The State-of-the-Art of Set Visualization

Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net

Formalizing graphical notations

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach

Information enforcement in learning with graphics : improving syllogistic reasoning skills

This thesis is an investigation into the factors that contribute to good choices among graphical systems used in teaching, and the feasibility of implementing teaching software that uses this knowledge.The thesis describes a mathematical metric derived from a cognitive theory of human diagram processing. The theory characterises differences among representations by their ability to express information. The theory provides the factors and relationships needed to build the metric. It says that good representations are easily processed because they are more vivid, more tractable and less expressive, than poor representations.The metric is applied to abstract systems for teaching and learning syllogistic reasoning, TARSKI'S WORLD, EULER CIRCLES, VENN DIAGRAMS and CARROLL'S GAME OF LOGIC. A rank ordering reflects the value of each system predicted by the theory and the metric. The theory, the metric and the systems are then tested in empirical studies. Five studies involving sixty-eight learners, examined the benefit of software based on these abstract systems.Studies showed the theory correctly predicted learners' success with the circle systems and poorer performance with TARSKI'S WORLD. The metric showed small but clear differences in expressivity between the circle systems. Differences between results of the learners using the circle systems contradicted the predictions of the metric.Learners with mathematical training were better equipped and more successful at learning syllogistic reasoning with the systems. Performance of learners without mathematical training declined after using the software systems. Diagrams drawn by learners together with video footage collected during problem solving, led to a catalogue of errors, misconceptions and some helpful strategies for learning from graphical systems.A cognitive style test investigated the poor performance of non-mathematically trained learners. Learners with mathematics training showed serialist and versatile learning styles while learners without this training showed a holist learning style. This is consistent with the hypothesis that non-mathematically trained learners emphasise the use of semantic cues during learning and problem solving.A card-sorting task investigated learners' preferences for parts of the graphical lexicon used in the diagram systems. Preferences for the EULER lexicon increased difficulty in explaining the system's poor results in earlier studies. Video footage of learners using the systems in the final study illustrated useful learning strategies and improved performance with EULER while individual instruction was available.Further work describes a preliminary design for an adaptive syllogism tutor and other related work

Visualisation of Large-Scale Call-Centre Data

The contact centre industry employs 4% of the entire United King-dom and United States’ working population and generates gigabytes of operational data that require analysis, to provide insight and to improve efficiency. This thesis is the result of a collaboration with QPC Limited who provide data collection and analysis products for call centres. They provided a large data-set featuring almost 5 million calls to be analysed. This thesis utilises novel visualisation techniques to create tools for the exploration of the large, complex call centre data-set and to facilitate unique observations into the data.A survey of information visualisation books is presented, provid-ing a thorough background of the field. Following this, a feature-rich application that visualises large call centre data sets using scatterplots that support millions of points is presented. The application utilises both the CPU and GPU acceleration for processing and filtering and is exhibited with millions of call events.This is expanded upon with the use of glyphs to depict agent behaviour in a call centre. A technique is developed to cluster over-lapping glyphs into a single parent glyph dependant on zoom level and a customizable distance metric. This hierarchical glyph repre-sents the mean value of all child agent glyphs, removing overlap and reducing visual clutter. A novel technique for visualising individually tailored glyphs using a Graphics Processing Unit is also presented, and demonstrated rendering over 100,000 glyphs at interactive frame rates. An open-source code example is provided for reproducibility.Finally, a novel interaction and layout method is introduced for improving the scalability of chord diagrams to visualise call transfers. An exploration of sketch-based methods for showing multiple links and direction is made, and a sketch-based brushing technique for filtering is proposed. Feedback from domain experts in the call centre industry is reported for all applications developed

Vanishing points: a personal approach to non-tempered tuning

The tuning of keyboard and zither instruments is tempered, that is, the system of tuning their intervals pragmatically approximates that of just (or pure) intervallic tuning. This has certain advantages, but results in a rigid, cyclic, closed system of tuning (and by extension, harmony). By comparison, non-tempered tuning is an open system requiring a flexible approach to tuning each interval in turn. The resulting harmonies are sonorous and distinctive. Much music written using non-tempered tunings has an acute awareness of the phenomena arising from the interactions between the vibrations causing the sensation of sound, the physiology of our ears and the psychology of our hearing faculty. Without diminishing this awareness, my work also investigates the evocative potential of this approach to harmony, in part through visual analogies and tactile processes of sketching. Examples informing this investigation include Vija Celmins’ drawings, Dan Graham’s pavilion Double Exposure, the architectural concept terrain vague, the poetry of Gerard Manley Hopkins, animated sound pioneers such as Arseni M. Avraamov, Percy Grainger’s “free music machine” and the works of Giovanni Battista Piranesi. My portfolio spans works for chamber orchestra to pieces for ensemble or soloist with pre-recorded sound and image. Through composing, I grappled with recurring questions concerning my evolving approach to non-tempered tuning—questions arising out of a meeting of theory, practice and imagination. These include the place of melody in my works, the place of traditional acoustic instruments (including those tuned in —or tuning to—equal temperament) and the relationship between perceptual phenomena and a personal evocative world. My study is indebted to—and extends—the work of composers like James Tenney, Ben Johnston and Marc Sabat. The title Vanishing Points poetically encapsulates different aspects of this exploration

The use of multiple representation approach in enhancing the learning of fluid mechanics in undergraduate physics classes in Ethiopia

The inadequate understanding of fluid mechanics is a phenomenon widely experienced by undergraduate Physics students. The study aimed to establish students’ preconceptions on this topic then develop Multiple Representation teaching sequences and establish the effect thereof in two iterations. Multiple intelligence theory, variation theory, and cognitive theory were used to guide the study. This study was conducted at two Ethiopian universities. Students’ preconceptions were first categorised and then analysed using categories and frequency counts. This informed the development of a Multiple Representation Approach aimed at enhancing the learning of fluid mechanics. Research methods used to evaluate multiple representations' effectiveness comprised a quasi-experimental design. Open-ended questionnaires, the Fluid Mechanics Concept Inventory and the Test of Multiple Representation Approach Related Attitudes were used to collect data from N = 128 undergraduate students, 64 in Iteration I and 64 in Iteration II. Every iteration consisted of two groups of students selected from two universities. Before any intervention, the students’ prior knowledge was established by using the Open Ended Questionnaire and fluid mechanics conceptual inventory. Both groups received instruction based on both the Multiple Representation Approach and the traditional lecture method. The first version of the multiple representations only used four representations, which resulted in no significant difference between the experimental and control groups. Before the second intervention, the new group of students included 64 students, of which 32 were from each group. The second development of the multiple representations followed, using eight representations. This resulted in a significant difference between the intervention and control groups on both Open-Ended Questionnaire and fluid mechanics conceptual inventory. The results showed that using eight multiple representations was significantly effective compared to using two, three, or four in students’ understanding of fluid mechanics concepts. In addition, students had positive attitudes towards the use of the Multiple Representation Approach. The study included two phases, perhaps it would have been better to include more than two phases. It is recommended that scholars in the field of study ought to conduct further research on other Physics topics.Science and Technology EducationD. Phil. (Mathematics, Science, and Technology Education

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes

Using Diagrammatic Reasoning for Theorem Proving in a Continuous Domain

Centre for Intelligent Systems and their ApplicationsThis project looks at using diagrammatic reasoning to prove mathematical theorems. The work is motivated by a need for theorem provers whose reasoning is readily intelligible to human beings. It should also have practical applications in mathematics teaching. We focus on the continuous domain of analysis - a geometric subject, but one which is taught using a dry algebraic formalism which many students find hard. The geometric nature of the domain makes it suitable for a diagram-based approach. However it is a difficult domain, and there are several problems, including handling alternating quantifiers, sequences and generalisation. We developed representations and reasoning methods to solve these. Our diagram logic isn't complete, but does cover a reasonable range of theorems. It utilises computers to extend diagrammatic reasoning in new directions – including using animation. This work is tested for soundness, and evaluated empirically for ease of use. We demonstrate that computerised diagrammatic theorem proving is not only possible in the domain of real analysis, but that students perform better using it than with an equivalent algebraic computer system