Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND HUMANITIES. / Bibliography: leaves 205-206. / by Fredric M. Katz. / Ph.D.

Predição de Links é uma área de pesquisa importante no contexto de Análise de Redes Sociais tendo em vista que predizer sua evolução é um mecanismo útil para melhorar e propiciar a comunicação entre usuários. Nas redes de coautoria isso pode ser utilizado para recomendação de usuários com interesses de pesquisa comuns. Este trabalho propõe um processo sistemático baseado em métricas não-dicotômicas para avaliação de predição de links em redes de coautoria, sendo considerada a definição de métodos para as seguintes tarefas identificadas: seleção de dados, determinação de novos links e avaliação dos resultados. Para seleção de dados definiu-se um sensor fuzzy baseado em atributos dos nós. O uso de composições fuzzy foi considerado para determinação de novos links _ponderados_ entre dois autores, adotando-se não apenas atributos dos nós, mas também a combinação de atributos de outros links observados. O link ponderado é denominado _qualidade da relação_ e é obtido pelo uso de propriedades estruturais da rede. Para avaliação dos resultados foi proposta a curva ROC fuzzy, que permite explorar os pesos dos links não apenas para ordenação dos exemplos. / Link prediction is an important research line in the Social Network Analysis context, as predicting the evolution of such nets is a useful mechanism to improve and encourage communication among users. In co-authorship networks, it can be used for recommending users with common research interests. This work proposes a systematic process based on non-dichotomic metrics for evaluation of link prediction in co-authorship networks considering the definition of methods for the following tasks: data selection, new link determination and result evaluation. Fuzzy sensor based on node attributes is adopted for data selection. Fuzzy compositions are used to predict new link weights between two authors, adopting not only attributes nodes, but also the combination of attributes of other observed links. The link weight called _relation quality_ is obtained by using structural features of the social network. The fuzzy roc curve is used for results evaluation, allowing us to consider the weights of the links and not only the ordering of examples.

Predição de Links é uma área de pesquisa importante no contexto de Análise de Redes Sociais tendo em vista que predizer sua evolução é um mecanismo útil para melhorar e propiciar a comunicação entre usuários. Nas redes de coautoria isso pode ser utilizado para recomendação de usuários com interesses de pesquisa comuns. Este trabalho propõe um processo sistemático baseado em métricas não-dicotômicas para avaliação de predição de links em redes de coautoria, sendo considerada a definição de métodos para as seguintes tarefas identificadas: seleção de dados, determinação de novos links e avaliação dos resultados. Para seleção de dados definiu-se um sensor fuzzy baseado em atributos dos nós. O uso de composições fuzzy foi considerado para determinação de novos links _ponderados_ entre dois autores, adotando-se não apenas atributos dos nós, mas também a combinação de atributos de outros links observados. O link ponderado é denominado _qualidade da relação_ e é obtido pelo uso de propriedades estruturais da rede. Para avaliação dos resultados foi proposta a curva ROC fuzzy, que permite explorar os pesos dos links não apenas para ordenação dos exemplos. / Link prediction is an important research line in the Social Network Analysis context, as predicting the evolution of such nets is a useful mechanism to improve and encourage communication among users. In co-authorship networks, it can be used for recommending users with common research interests. This work proposes a systematic process based on non-dichotomic metrics for evaluation of link prediction in co-authorship networks considering the definition of methods for the following tasks: data selection, new link determination and result evaluation. Fuzzy sensor based on node attributes is adopted for data selection. Fuzzy compositions are used to predict new link weights between two authors, adopting not only attributes nodes, but also the combination of attributes of other observed links. The link weight called _relation quality_ is obtained by using structural features of the social network. The fuzzy roc curve is used for results evaluation, allowing us to consider the weights of the links and not only the ordering of examples.

Minimal Walks are a method of demonstrations in set theory and general topology. Although the main work of this document will be the construction of the L space, we intend to explain walk\'s fundamentals in a bit more detail. / Passeios mínimos são um método de demonstrações em teoria dos conjuntos e topologia geral. Apesar do trabalho principal dessa dissertação ser a existência do L espaço, a intenção é explicar os fundamentos dos passeios mínimos um tanto detalhadamente.

This thesis explores functionally Alexandroff topologies and the order theory asso- ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set. The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of functionally Alexandroff topologies ad presents a characterization for the functionally Alexandroff topologies on a finite set X. The third and fourth chapters present facts about the lattice of functionally Alexandroff topologies, with Chapter 4 being dedicated to an algorithm which generates a complement in this lattice.

The Hirsch Conjecture states that for a d-dimensional polytope with n facets, the diameter of the graph of the polytope is at most n-d. This conjecture was disproven in 2010 by Francisco Santos Leal. However, a polynomial bound in n and d on the diameter of a polytope may still exist. Finding a polynomial bound would provide a worst-case scenario runtime for the Simplex Method of Linear Programming. However working only with polytopes in higher dimensions can prove challenging, so other approaches are welcome. There are many equivalent formulations of the Hirsch Conjecture, one of which is the Combinatorial Polynomial Hirsch Conjecture, which turns the problem into a matter of counting sets. This thesis explores the Combinatorial Polynomial Hirsch Conjecture.

We begin by introducing matroids in the context of finite collections of vectors from a vector space over a specified field, where the notion of independence is linear independence. Then we will introduce the concept of a matroid invariant. Specifically, we will look at the Tutte polynomial, which is a well-defined two-variable invariant that can be used to determine differences and similarities between a collection of given matroids. The Tutte polynomial can tell us certain properties of a given matroid (such as the number of bases, independent sets, etc.) without the need to manually solve for them. Although the Tutte polynomial gives us significant information about a matroid, it does not uniquely determine a matroid. This thesis will focus on non-isomorphic matroids that have the same Tutte polynomial. We call such matroids Tutte-equivalent, and we will study the characteristics needed for two matroids to be Tutte-equivalent. Finally, we will demonstrate methods to construct families of Tutte-equivalent matroids.

The scheduling and Control Group at the University of South Australia has been studying the optimal control of trains for many years, and has developed in-cab devices that help drivers stay on time and minimise energy use. In this thesis, we re-examine the optimal control theory for the train control problem. In particular, we study the optimal control around steep sections of track. To calculate an optimal driving strategy we need a realistic model of train performance. In particular, we need to know a coefficient of rolling resistance and a coefficient of aerodynamic drag. In practice, these coefficients are different for every train and difficult to predict. In the thesis, we study the use of mathematical filters to estimate model parameters from observations of actual train performance.

Anecdotal observation of the way in which data visualisation techniques are utilised to present relationships in data to audiences informed the author's view that data visualisation had not evolved to utilise the capabilities of ubiquitous business computer equipment. In an information rich but attention poor business environment, a search for a new tool was undertaken to supplement those techniques available to help audiences understand statistical relationships in presentation data. This search resulted in the development of a practical software tool based on animated Venn diagrams (Dvenn) that attempted to exploit the inherent human ability to perceive quantities visually, a faculty described herein as visual numeracy. The exploitation of this faculty is considered here to be a valuable aid for group understanding of business presentation data. The development of the tool was an essential part of the research that was undertaken and the resulting software forms a significant portion of this practise based research. The aim of the software development was to develop a readily accessible tool that could be utilised in a non-specialist business environment to better facilitate an honest shared meaning of numerical data between a presenter and their audience. The development of the tool progressed through a number of iterations and the software that accompanies this work is an important component that needs to be viewed in conjunction with the text. The test of the final version was undertaken with undergraduate University students in an attempt to validate the efficacy of the data visualisation technique. The test of the Dvenn software was made against the mature yardstick of scatter-plots. Interestingly, the correlations presented by scatter-plot were not as readily identified as would have been assumed, however, the results for the Dvenn tests were not supportive of the technique for widespread adoption. Nevertheless, further research into the best method of harnessing visual numeracy would seem to be justified.

The percentage of shop fabrication, including pipe spool fabrication, has been increasing on industrial construction projects during the past years. Industrial fabrication has a great impact on construction projects due to the fact that the productivity is higher in a controlled environment than in the field, and therefore time and cost of construction projects are reduced by making use of industrial fabrication. Effective planning and scheduling of the industrial fabrication processes is important for the success of construction projects. This thesis focuses on developing a new framework for optimizing shop scheduling, particularly pipe spool fabrication shop scheduling. The proposed framework makes it possible to capture uncertainty of the pipe spool fabrication shop while accounting for linguistic vagueness of the decision makers preferences using simulation modeling and fuzzy set theory. The implementation of the proposed framework is discussed using a real case study of a pipe spool fabrication shop. In this thesis, first, a simulation based scheduling framework is presented based on the integration of relational database management system, product modeling, process modeling, and heuristic approaches. Next, a framework for optimization of the industrial shop scheduling with respect to multiple criteria is proposed. Fuzzy set theory is used to linguistically assess different levels of satisfaction for the selected criteria. Additionally, an executable scheduling toolkit is introduced as a decision support system for pipe spool fabrication shop. / Construction Engineering and Management