In this work Voronoi diagrams which are drawn by the cellular automaton are discussed. The square and hexagon cellular automata were created and used for drawing Voronoi diagrams. As a result of using the created programs Voronoi diagrams, which are obtained in case of two and more dots, are observed. The following results of the research were achieved: § Voronoi diagram can be obtained by the cellular automaton. § Voronoi diagrams, which were obtained, are not precise due to different speed of movement in different directions. § In square - cell case the obtained diagrams depend on the chosen situation of the neighbors. § In hexagon - cell case the obtained Voronoi diagrams are more but not completely precise. The mathematic calculations are not being made while creating Voronoi diagrams by the cellular automaton.. The diagrams are obtained in short period of time. It is possible to watch the process of the diagram creation. A lot of computer's operation time is lost not during the calculation but for re-drawing the obtained image. This is the reason why it is necessary to optimize the image creating algorithm.

This thesis consists of two parts. Part one revolves around a construction for homogeneous Gorenstein ideals and properties of these ideals. Part two focuses on the behavior of the Boij-Söderberg decomposition of lex ideals. Gorenstein ideals are known for their nice duality properties. For codimension two and three, the structures of Gorenstein ideals have been established by Hilbert-Burch and Buchsbaum-Eisenbud, respectively. However, although some important results have been found about Gorenstein ideals of higher codimension, there is no structure theorem proven for higher codimension cases. Kustin and Miller showed how to construct a Gorenstein ideals in local Gorenstein rings starting from smaller such ideals. A modification of their construction in the case of graded rings is discussed. In a Noetherian ring, for a given two homogeneous Gorenstein ideals, we construct another homogeneous Gorenstein ideal and so we describe the resulting ideal in terms of the initial homogeneous Gorenstein ideals. Gorenstein liaison theory plays a central role in this construction. Using liaison properties, we examine structural relations between the constructed homogeneous ideal and the starting ideals. Boij-Söderberg theory is a very recent theory. It arose from two conjectures given by Boij and Söderberg and their proof by Eisenbud and Schreyer. It establishes a unique decomposition for Betti diagram of graded modules over polynomial rings. In the second part of this thesis, we focus on Betti diagrams of lex ideals which are the ideals having the largest Betti numbers among the ideals with the same Hilbert function. We describe Boij-Söderberg decomposition of a lex ideal in terms of Boij-Söderberg decompositions of some related lex ideals.

Software reconnaissance is a very useful technique for locating features in software systems that are unfamiliar to a developer. The technique was, however, limited by the need to execute multiple test cases and record the components used in each one. Tools that recorded the execution traces of a program made it more practical to use the software reconnaissance technique. Diver was developed as an execution trace visualization tool using sequence diagrams to display the dynamic behaviour of a program. The addition of software reconnaissance to Diver and its trace-focused user interface feature improved the filtering of the Eclipse environment based on the contents of execution traces and led to a very powerful program comprehension tool. Myers' work on Diver was grounded in cognitive support theory research into how to build tools. He conducted a user study to validate the work done on Diver, but the study's findings were limited due to a number of issues. In this thesis, we expand on the study run by Myers, improve on its design, and investigate if software reconnaissance improves Diver's effectiveness and efficiency for program comprehension tasks. We also analyze the influence of software reconnaissance on the interactions of Diver's users, which allows us to identify successful usage patterns for completing program comprehension and feature location tasks. We research the connection between cognitive support theory and the design of Diver and use the study to attempt to validate the cognitive support offered by Diver. Finally, we present the results of a survey of the study participants to determine the usefulness, ease of use, and ease of learning of the tool. / Graduate / 0984

The goal of this thesis is to first give an overview of the modern approach, using the paper of A. Vershik and A. Okounkov, to inductively parametrizing all irreducible representations of the symmetric groups. This theory is then used to answer questions concerning to central projections in the group algebra. We index units first by partitions, and then by so called standard tableaux. We also present a new result and discuss future research exploring the connections between this theory and Quantum Information.

In this thesis, we will present examples of Voronoi diagrams that are not tessellations. Moreover, we will find sufficient conditions on subspaces of E2, S2 and the Poincaré disk and the sets of sites that guarantee that the Voronoi diagrams are pre-triangulations. We will also study g-spaces, which are metric spaces with ‘extendable’ geodesics joining any 2 points and give properties for a set of sites in a g-space that again guarantees that the Voronoi diagram is a pre-triangulation.

Successful learning about physical systems is thought to depend on the development of a mental representation of the system's dynamic behavior, which constitutes a mental model, rather than only its static structure (e.g., Schnotz, 2005). Because dynamic mental models must be generated by learners from static diagrams, learning might be promoted by encouraging learners to visualize motion in static diagrams. However, mental models represent dynamic spatial information that might be difficult to construct for learners with lower spatial ability; they might benefit from instructional designs that support spatial reasoning, such as phase diagrams and depictive arrows. In Experiment 1, participants learned about air pumps, carburetors, and toilet tanks from single phase diagrams, multiphase diagrams, or multiphase diagrams followed by a prediction activity in which they predicted system behavior in novel situations. This prediction activity was expected to implicitly prompt mental visualization of motion. Learning in the latter condition (i.e., with the prediction activity) was significantly better than learning in the single phase condition. In the prediction condition, the enhancing effect of spatial ability on learning outcome was partially mediated by performance in the prediction activity. The mediation suggested that high spatial ability helped participants to accurately visualize the systems as they made predictions, which contributed to better performance on the learning assessment. Experiment 1 assessed visualizations during the prediction activity, whereas Experiment 2 assessed visualizations during the lessons. In two conditions in Experiment 2, participants were explicitly prompted to visualize motion in the system while viewing the lessons. Because learners with lower spatial ability were expected to have difficulty visualizing motion, arrows depicting motion were added in one condition. A baseline condition excluded the arrows and the prompt to visualize motion. In all three conditions, participants viewed multiphase diagrams followed by the prediction activity. Learning outcomes among the three conditions did not differ significantly: Depictive arrows and prompts to visualize motion were not significantly effective. Also, spatial ability did not interact with instructional condition. However, both spatial ability and subjective ratings of attempts to visualize motion were predictive of learning outcome. Overall, results from the two experiments indicated that participants with higher spatial ability were better able than participants with lower spatial ability to generate dynamic mental models from static instructions, particularly when they were implicitly prompted to reason about the system as they made predictions. Learners with lower spatial ability might need other forms of assistance for mental model generation, such as animated instructions.

Thesis (M. S.)--Psychology, Georgia Institute of Technology, 2009. / Committee Chair: Rogers, Wendy; Committee Member: Fisk, Arthur; Committee Member: Walker, Bruce

Thesis (M.S. in Engineering Science)--Naval Postgraduate School, December 1990. / Thesis Advisor: Lum, Vincent Y. Second Reader: Wu, Thamas C. "December 1990." Description based on title screen as viewed on March 30, 2010. DTIC Identifier(s): Data base management systems, data management, multimedia data bases, data bases, data processing, tables(data), computer files, MDBMS (multimedia data base management system), Ingres data bases, abstract data types, catalog management, integrated systems, theses. Author(s) subject terms: Multimedia Database Management System, Multimedia, DBMS, MDBMS, media database. Includes bibliographical references (p. 186-187). Also available in print.

Thesis (M.Sc.(Metallurgical Engineering))--University of Pretoria, 2003. / Includes bibliographical references (leaves 127-128).

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 65-70).