. Finalmente, es preciso mencionar que, si bien, este trabajo posee un carácter fundamentalmente experimental, no se aparta del estudio, análisis y manejo abstracto de la teoría de matrices aleatorias que se requieren necesariamente para llevarlo a cabo. / Este trabajo ha sido parcialmente financiado por Núcleo Milenio: "Modelos estocásticos de sistemas complejos y desordenados"

No description available.

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Master / Master of Science