Advanced Proof Viewing in ProofTool

Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but since they normally utilize Gentzen's original notation, some of the problems persist. In this paper, we introduce a number of criteria for proof visualization which we have found out to be crucial for analyzing proofs. We then evaluate recent developments in tree visualization with regard to these criteria and propose the Sunburst Tree layout as a complement to the traditional tree structure. This layout constructs inferences as concentric circle arcs around the root inference, allowing the user to focus on the proof's structural content. Finally, we describe its integration into ProofTool and explain how it interacts with the Gentzen layout.Comment: In Proceedings UITP 2014, arXiv:1410.785

Relationship and association of information visualization, insight and sense making

No AbstractKeywords: information visualization; insight; sense making; cognitive; data abstractio

Visualizing the dynamics of London's bicycle hire scheme

Visualizing flows between origins and destinations can be straightforward when dealing with small numbers of journeys or simple geographies. Representing flows as lines embedded in geographic space has commonly been used to map transport flows, especially when geographic patterns are important as they are when characterising cities or managing transportation. However, for larger numbers of flows, this approach requires careful design to avoid problems of occlusion, salience bias and information overload. Driven by the requirements identified by users and managers of the London Bicycle Hire scheme we present three methods of representation of bicycle hire use and travel patterns. Flow maps with curved flow symbols are used to show overviews in flow structures. Gridded views of docking station location that preserve geographic relationships are used to explore docking station status over space and time in a graphically efficient manner. Origin-Destination maps that visualise the OD matrix directly while maintaining geographic context are used to provide visual details on demand. We use these approaches to identify changes in travel behaviour over space and time, to aid station rebalancing and to provide a framework for incorporating travel modelling and simulation

Understanding the structure of information visualization through visual metaphors

Information visualization is an increasingly widespread way to present and analyze complex data, but there is much we still do not know about how people understand vi- sually presented information. Every visualization contains certain assumptions about the structure of its information: how the data can be broken down into pieces, how those pieces relate to one another, what actions can and cannot be performed with the data, and so forth. Yet information visualization still lacks the language and the- ory to analyze these properties of visual information structure. I propose that these structural properties can be thought of as visual metaphors that drive a visualization, analogous to the verbal metaphors that structure abstract information in speech and writing. In this model, people analyze visual relationships among shapes and patterns in a visualization in the same way that they analyze other kinds of visual scenes, then metaphorically interpret those visual relationships as conceptual relationships. I have grounded this proposed model through empirical studies showing how metaphors af- fect visualization use and how minor structural changes can have significant effects on the way people interpret visual information. I argue that this framework sheds new light on the importance of design and conceptual structure in visualization and can substantially improve future techniques and evaluation

Information visualization for DNA microarray data analysis: A critical review

Graphical representation may provide effective means of making sense of the complexity and sheer volume of data produced by DNA microarray experiments that monitor the expression patterns of thousands of genes simultaneously. The ability to use ldquoabstractrdquo graphical representation to draw attention to areas of interest, and more in-depth visualizations to answer focused questions, would enable biologists to move from a large amount of data to particular records they are interested in, and therefore, gain deeper insights in understanding the microarray experiment results. This paper starts by providing some background knowledge of microarray experiments, and then, explains how graphical representation can be applied in general to this problem domain, followed by exploring the role of visualization in gene expression data analysis. Having set the problem scene, the paper then examines various multivariate data visualization techniques that have been applied to microarray data analysis. These techniques are critically reviewed so that the strengths and weaknesses of each technique can be tabulated. Finally, several key problem areas as well as possible solutions to them are discussed as being a source for future work

Interactive Visual Analysis of Networked Systems: Workflows for Two Industrial Domains

We report on a first study of interactive visual analysis of networked systems. Working with ABB Corporate Research and Ericsson Research, we have created workflows which demonstrate the potential of visualization in the domains of industrial automation and telecommunications. By a workflow in this context, we mean a sequence of visualizations and the actions for generating them. Visualizations can be any images that represent properties of the data sets analyzed, and actions typically either change the selection of data visualized or change the visualization by choice of technique or change of parameters

BallotMaps: Detecting name bias in alphabetically ordered ballot papers

The relationship between candidates’ position on a ballot paper and vote rank is explored in the case of 5000 candidates for the UK 2010 local government elections in the Greater London area. This design study uses hierarchical spatially arranged graphics to represent two locations that affect candidates at very different scales: the geographical areas for which they seek election and the spatial location of their names on the ballot paper. This approach allows the effect of position bias to be assessed; that is, the degree to which the position of a candidate’s name on the ballot paper influences the number of votes received by the candidate, and whether this varies geographically. Results show that position bias was significant enough to influence rank order of candidates, and in the case of many marginal electoral wards, to influence who was elected to government. Position bias was observed most strongly for Liberal Democrat candidates but present for all major political parties. Visual analysis of classification of candidate names by ethnicity suggests that this too had an effect on votes received by candidates, in some cases overcoming alphabetic name bias. The results found contradict some earlier research suggesting that alphabetic name bias was not sufficiently significant to affect electoral outcome and add new evidence for the geographic and ethnicity influences on voting behaviour. The visual approach proposed here can be applied to a wider range of electoral data and the patterns identified and hypotheses derived from them could have significant implications for the design of ballot papers and the conduct of fair elections