<p> This thesis is both classically and abstractly oriented in a geometrical sense. The discussion is centred around the motion distance.</p> <p> In the first chapter, the concept of a regular set is defined and discussed. The idea of a regular set is a natural generalization of equilateral triangles and regular tetrahedra in Euclidean spaces.</p> <p> In chapter two, two kinds of scalar multiplication associated with metric spaces are studied.</p> <p> In chapter three, the concept of distance is abstracted to a level where it loses most of its structure. This abstraction is then examined.</p> <p> In chapter four, generalized metric spaces are examined. These are specializations of the abstract spaces of chapter three.</p> / Thesis / Doctor of Philosophy (PhD)

Submitted by PPG Ci?ncia da Computa??o (ppgcc@pucrs.br) on 2018-08-22T17:39:55Z No. of bitstreams: 1 ADRIANO_JOS?_VOGEL_DIS.pdf: 2344216 bytes, checksum: e0dd6229d4a98c039e793851290beab0 (MD5) / Approved for entry into archive by Sheila Dias (sheila.dias@pucrs.br) on 2018-08-24T14:50:33Z (GMT) No. of bitstreams: 1 ADRIANO_JOS?_VOGEL_DIS.pdf: 2344216 bytes, checksum: e0dd6229d4a98c039e793851290beab0 (MD5) / Made available in DSpace on 2018-08-24T17:31:58Z (GMT). No. of bitstreams: 1 ADRIANO_JOS?_VOGEL_DIS.pdf: 2344216 bytes, checksum: e0dd6229d4a98c039e793851290beab0 (MD5) Previous issue date: 2018-03-28 / As aplica??es de stream se tornaram cargas de trabalho representativas nos sistemas computacionais. Diversos dom?nios de aplica??es representam stream, como v?deo, ?udio, processamento de gr?ficos e imagens. Uma parcela significativa dessas aplica??es demanda paralelismo para aumentar o desempenho. Por?m, programadores frequentemente enfrentam desafios entre produtividade de c?digo e desempenho devido ?s complexidades decorrentes do paralelismo. Buscando facilitar a paraleliza??o, a DSL SPar foi criada usando atributos (stage, input, output, and replicate) do C++-11 para representar paralelismo. O compilador reconhece os atributos da SPar e gera c?digo paralelo automaticamente. Um desafio relevante que ocorre em est?gios paralelos da SPar ? a demanda pela defini??o manual do grau de paralelismo, o que consome tempo e pode induzir a erros. O grau de paralelismo ? definido atrav?s do n?mero de r?plicas em est?gios paralelos. Por?m, a execu??o de diversas aplica??es pode ser pouco eficiente se executadas com um n?mero de r?plicas inadequado ou usando um n?mero est?tico que ignora a natureza din?mica de algumas aplica??es. Para resolver esse problema, ? introduzido o conceito de um n?mero de r?plicas transparente e adaptativo para a SPar. Al?m disso, os mecanismos implementados e as regras de transforma??o s?o descritos para possibilitar a gera??o de c?digo paralelo na SPar com um n?mero adaptativo de r?plicas. Os mecanismos adaptativos foram avaliados demonstrando a sua efic?cia. Ainda, aplica??es reais foram usadas para demonstrar que os mecanismos adaptativos propostos podem oferecer abstra??es de alto n?vel sem significativas perdas de desempenho. / In recent years, stream processing applications have become a traditional workload in computing systems. They are traditionally found in video, audio, graphic and image processing. Many of these applications demand parallelism to increase performance. However, programmers must often face the trade-off between coding productivity and performance that introducing parallelism creates. SPar Domain-Specific Language (DSL) was created to achieve the optimal balance for programmers, with the C++-11 attribute annotation mechanism to ensure that essential properties of stream parallelism could be represented (stage, input, output, and replicate). The compiler recognizes the SPar attributes and generates parallel code automatically. The need to manually define parallelism is one crucial challenge for increasing SPAR?s abstraction level, because it is time consuming and error prone. Also, executing several applications can fail to be efficient when running a non suitable number of replicas. This occurs when the defined number of replicas in a parallel region is not optimal or when a static number is used, which ignores the dynamic nature of stream processing applications. In order to solve this problem, we introduced the concept of the abstracted and adaptive number of replicas for SPar. Moreover, we described our implemented strategy as well as transformation rules that enable SPar to generate parallel code with the adaptive degree of parallelism support. We experimentally evaluated the implemented adaptive strategies regarding their effectiveness. Thus, we used real-world applications to demonstrate that our adaptive strategy implementations can provide higher abstraction levels without significant performance degradation.

Formal systems in architectural design aim at the systematic description, interpretation, and evaluation of existing works of architecture as well the systematic creation of new works of architecture. Currently all formal analysis using group theoretical tools focus on repetitive designs that show immediately their recursive structure. It is suggested here that highly complex designs can still be described and analyzed with group theoretical manner. The broader question that is opened up here is whether a complex architecture object or part depending on the interest of the researcher, can be interpreted as a layered object whose parts are all related symmetrically; in other words whether an asymmetric shape or configuration can be understood in terms of nested arrangements of some order of symmetry. The object of analysis has been polemically selected here to be the NY5 architecture, a set of designs that are all clearly exemplifying formal qualities of abstraction, layering, complexity, depth and so on, all appearing impenetrable to a systematic and rigorous analysis using the existing group theoretical formal methods. For example, Richard Meier s work has been presented here as a hyper-refinement of the modernist imagery. The computation is entirely visual. A reassembly of the layered symmetries explains the structure of the symmetry of the house and provides an illustration of the basic thesis of this research on the foundation of a theory of emergence based on symmetry considerations. All plans of the house are represented in three different levels of abstraction moving successively away from the architectural representation to a purely diagrammatic one that foregrounds divisions of space. All representations are fed into an analysis algorithm to pick up all symmetry relationships and the parts are constructed as instances of a binary composition of a family of rectangular grids. Finally the process is reversed to fully account for the construction of the space of the house as a three dimensional layered composition. Lastly, this research points to two categories of extension; a) on the improvement of the system itself; and b) on the interpretative capabilities it affords for the construction and evaluation of critical languages of design.