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Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (leaves [77]-80).

Thesis (Ph. D.)--Oregon State University, 1968. / Typescript (photocopy). Includes bibliographical references (leaves 57-58). Also available on the World Wide Web.

Orientador: Dr. Florivaldo Menezes Filho / Banca: Dr. Marcos Pupo Nogueira / Banca: Dr. Eduardo Seicman / Resumo: Este trabalho aborda as relações interdisciplinares entre música e arquitectura nas obras multimídia de Iannis Xenakis, denominadas Polytopes. O texto analisa os principais procedimentos composicionais utilizados na construção das peças musicais e arquitetônicas de suas obras iniciais e, posteriormente, dos Polytopes. Ao demonstrar a transferência de conceitos entre composição musical e arquitetônica, identificam-se similares estético-estruturais entre essas duas expressões artísticas. A história existencial de Xenakis, com especial ênfase à sua experiência de guerra é, por fim, reconhecida como uma das mais significantes influências de suas obras multimídia. As análises realizadas contaram com investigações dos contextos histórico-geográfico e sócio-cultural em que os Polytopes se inseriram, bem como com pesquisas sobre os escritos do compositor e outras referências bibliográficas relevantes / Abstract: This work approaches the transdiciplinary relationship between music and architeture on Iannis Xenakis' multimedia works, named Polytopes. The text analyses the major compositional procedures used on construction of the musical and architectural pieces of his earlier works, and later to the Polytopes. By the demonstrating the transfer of concepts between musical and architectural compositions, it identifies aesthetical-structural similarities between these two artistic expressions. Xenakis' existential history, whith special emphasis to his war experience is, at last, acknowledged as one the most significant influences to his multimedia works. The analysis performed counted on investigation of the historical, geographical, social and cultural contexts in which the Polytopes are embedded, as well as a research on the author's literary works, including other relevant bibliographical references / Mestre

Linear optimization aims at maximizing, or minimizing, a linear objective function over a feasible region defined by a finite number of linear constrains. For several well-studied problems such as maxcut, all the vertices of the feasible region are integral, that is, with integer-valued coordinates. The diameter of the feasible region is the diameter of the edge-graph formed by the vertices and the edges of the feasible region. This diameter is a lower bound for the worst-case behaviour for the widely used pivot-based simplex methods to solve linear optimization instances. A lattice (d,k)-polytope is the convex hull of a set of points whose coordinates are integer ranging from 0 to k. This dissertation provides new insights into the determination of the largest possible diameter δ(d,k) over all possible lattice (d,k)-polytopes. An enhanced algorithm to determine δ(d,k) is introduced to compute previously intractable instances. The key improvements are achieved by introducing a novel branching that exploits convexity and combinatorial properties, and by using a linear optimization formulation to significantly reduce the search space. In particular we determine the value for δ(3,7). / Thesis / Doctor of Philosophy (PhD)

Linear optimization is concerned with maximizing, or minimizing, a linear objective function over a feasible region defined as the intersection of a finite number of hyperplanes. Pivot-based simplex methods and central-path following interior point methods are the computationally most efficient algorithms to solve linear optimization instances. Discrete optimization further assumes that some of the variables are integer-valued. This dissertation focuses on the geometric properties of the feasible region under some structural assumptions. In the first part, we consider lattice (d,k)-polytopes; that is, the convex hull of a set of points drawn from {0,1,...,k}^d, and study the largest possible diameter, delta(d,k), that a lattice (d,k)- polytope can achieve. We present novel properties and an enumeration algorithm to determine previously unknown values of delta(d,k). In particular, we determine the values for delta(3,6) and delta(5,3), and enumerate all the lattice (3,3)-polytopes achieving delta(3,3). In the second part, we consider the convex hull of all the 2^(2^d - 1) subsums of the 2^d - 1 nonzero {0,1}-valued vectors of length d, and denote by a(d) the number of its vertices. The value of a(d) has been determined until d =8 as well as asymptotically tight lower and upper bounds for loga(d). This convex hull forms a so-called primitive zonotope that is dual to the resonance hyperplane arrangement and belongs to a family that is conjectured to include lattice polytopes achieving the largest possible diameter over all lattice (d,k)-polytopes. We propose an algorithm exploiting the combinatorial and geometric properties of the input and present preliminary computational results. / Thesis / Doctor of Philosophy (PhD)

Thesis (Ph. D.)--University of North Texas, May, 2009. / Title from title page display. Includes bibliographical references.

The Ehrhart function L_P(t) of a polytope P is defined to be the number of integer points in the dilated polytope tP. Classical Ehrhart theory is mainly concerned with integer values of t; in this master thesis, we focus on how the Ehrhart function behaves when the parameter t is allowed to be an arbitrary real number. There are three main results concerning this behavior in this thesis. Some rational polytopes (like the unit cube [0, 1]^d) only gain integer points when the dilation parameter t is an integer, so that computing L_P(t) yields the same integer point count than L_P(t). We call them semi-reflexive polytopes. The first result is a characterization of these polytopes in terms of the hyperplanes that bound them. The second result is related to the Ehrhart theorem. In the classical setting, the Ehrhart theorem states that L_P(t) will be a quasipolynomial whenever P is a rational polytope. This is also known to be true with real dilation parameters; we obtained a new proof of this fact starting from the chraracterization mentioned above. The third result is about how the real Ehrhart function behaves with respect to translation in this new setting. It is known that the classical Ehrhart function is invariant under integer translations. This is far from true for the real Ehrhart function: not only there are infinitely many different functions L_{P + w}(t) (for integer w), but under certain conditions the collection of these functions identifies P uniquely. / A função de Ehrhart L_P(t) de um politopo P é definida como sendo o número de pontos com coordenadas inteiras no politopo dilatado tP. A teoria de Ehrhart clássica lida principalmente com valores inteiros de t; esta dissertação de mestrado foca em como a função de Ehrhart se comporta quando permitimos que o parâmetro t seja um número real arbitrário. São três os resultados principais desta dissertação a respeito deste comportamento. Alguns politopos racionais (como o cubo unitário [0, 1]^d) apenas ganham pontos inteiros quando o parâmetro de dilatação t é um inteiro, de tal forma que computar L_P(t) devolve a mesma contagem de pontos que L_P(t). Eles são chamados de politopos semi-reflexivos. O primeiro resultado desta dissertação é uma caracterização destes politopos em termos de suas descrições como interseção de semi-espaços. O segundo resultado é relacionado ao teorema de Ehrhart. No contexto clássico, o teorema de Ehrhart afirma que L_P(t) será um quasi-polinômio sempre que P for um politopo racional. Sabe-se que este teorema generaliza para parâmetros reais de dilatação; nesta dissertação é apresentada uma nova demonstração deste fato, baseada na caracterização mencionada acima. O terceiro resultado é sobre como a função real de Ehrhart se comporta com respeito à translação neste novo contexto. Sabe-se que a função de Ehrhart clássica é invariante sob translações por vetores com coordenadas inteiras. Por outro lado, a função real de Ehrhart está bem longe de ser invariante: não só existem infinitas funções L_{P + w}(t) distintas, mas também, sob certas condições, esta coleção de funções identifica P unicamente.

La classification des groupes simples finies achevée en 2004 par Aschbacher et Smith au terme de décennies de travaux par des centaines de mathématiciens livre 18 familles infinies et 26 groupes appelés sporadiques. Ces derniers sont dotés de propriétés singulières. Dans ma thèse de doctorat, nous étudions le groupe sporadique de O'Nan -- usuellement dénoté O'N -- d'un point de vue géométrique, dans la lignée des travaux des Professeurs Buekenhout, Dehon et Leemans.<p><p>Nous abordons essentiellement quatre facettes de la géométrie de O'N. Tout d'abord, nous produisons la classification complète des géométries Buekenhout--Cara--Dehon--Leemans (BCDL) de O'N, une tâche commencée par Leemans en 2010. Les géomé-tries BCDL sont caractérisées par des axiomes inspirés de la Théorie des Immeubles de Jacques Tits. La majorité des groupes simples finis sont caractérisés par un immeuble et un diagramme. Parmi les exceptions se trouvent les groupes sporadiques. Une géométrie BCDL est plus générale qu'un immeuble, mais s'en rapproche.<p><p>Ensuite, nous étudions une géométrie pour le groupe d'automorphismes de O'N construite à partir de paires d'involutions commutantes. Les involutions jouent un rôle majeur dans la théorie des groupes simples finis. Ces travaux sont inspirés de la construction d'une tour de géométries pour les groupes de Fischer construite à partir de paires d'involutions commutantes due à Buekenhout.<p><p>Nous poursuivons en étudiant les polytopes abstraits réguliers sur lesquels O'N agit. Nous produisons la classification des polytopes de rang maximum, à savoir 4.<p><p>Enfin, nous étudions O'N sous le spectre des cartes régulières. Tout polyèdre abstrait régulier est une carte régulière, mais la réciproque n'est pas vraie. Nous donnons un algorithme permettant d'énumérer par type les cartes régulières pour un groupe fini donné. Ceci nous permet de borner le nombre de polyèdres abstraits réguliers sur lesquels O'N agit.<p><p>Nous produisons également les treillis de sous-groupes de O'N et de son groupe d'automorphismes. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished