Many areas of computer science use graph theory and thus benefit from research in graph theory. Some of the important activities involved in graph theory work are the study of concepts, algorithm development, and theorem proving. These can be facilitated by providing computerized tools for graph drawing, algorithm animation and accessing graph theory information bases. Project G-Net is aimed at developing a set of such tools.Project G-Net has chosen to provide the tools in hypertext form based on the analysis of users' requirements. The project is presently developing a hypertext application and a hypertext system for providing the above set of tools. In the process of this development various issues pertaining to hypertext authoring, hypertext usability and application of graph theory to hypertext are being explored.The focus of this thesis is in proving that hypertext approach is most appropriate for realizing the goals of the G-Net project. The author was involved in the research that went into analysis of requirements, design of hypertext application and system, and the investigation of the complementary relationship between graph theory and hypertext. / Department of Computer Science

The closed neighbourhood of a vertex in a graph is the vertex together with the set of adjacent vertices. A di®erentiating-dominating set, or identifying code, is a collection of vertices whose intersection with the closed neighbour- hoods of each vertex is distinct and nonempty. A di®erentiating-dominating set in a graph serves to uniquely identify all the vertices in the graph. Chapter 1 begins with the necessary de¯nitions and background results and provides motivation for the following chapters. Chapter 1 includes a summary of the lower identi¯cation parameters, °L and °d. Chapter 2 de- ¯nes co-distinguishable graphs and determines bounds on the number of edges in graphs which are distinguishable and co-distinguishable while Chap- ter 3 describes the maximum number of vertices needed in order to identify vertices in a graph, and includes some Nordhaus-Gaddum type results for the sum and product of the di®erentiating-domination number of a graph and its complement. Chapter 4 explores criticality, in which any minor modi¯cation in the edge or vertex set of a graph causes the di®erentiating-domination number to change. Chapter 5 extends the identi¯cation parameters to allow for orientations of the graphs in question and considers the question of when adding orientation helps reduce the value of the identi¯cation parameter. We conclude with a survey of complexity results in Chapter 6 and a collection of interesting new research directions in Chapter 7. / Mathematical Sciences / PhD (Mathematics)

Objects can be said to be structured when their representation also contains their parts. While OWL in general can describe structured objects, description graphs are a recent, decidable extension to OWL which support the description of classes of structured objects whose parts are related in complex ways. Classes of chemical entities such as molecules, ions and groups (parts of molecules) are often characterised by the way in which the constituent atoms of their instances are connected via chemical bonds. For chemoinformatics tools and applications, this internal structure is represented using chemical graphs. We here present a chemical knowledge base based on the standard chemical graph model using description graphs, OWL and rules. We include in our ontology chemical classes, groups, and molecules, together with their structures encoded as description graphs. We show how role-safe rules can be used to determine parthood between groups and molecules based on the graph structures and to determine basic chemical properties. Finally, we investigate the scalability of the technology used through the development of an automatic utility to convert standard chemical graphs into description graphs, and converting a large number of diverse graphs obtained from a publicly available chemical database. / Computer Science (School of Computing) / M. Sc. (Computer Science)

The lower and upper independent, domination and irredundant numbers of the graph G = (V, E) are denoted by i ( G) , f3 ( G), 'Y ( G), r ( G), ir ( G) and IR ( G) respectively. These six numbers are called the domination parameters. For each of these parameters n:, we define six types of criticality. The graph G is n:-critical (n:+ -critical) if the removal of any vertex of G causes n: (G) to decrease (increase), G is n:-edge-critical (n:+-edge-critical) if the addition of any missing edge causes n: (G) to decrease (increase), and G is Ir-ER-critical (n:- -ER-critical) if the removal of any edge causes n: (G) to increase (decrease). For all the above-mentioned parameters n: there exist graphs which are n:-critical, n:-edge-critical and n:-ER-critical. However, there do not exist any n:+-critical graphs for n: E {ir,"f,i,/3,IR}, no n:+-edge-critical graphs for n: E {ir,"f,i,/3} and non:--ER-critical graphs for: E {'Y,/3,r,IR}. Graphs which are "I-critical, i-critical, "I-edge-critical and i-edge-critical are well studied in the literature. In this thesis we explore the remaining types of criticality. We commence with the determination of the domination parameters of some wellknown classes of graphs. Each class of graphs we consider will turn out to contain a subclass consisting of graphs that are critical according to one or more of the definitions above. We present characterisations of "I-critical, i-critical, "I-edge-critical and i-edge-critical graphs, as well as ofn:-ER-critical graphs for n: E {/3,r,IR}. These characterisations are useful in deciding which graphs in a specific class are critical. Our main results concern n:-critical and n:-edge-critical graphs for n: E {/3, r, IR}. We show that the only /3-critical graphs are the edgeless graphs and that a graph is IRcritical if and only if it is r-critical, and proceed to investigate the r-critical graphs which are not /3-critical. We characterise /3-edge-critical and r-edge-critical graphs and show that the classes of IR-edge-critical and r-edge-critical graphs coincide. We also exhibit classes of r+ -critical, r+ -edge-critical and i- -ER-critical graphs. / Mathematical Sciences / D. Phil. (Mathematics)

CAPES; CNPQ / Dada a importância mundial da cultivar soja, é imprescindível a aplicação de metodologias para o monitoramento eficiente dos parâmetros fisíco-químicos que determinam a qualidade dos grãos com agilidade e confiabilidade adequadas. Entretanto, os métodos analíticos empregados para as análises tradicionais envolvem técnicas demoradas, utilizam vários equipamentos e reagentes, além de gerarem resíduos químicos. Desta forma, o desenvolvimento de metodologias alternativas para esta finalidade pode trazer benefícios tanto para as indústrias e órgãos reguladores quanto para os analistas. Este estudo propõe a utilização de Espectroscopia de Infravermelho Próximo (NIR) associada a métodos quimiométricos para a construção de modelos multivariados para previsão do percentual de lipídios totais, índice de acidez, teor de clorofila, proteína bruta e umidade em soja. Na construção dos modelos foram avaliadas 300 amostras de soja Glycine max (L.) Merrill. Os dados espectrais foram processados por meio do método de Mínimos Quadrados Parciais (PLS). Os resultados sugerem que os modelos desenvolvidos podem ser utilizados como uma metodologia alternativa para determinar parâmetros físico-químicos e poderiam ser aplicados no controle de qualidade em indústrias de soja. / Given the worldwide importance of soybean cultivars, it is essential to apply methodologies for the efficient monitoring of the physico-chemical parameters that determine the grain quality with adequate agility and reliability. Nonetheless, the analytical methods used in the traditional analysis involves time-consuming techniques, usage of various equipment and reagents besides generating chemical residues. Considering that, the development of alternative methodologies for this purpose can bring benefits to both industries and regulatory bodies as for the analysts. This study proposes the use of Near Infrared Spectroscopy (NIR) associated with chemometric methods for the construction of multivariate models to predict the percentage of total lipids, acidity index, chlorophyll content, crude protein and moisture in soybean. For this, 300 samples of Glycine max (L.) Merrill soybean were evaluated. The spectral data were processed by the method of Partial Least Squares (PLS). The results suggest that the developed model can be used as an alternative methodology to determine the physical-chemical parameters and could be applied in quality control in the soybean industries.

CAPES; CNPQ / Dada a importância mundial da cultivar soja, é imprescindível a aplicação de metodologias para o monitoramento eficiente dos parâmetros fisíco-químicos que determinam a qualidade dos grãos com agilidade e confiabilidade adequadas. Entretanto, os métodos analíticos empregados para as análises tradicionais envolvem técnicas demoradas, utilizam vários equipamentos e reagentes, além de gerarem resíduos químicos. Desta forma, o desenvolvimento de metodologias alternativas para esta finalidade pode trazer benefícios tanto para as indústrias e órgãos reguladores quanto para os analistas. Este estudo propõe a utilização de Espectroscopia de Infravermelho Próximo (NIR) associada a métodos quimiométricos para a construção de modelos multivariados para previsão do percentual de lipídios totais, índice de acidez, teor de clorofila, proteína bruta e umidade em soja. Na construção dos modelos foram avaliadas 300 amostras de soja Glycine max (L.) Merrill. Os dados espectrais foram processados por meio do método de Mínimos Quadrados Parciais (PLS). Os resultados sugerem que os modelos desenvolvidos podem ser utilizados como uma metodologia alternativa para determinar parâmetros físico-químicos e poderiam ser aplicados no controle de qualidade em indústrias de soja. / Given the worldwide importance of soybean cultivars, it is essential to apply methodologies for the efficient monitoring of the physico-chemical parameters that determine the grain quality with adequate agility and reliability. Nonetheless, the analytical methods used in the traditional analysis involves time-consuming techniques, usage of various equipment and reagents besides generating chemical residues. Considering that, the development of alternative methodologies for this purpose can bring benefits to both industries and regulatory bodies as for the analysts. This study proposes the use of Near Infrared Spectroscopy (NIR) associated with chemometric methods for the construction of multivariate models to predict the percentage of total lipids, acidity index, chlorophyll content, crude protein and moisture in soybean. For this, 300 samples of Glycine max (L.) Merrill soybean were evaluated. The spectral data were processed by the method of Partial Least Squares (PLS). The results suggest that the developed model can be used as an alternative methodology to determine the physical-chemical parameters and could be applied in quality control in the soybean industries.

The problems with which this study was concerned were threefold: (a) to design a computer-based graphics presentation on the topics of functions and graphing, (b) to develop the presentation, and (c) to determine the instructional effectiveness of this computer-based graphics instruction. The computerized presentation was written in Authorware for the Macintosh computer. The population of this study consisted of three intermediate algebra classes at Collin County Community College (n = 51). A standardized examination, the Descriptive Tests of Mathematics Skills for Functions and Graphs, was used for pretest and posttest purposes. Means were calculated on these scores and compared using a t-test for correlated means. The level of significance was set at .01. The results of the data analysis indicated: 1. There was a significant difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 2. There was no significant gender difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 3. There was no significant difference between the pretest and posttest performance of the traditional and nontraditional age students after exposure to the computer-based graphics presentation. Females had a lower posttest score than the mean male posttest score, but an analysis of the differences showed no significance. Traditional age students had a higher posttest performance score than the mean traditional age student posttest score, but their pretest performance scores were higher as well. An analysis of the differences showed no significance. In summary, this computer-based graphics presentation was an effective teaching technique for increasing mathematics performance.

Thesis: Ph. D., Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science; and the Woods Hole Oceanographic Institution), 2017. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 335-357). / This thesis presents a sum-product inference algorithm for in-situ, nonparametric platform navigation called Multi-modal iSAM (incremental smoothing and mapping), for problems of thousands of variables. Our method tracks dominant modes in the marginal posteriors of all variables with minimal approximation error, while suppressing almost all low likelihood modes (in a non-permanent manner) to save computation. The joint probability is described by a non-Gaussian factor graph model. Existing inference algorithms in simultaneous localization and mapping assume Gaussian measurement uncertainty, resulting in complex front-end processes that attempt to deal with non-Gaussian measurements. Existing robustness approaches work to remove "outlier" measurements, resulting heuristics and the loss of valuable information. Track different hypotheses in the system has prohibitive computational cost and and low likelihood hypotheses are permanently pruned. Our approach relaxes the Gaussian only restriction allowing the frontend to defer ambiguities (such as data association) until inference. Probabilistic consensus ensures dominant modes across all measurement information. Our approach propagates continuous beliefs on the Bayes (Junction) tree, which is an efficient symbolic refactorization of the nonparametric factor graph, and approximates the underlying Chapman-Kolmogorov equations. Like the predecessor iSAM2 max-product algorithm [Kaess et al., IJRR 2012], we retain the Bayes tree incremental update property, which allows for tractable recycling of previous computations. Several non-Gaussian measurement likelihood models are introduced, such as ambiguous data association or highly non-Gaussian measurement modalities. In addition, keeping with existing inertial navigation for dynamic platforms, we present a novel continuous-time inertial odometry residual function. Inertial odometry uses preintegration to seamlessly incorporate pure inertial sensor measurements into a factor graph, while supporting retroactive (dynamic) calibration of sensor biases. By centralizing our approach around a factor graph, with the aid of modern starved graph database techniques, concerns from different elements of the navigation ecosystem can be separated. We illustrate with practical examples how various sensing modalities can be combined into a common factor graph framework, such as: ambiguous loop closures; raw beam-formed acoustic measurements; inertial odometry; or conventional Gaussian-only likelihoods (parametric) to infer multi-modal marginal posterior belief estimates of system variables. / by Dehann Fourie. / Ph. D.

One major challenge facing mathematics education in South Africa in general and Limpopo in particular, is learners’ underachievement and lack of motivation to learn the subject. Some studies have shown that one of the topics that learners dread is linear functions. Many teachers also find it difficult to teach the topic effectively. Studies in other parts of the world have advocated the integration of graphing software with the teaching and learning of functions to enhance learners’ learning of mathematics. This study therefore investigated the effect of integrating GeoGebra graphing software into the teaching of linear functions on the achievement of Grade 9 learners. The study was guided by APOS theory which, in accordance with constructivist theories, posits that an individual needs to construct the necessary cognitive structures in order to make sense of mathematical concepts. A total of 127 Grade 9 learners from four schools in a circuit in Mopani district of Limpopo Province participated in the study which followed a pretestpost- test quasi-experimental study design. Two schools, namely B (35 learners) and D (33 learners) formed the experimental groups while school A (31 learners) and school C (28 learners) were the control groups. Data were collected using an achievement test and analyzed using descriptive and inferential statistics. The pretest results showed that the groups were of comparable cognitive abilities. The post-test results showed that there was a significant difference between the mean scores of the experimental groups and control groups. There were also statistically significant differences between group treatment means (p < .05). Bonferroni post-hoc test results showed that there were no statistically significant differences between treatments A and C. The results showed that the learners in the two control groups were of comparable cognitive abilities. The implications of the findings are discussed and recommendations made. / Mathematics Education / M. Sc. (Mathematics Education)

The crucial role of representation in mathematical and statistical modeling and problem solving as evident in learners' arrangement and representation of statistical data were investigated with focus points data arrangement, data representation and statistical thinking levels. The representation tasks required learners to arrange and represent data through modeling, focusing on spontaneous representations. Successful transnumeration determine the ultimate success of a representation and the ability to organise data is regarded as critical. Arrangement types increased in sophistication with increased grade level and the hierarchical nature of arrangement types became apparent when regarded in the context of an adapted SOLO Taxonomy framework. A higher level arrangement strategy pointed to a higher SOLO level of statistical thinking. Learners in the two tasks produced a rich variety of representations which included idiosyncratic, unsophisticated responses as well as standard statistical representations. The context of the two tasks, the quantitative versus qualitative nature of the data in the tasks, and the statistical tools or representational skills learners have at their disposal, played an important role in their representations. Well-planned data handling activities develop representational and higher order thinking skills. The variety of responses and different response levels elicited in the two tasks indicate that the nature of the tasks rather than the size of the data set play a conclusive role in data tasks. Multiple representations by an individual were an indication of successful modeling, are effective in problem solving and are associated with good performance. The SOLO model which incorporates a structural approach as well as a multimodal component proved valuable in the analysis of responses. Using this model with accompanying acknowledgement of different problem solving paths and the contribution of ikonic support in the concrete symbolic mode, promote the in-depth analysis of responses. This study contributes to the research in the field of data representation and statistical thinking. The analysis and results led to an integrated picture of Grade 4-7 learners' representation of statistical data and of the statistical thinking levels evident in their representations. / Educational Studies / D. Ed. (Didactics)