Master of Science / Department of Statistics / Susan J. Brown / Haiyan Wang / DNA hybridization microarray technologies have made it possible to gain an unbiased perspective of whole genome transcriptional activity on such a scale that is increasing more and more rapidly by the day. However, due to biologically irrelevant bias introduced by the experimental process and the machinery involved, correction methods are needed to restore the data to its true biologically meaningful state. Therefore, it is important that the algorithms developed to remove any sort of technical biases are accurate and robust. This report explores the concept of background correction in microarrays by using a real data set of five replicates of whole genome tiling arrays hybridized with genetic material from Tribolium castaneum. It reviews the literature surrounding such correction techniques and explores some of the more traditional methods through implementation on the data set. Finally, it introduces an alternative approach, implements it, and compares it to the traditional approaches for the correction of such errors.

The need to establish baseline artisan productivities in the South African employmentintensive construction sector stems from the fact that these productivity norms have not been reviewed on a frequent basis. To others, these productivity norms hardly exist. With both scenarios, it is difficult to compare artisan productivity trends in the last fifty years to the trend of international standards. Constructive efforts have been made in this document to highlight the productivity norms that have existed within the building industry since the 1950’s. A similar exercise has been done for the USA and other European countries, notably the UK. A comparison of these trends of productivity norms has revealed that the current artisan productivity figures in South Africa are the lowest since the 1950’s. Again, they are the lowest amongst these countries. In the 1950’s, the artisan productivity norms in South Africa were quite close and thus comparable to the European countries but the gap has widened thereafter. The USA has generally experienced a continuous improvement in their productivity norms on an annual basis and this has been due partly to the improvement in the working tools of artisans. Another important factor is the poor quality of artisanship. The constructive effort being made by the South African government towards ensuring the sustainability of small and emerging contractors in employment-intensive construction is not in balance; the Contractor learnership programme of the Expanded Public Works Programme (EPWP) must go hand-in- hand with an artisan learnership programme. Key words: baseline artisan productivity, task-group, work-study, construction, face & stock-bricks, plastering, painting and tiling.

Durant ces dernières années, Il est de plus en plus compliqué d'écrire du code qui utilise une architecture au mieux de ses capacités. Certaines opérations clefs ont soit un accélérateur dédié, ou admettent une implémentation finement optimisée qui délivre les meilleurs performances. Ainsi, il est intéressant d'identifier ces opérations pendant la compilation d'un programme, et de faire appel à une implémentation optimisée.Nous nous intéressons dans cette thèse au problème de détection de ces opérations. Nous proposons un procédé qui détecte des sous-calculs correspondant à des opérations d'algèbre linéaire à l'intérieur de programmes polyédriques. L'idée principale de ce procédé est de découper le programme en sous-calculs isolés, et essayer de reconnaître chaque sous-calculs comme une combinaison d'opérateurs d'algèbre linéaire.Le découpage du calcul est effectué en utilisant une transformation de programme appelée tuilage monoparamétrique. Cette transformation partitionne le calcul en tuiles dont la forme est un agrandissement paramétrique d'une tuile de taille constante. Nous montrons que le programme tuilé reste polyédrique tout en permettant une paramétrisation limitée des tailles de tuile. Les travaux précédents sur le tuilage nous forçaient à choisir l'une de ces deux propriétés.Ensuite, afin d'identifier les opérateurs, nous introduisons un algorithme de reconnaissance de template, qui est une extension d'un algorithme d'équivalence de programme. Nous proposons plusieurs extensions afin de tenir compte des propriétés sémantiques communément rencontrées en algèbre linéaire.Enfin, nous combinons les deux contributions précédentes en un procédé qui détecte les sous-calculs correspondant à des opérateurs d'algèbre linéaire. Une de ses composantes est une librairie de template, inspirée de la spécification BLAS. Nous démontrons l'efficacité de notre procédé sur plusieurs applications. / Writing a code which uses an architecture at its full capability has become an increasingly difficult problem over the last years. For some key operations, a dedicated accelerator or a finely tuned implementation exists and delivers the best performance. Thus, when compiling a code, identifying these operations and issuing calls to their high-performance implementation is attractive. In this dissertation, we focus on the problem of detection of these operations. We propose a framework which detects linear algebra subcomputations within a polyhedral program. The main idea of this framework is to partition the computation in order to isolate different subcomputations in a regular manner, then we consider each portion of the computation and try to recognize it as a combination of linear algebra operations.We perform the partitioning of the computation by using a program transformation called monoparametric tiling. This transformation partitions the computation into blocks, whose shape is some homothetic scaling of a fixed-size partitioning. We show that the tiled program remains polyhedral while allowing a limited amount of parametrization: a single size parameter. This is an improvement compared to the previous work on tiling, that forced us to choose between these two properties.Then, in order to recognize computations, we introduce a template recognition algorithm. This template recognition algorithm is built on a state-of-the-art program equivalence algorithm. We also propose several extensions in order to manage some semantic properties.Finally, we combine these two previous contributions into a framework which detects linear algebra subcomputations. A part of this framework is a library of template, based on the BLAS specification. We demonstrate our framework on several applications.

An isohedral tiling is a tiling of congruent polygons that are also transitive, which is to say the configuration of degrees of vertices around each face is identical. Regular tessellations, or tilings of congruent regular polygons, are a special case of isohedral tilings. Viewing these tilings as graphs in planes, both Euclidean and non-Euclidean, it is possible to pose various problems of enumeration on the respective graphs. In this paper, we investigate some near-regular isohedral tilings of triangles and quadrilaterals in the hyperbolic plane. For these tilings we enumerate vertices as classified by number of edges in the shortest path to a given origin, by combinatorially deriving their respective generating functions.

Dans cette thèse, nous montrons que le groupe de K-théorie $K_0$ de la $C^*$-algèbre associée aux pavages de type pinwheel est isomorphe à la somme de $\ZZ \oplus \ZZ^6$ et d'un groupe cohomologique $H$.\\ Cette $C^*$-algèbre est de plus munie d'une trace qui induit une application linéaire sur ce groupe de $K$-théorie.\\ Nous calculons explicitement l'image, sous cette application, du sommant $\ZZ \oplus \ZZ^6$, montrant que l'image de $\ZZ$ est nulle et que l'image de $\ZZ^6$ est contenue dans le module de fréquences des patchs du pavage de type pinwheel.\\ Nous montrons également que l'on peut appliquer le théorème de l'indice mesuré dû à A. Connes pour relier l'image de $H$ à une formule cohomologique plus calculable.\\ Pour l'étude de cette partie cohomologique, nous adaptons la cohomologie PV, introduite par J. Savinien et J. Bellissard, au cas des pavages de type pinwheel pour montrer que le groupe de cohomologie de \v{C}ech de dimension maximale de ces pavages est isomorphe au groupe des coinvariants entiers de la transversale canonique associée à ces pavages.\\ Ce résultat nous permet alors de prouver la conjecture du gap-labeling fait par J. Bellissard, dans le cas particulier des pavages de type pinwheel.\\ Nous terminons cette étude par un calcul explicite, montrant que le gap-labeling (ou module de fréquences des patchs) est donné par $\frac{1}{264}\ZZ \left [ \frac{1}{5} \right ]$.

Nous étudions, dans la première partie de notre thèse, les polysimplexes d’un espace euclidien de dimension quelconque, c’est-à-dire les objets consistant en une juxtaposition de simplexes réguliers (de tétraèdres si la dimension est 3) accolés le long de leurs faces. Nous étudions principalement le groupe des symétries de ces polysimplexes. Nous présentons une façon de représenter un polysimplexe à l’aide d’un diagramme. Ceci fournit une classification complète des polysimplexes à similitude près. De plus, le groupe des symétries se déduit du groupe des automorphismes du diagramme. Il découle en particulier de notre étude qu’en dimension supérieure à 2, une telle structure ne possède jamais deux faces parallèles et ne contient jamais de circuit fermé de simplexes. Dans la seconde partie de notre thèse, nous abordons un problème classique de combinatoire : l’énumération des pavages d’un rectangle mxn à l’aide de dominos. Klarner et Pollack ont montré qu’en fixant m la suite obtenue vérifie une relation de récurrence linéaire à coefficients constants. Nous établissons une nouvelle méthode nous permettant d’obtenir la fonction génératrice correspondante et la calculons pour m <= 16, alors qu’elle n’était connue que pour m <= 10.

Tessellations have a rich mathematical structure and are especially appropriate as a context for teaching geometry in the middle grades. Few studies have researched how children conceptualize and learn tessellations in spite of their international use in educational contexts. This exploratory study looks at how fourth grade students conceptualize tessellations before instruction. The analysis is done from a Piagetian, cognitive viewpoint and from an aesthetic viewpoint. It is argued that the aesthetic viewpoint is crucial and foundational to children's mathematical understanding, just as it is for mathematicians. A series of clinical interviews was conducted with six fourth grade children. The results identified common themes of children's understanding, strategies, reasoning, and aesthetic criteria for tessellations. Children's ontology varied between object and process conceptions of tessellations. Children struggled especially with the infinite space of mathematical tessellations. Children's aesthetics, including symmetry, influenced their choices in creating tessellations and are shown to have played a cognitive role in children's mathematical exploration of tessellation structures. Mathematics influences students' aesthetic appreciation of tessellations and, more importantly, aesthetics drives the study of the mathematical structure of tessellations. Children's aesthetic criteria were the same as mathematicians', but with much different emphases. Other results are discussed, including the mathematical content elicited by the tasks, the influence of the tools used to create tessellations, the children's epistemology of their tessellations, and the role symmetry played in giving children confidence. Recommendations for future research and possible implications for curriculum and instruction are noted. / text

Erdos proved the well-known result that every graph has a spanning, bipartite subgraph such that every vertex has degree at least half of its original degree. Bollobas and Scott conjectured that one can get a slightly weaker result if we require the subgraph to be not only spanning and bipartite, but also balanced. We prove this conjecture for graphs of maximum degree 3. The majority of the paper however, will focus on graph tiling. Graph tiling (or sometimes referred to as graph packing) is where, given a graph H, we find a spanning subgraph of some larger graph G that consists entirely of disjoint copies of H. With the Regularity Lemma and the Blow-up Lemma as our main tools, we prove an asymptotic minimum degree condition for an arbitrary bipartite graph G to be tiled by another arbitrary bipartite graph H. This proves a conjecture of Zhao and also implies an asymptotic version of a result of Kuhn and Osthus for bipartite graphs.

Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 140-144).

Orientador: Eduardo Garibaldi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T00:20:51Z (GMT). No. of bitstreams: 1 Colle_CleberFernando_M.pdf: 1068657 bytes, checksum: 78c9700800b05194ffcf66838581b081 (MD5) Previous issue date: 2011 / Resumo: Focaremos sobre aspectos dinâmicos e ergódicos de shifts multidimensionais, atentando especialmente para suas relações com estados fundamentais e quase-cristais em reticulados. Por exemplo, em mecânica estatística, dado um potencial invariante por translação, seus estados fundamentais são medidas de probabilidade invariantes por translação suportadas no conjunto de suas configurações fundamentais, isto é, das configurações com energia específica mínima. Estados fundamentais são naturalmente associados com o bordo de certos polítopos convexos dimensionalmente finitos. Esse bordo se torna drasticamente diferente se a dimensão do modelo em questão passa de d = 1 para d > 1, pois no caso multidimensional existe shift de tipo finito unicamente ergódico sem configurações periódicas / Abstract: We will focus on dynamic and ergodic aspects of multidimensional shifts, with particular care to their relations with ground states and quasicrystals in lattices. For example, in statistical mechanics, given a translation-invariant potential, its ground states are translation-invariant probability measures supported on the set of its ground configurations, i.e., of configurations with minimal specific energy. Ground states are naturally associated with the boundary of certain finite-dimensional convex polytopes. This boundary becomes drastically different if the dimension of the model in question changes from d = 1 to d > 1, because in the multidimensional case there exists uniquely ergodic shift of finite type with no periodic configurations / Mestrado / Matematica / Mestre em Matemática