Drawing Area-Proportional Euler Diagrams Representing Up To Three Sets

Area-proportional Euler diagrams representing three sets are commonly used to visualize the results of medical experiments, business data, and information from other applications where statistical results are best shown using interlinking curves. Currently, there is no tool that will reliably visualize exact area-proportional diagrams for up to three sets. Limited success, in terms of diagram accuracy, has been achieved for a small number of cases, such as Venn-2 and Venn-3 where all intersections between the sets must be represented. Euler diagrams do not have to include all intersections and so permit the visualization of cases where some intersections have a zero value. This paper describes a general, implemented, method for visualizing all 40 Euler-3 diagrams in an area-proportional manner. We provide techniques for generating the curves with circles and convex polygons, analyze the drawability of data with these shapes, and give a mechanism for deciding whether such data can be drawn with circles. For the cases where non-convex curves are necessary, our method draws an appropriate diagram using non-convex polygons. Thus, we are now always able to automatically visualize data for up to three sets

Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams

In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities. The data sets are represented by closed curves and the data set relationships are depicted by the overlaps between these curves. Both the sets and their intersections are easily visible as the closed curves are preattentively processed and form common regions that have a strong perceptual grouping effect. Besides set relations such as intersection, containment and disjointness, the cardinality of the sets and their intersections can also be depicted in the same diagram (referred to as area-proportional) through the size of the curves and their overlaps. Size is a preattentive feature and so similarities, differences and trends are easily identified. Thus, such diagrams facilitate data analysis and reasoning about the sets. However, drawing these diagrams manually is difficult, often impossible, and current automatic drawing methods do not always produce appropriate diagrams. This dissertation presents novel automatic drawing methods for different types of Euler diagrams and a user study of how such diagrams can help probabilistic judgement. The main drawing algorithms are: eulerForce, which uses a force-directed approach to lay out Euler diagrams; eulerAPE, which draws area-proportional Venn diagrams with ellipses. The user study evaluated the effectiveness of area- proportional Euler diagrams, glyph representations, Euler diagrams with glyphs and text+visualization formats for Bayesian reasoning, and a method eulerGlyphs was devised to automatically and accurately draw the assessed visualizations for any Bayesian problem. Additionally, analytic algorithms that instantaneously compute the overlapping areas of three general intersecting ellipses are provided, together with an evaluation of the effectiveness of ellipses in drawing accurate area-proportional Venn diagrams for 3-set data and the characteristics of the data that can be depicted accurately with ellipses

Equivalences in Euler-based diagram systems through normal forms

AbstractThe form of information presented can influence its utility for the conveying of knowledge by affecting an interpreter’s ability to reason with the information. There are distinct types of representational systems (for example, symbolic versus diagrammatic logics), various sub-systems (for example, propositional versus predicate logics), and even within a single representational system there may be different means of expressing the same piece of information content. Thus, to display information, choices must be made between its different representations, depending upon many factors such as: the context, the reasoning tasks to be considered, user preferences or desires (for example, for short symbolic sentences or minimal clutter within diagrammatic systems). The identification of all equivalent representations with the same information content is a sensible precursor to attempts to minimise a metric over this class. We posit that defining notions of semantic redundancy and identifying the syntactic properties that encapsulate redundancy can help in achieving the goal of completely identifying equivalences within a single notational system or across multiple systems, but that care must be taken when extending systems, since refinements of redundancy conditions may be necessary even for conservative system extensions. We demonstrate this theory within two diagrammatic systems, which are Euler-diagram-based notations. Such notations can be used to represent logical information and have applications including visualisation of database queries, social network visualisation, statistical data visualisation, and as the basis of more expressive diagrammatic logics such as constraint languages used in software specification and reasoning. The development of the new associated machinery and concepts required is important in its own right since it increases the growing body of knowledge on diagrammatic logics. In particular, we consider Euler diagrams with shading, and then we conservatively extend the system to include projections, which allow for a much greater degree of flexibility of representation. We give syntactic properties that encapsulate semantic equivalence in both systems, whilst observing that the same semantic concept of redundancy is significantly more difficult to realise as syntactic properties in the extended system with projections.</jats:p

Declarative operations on nets

To increase the expressiveness of knowledge representations, the graph-theoretical basis of semantic networks is reconsidered. Directed labeled graphs are generalized to directed recursive labelnode hypergraphs, which permit a most natural representation of multi-level structures and n-ary relationships. This net formalism is embedded into the relational/functional programming language RELFUN. Operations on (generalized) graphs are specified in a declarative fashion to enhance readability and maintainability. For this, nets are represented as nested RELFUN terms kept in a normal form by rules associated directly with their constructors. These rules rely on equational axioms postulated in the formal definition of the generalized graphs as a constructor algebra. Certain kinds of sharing in net diagrams are mirrored by binding common subterms to logical variables. A package of declarative transformations on net terms is developed. It includes generalized set operations, structure-reducing operations, and extended path searching. The generation of parts lists is given as an application in mechanical engineering. Finally, imperative net storage and retrieval operations are discussed

Contours in Visualization

This thesis studies the visualization of set collections either via or defines as the relations among contours. In the first part, dynamic Euler diagrams are used to communicate and improve semimanually the result of clustering methods which allow clusters to overlap arbitrarily. The contours of the Euler diagram are rendered as implicit surfaces called blobs in computer graphics. The interaction metaphor is the moving of items into or out of these blobs. The utility of the method is demonstrated on data arising from the analysis of gene expressions. The method works well for small datasets of up to one hundred items and few clusters. In the second part, these limitations are mitigated employing a GPU-based rendering of Euler diagrams and mixing textures and colors to resolve overlapping regions better. The GPU-based approach subdivides the screen into triangles on which it performs a contour interpolation, i.e. a fragment shader determines for each pixel which zones of an Euler diagram it belongs to. The rendering speed is thus increased to allow multiple hundred items. The method is applied to an example comparing different document clustering results. The contour tree compactly describes scalar field topology. From the viewpoint of graph drawing, it is a tree with attributes at vertices and optionally on edges. Standard tree drawing algorithms emphasize structural properties of the tree and neglect the attributes. Adapting popular graph drawing approaches to the problem of contour tree drawing it is found that they are unable to convey this information. Five aesthetic criteria for drawing contour trees are proposed and a novel algorithm for drawing contour trees in the plane that satisfies four of these criteria is presented. The implementation is fast and effective for contour tree sizes usually used in interactive systems and also produces readable pictures for larger trees. Dynamical models that explain the formation of spatial structures of RNA molecules have reached a complexity that requires novel visualization methods to analyze these model\''s validity. The fourth part of the thesis focuses on the visualization of so-called folding landscapes of a growing RNA molecule. Folding landscapes describe the energy of a molecule as a function of its spatial configuration; they are huge and high dimensional. Their most salient features are described by their so-called barrier tree -- a contour tree for discrete observation spaces. The changing folding landscapes of a growing RNA chain are visualized as an animation of the corresponding barrier tree sequence. The animation is created as an adaption of the foresight layout with tolerance algorithm for dynamic graph layout. The adaptation requires changes to the concept of supergraph and it layout. The thesis finishes with some thoughts on how these approaches can be combined and how the task the application should support can help inform the choice of visualization modality

Regulation of transcriptional elongation in pluripotency and cell differentiation by the PHD-finger protein Phf5a

Pluripotent embryonic stem cells (ESCs) self-renew or differentiate into all tissues of the developing embryo and cell-specification factors are necessary to balance gene expression. Here we delineate the function of the PHD-finger protein 5a (Phf5a) in ESC self-renewal and ascribe its role in regulating pluripotency, cellular reprogramming, and myoblast specification. We demonstrate that Phf5a is essential for maintaining pluripotency, since depleted ESCs exhibit hallmarks of differentiation. Mechanistically, we attribute Phf5a function to the stabilization of the Paf1 transcriptional complex and control of RNA polymerase II elongation on pluripotency loci. Apart from an ESC-specific factor, we demonstrate that Phf5a controls differentiation of adult myoblasts. Our findings suggest a potent mode of regulation by the Phf5a in stem cells, which directs their transcriptional program ultimately regulating maintenance of pluripotency and cellular reprogramming

Text in Visualization: Extending the Visualization Design Space

This thesis is a systematic exploration and expansion of the design space of data visualization specifically with regards to text. A critical analysis of text in data visualizations reveals gaps in existing frameworks and the use of text in practice. A cross-disciplinary review across fields such as typography, cartography and technical applications yields typographic techniques to encode data into text and provides the scope for the expanded design space. Mapping new attributes, techniques and considerations back to well understood visualization principles organizes the design space of text in visualization. This design space includes: 1) text as a primary data type literally encoded into alphanumeric glyphs, 2) typographic attributes, such as bold and italic, capable of encoding additional data onto literal text, 3) scope of mark, ranging from individual glyphs, syllables and words; to sentences, paragraphs and documents, and 4) layout of these text elements applicable most known visualization techniques and text specific techniques such as tables. This is the primary contribution of this thesis (Part A and B). Then, this design space is used to facilitate the design, implementation and evaluation of new types of visualization techniques, ranging from enhancements of existing techniques, such as, extending scatterplots and graphs with literal marks, stem & leaf plots with multivariate glyphs and broader scope, and microtext line charts; to new visualization techniques, such as, multivariate typographic thematic maps; text formatted to facilitate skimming; and proportionally encoding quantitative values in running text – all of which are new contributions to the field (Part C). Finally, a broad evaluation across the framework and the sample visualizations with cross-discipline expert critiques and a metrics based approach reveals some concerns and many opportunities pointing towards a breadth of future research work now possible with this new framework. (Part D and E)