Diplomarbeit - Technische Universität Berlin / Title from title screen (viewed on June 17, 2008). Abstract in German and English. Title from document title page. Includes bibliographical references. Available in PDF format via the World Wide Web.

Thesis (M. Sc.)--University of Canterbury, 2008. / Typescript (photocopy). "September 2008." Eighteen folded leaves of ill. in pocket. Includes bibliographical references (leaves 106-115).

Thesis (Ph. D.)--Oregon State University, 1995. / Typescript (photocopy). Includes bibliographical references (leaf 80). Also available on the World Wide Web.

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One technique for displaying a set of quantitative variables is to represent the set as a polygon. Such displays allow the observer to visualize complex information quickly, as a whole. Polygon displays have been employed to display information for analysis, status, or presentation. An experimental investigation was undertaken to ascertain the effect of variation in certain visual features of the display on the consistency with which people categorize information presented as polygons. Variables included background information of the display, shading, and form. Subjects performed a categorization task on two sets of data; the results are analyzed for consistency between individuals and for consistency with certain standard clustering algorithms. The effects of distinctive portions of the figures on the judgment of similarity, and of the nature of the data and of interactions of combinations of the variables used in the experiment on the consistency of clustering were noted. Implications for the design of polygon displays are discussed. / M.S.

published_or_final_version / Computer Science / Master / Master of Philosophy

Several explanations have been offered to account for information processing of visual forms and the influence of verbal labels associated with those forms. These accounts have differed in their emphasis on processes of encoding, storage, or retrieval as that primary locus of the effects of label-form association. While the three acounts are not incompatible, previous explanations have failed to provide an integrated explanation of the process of form memory. The present study was composed of two experiments that addressed psychological perception of form stimuli. In the first experiment, a novel mathematical method was used to describe and generate four families of random-polygon form stimuli of graded similarity. The model's Euclidean metric provided a close linear fit to the obtained judgments of similarity among polygons. The second experiment examined the associative influence of verbal labels on memory for the polygons used in the first experiment. Subjects learned to associate either the same label or two different labels with two form stimuli from the same family and one "control" polygon and one label from the third and fourth families. A paired comparison recognition test was used in which training stimuli were presented with unfamiliar stimuli from the same family either immediately, two days or four days after training. Subjects' recognition gradients on the control forms demonstrated a clear differentiation between the correct training form and incorrect variation forms. Recognition gradients were markedly different, however, for same- vs. different-labeled forms. Training with different labels produced a gradient with a mode centered over the correct target form. Training with same labels produced a recognition gradient with a mode shifted in the direction suggested by the same label. Results of the present study are most consistent with a model of form memory in which different processes may predominate as a function of stimulus complexity and degree of training. In some cases an associative encoding process is the result of label-form association. In others, including the present study, label-form association directs dynamic processing, resulting in novel assimilational representations of stimulus information.

Master of Science - Science / Axial line placement is one step in a method known as space syntax which is used in town planning to analyse architectural structures. This is becoming increasingly important in the quickly growing urban world of today. The field of axial line placement is an area of space syntax that has previously been done manually which is becoming increasingly impractical. Research is underway to automate the process and this research forms a large part of the automation. The general problem of axial line placement has been shown to be NP-complete. For this reason, previous research in this field has been focused on finding special cases where this is not the case or finding heuristics that approximate a solution. The majority of the research conducted has been on the simpler case of axial line placement in configurations of orthogonal rectangles and the only work done with convex polygons has been in the restricted case of deformed urban grids. This document presents research that finds two non-trivial special cases of convex polygons that have polynomial solutions and finds the first heuristic for general configurations of convex polygons.

The main topic of this thesis is the tropicalizations of Severi varieties, which we call tropical Severi varieties. Severi varieties are classical objects in algebraic geometry. They are parameter spaces of plane nodal curves. On the other hand, tropicalization is an operation defined in tropical geometry, which turns subvarieties of an algebraic torus into certain polyhedral objects in real vector spaces. By studying the tropicalizations, it may be possible to transform algebro-geometric problems into purely combinatorial ones. Thus, it is a natural question, “what are tropical Severi varieties?” In this thesis, we give a partial answer to this question: we obtain a description of tropical Severi varieties in terms of regular subdivisions of polygons. Given a regular subdivision of a convex lattice polygon, we construct an explicit parameter space of plane curves. This parameter space is a much simpler object than the corresponding Severi variety and it is closely related to a flat degeneration of the Severi variety, which in turn describes the tropical Severi variety. We present two applications. First, we understand G.Mikhalkin’s correspondence theorem for the degrees of Severi varieties in terms of tropical intersection theory. In particular, this provides a proof of the independence of point-configurations in the enumeration of tropical nodal curves. The second application is about Secondary fans. Secondary fans are purely combinatorial objects which parameterize all the regular subdivisions of polygons. We provide a relation between tropical Severi varieties and Secondary fans.