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

A Graph Theoretic Approach to General Euler Diagram Drawing

AbstractEuler diagrams are used in a wide variety of areas for representing information about relationships between collections of objects. Recently, several techniques for automated Euler diagram drawing have been proposed, contributing to the Euler diagram generation problem: given an abstract description, draw an Euler diagram with that description and which possesses certain properties, sometimes called well-formedness conditions. We present the first fully formalized, general framework that permits the embedding of Euler diagrams that possess any collection of the six typically considered well-formedness conditions. Our method first converts the abstract description into a vertex-labelled graph. An Euler diagram can then be formed, essentially by finding a dual graph of such a graph. However, we cannot use an arbitrary plane embedding of the vertex-labelled graph for this purpose. We identify specific embeddings that allow the construction of appropriate duals. From these embeddings, we can also identify precisely which properties the drawn Euler diagram will possess and ‘measure’ the number of times that each well-formedness condition is broken. We prove that every abstract description can be embedded using our method. Moreover, we identify exactly which (large) class of Euler diagrams can be generated

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

Authenticity and Ephemerality: The Memes of Transcultural Production in Italian Diasporic Culture

This dissertation seeks to contribute a new model for the observation, interpretation, and analysis of Italian and American cultures utilising a semiotic-memetic grammar for analysing and interpreting culture as it transforms and disseminates through time and space. Semioticians, linguists, philosophers, historians, and cultural theorists have written on culture and its relation to language, ethnicity, and identity perception. However, the mechanism for the arrival to specific loci is often overlooked. For the purposes of this study, the cultural systems in question are diasporic Italian manifested in the form of the Italian Americans operating in the periphery (USA) and peninsular/insular Italians operating in the centre (Italy). This dissertation addresses the question of how meaning is constructed, maintained, and propagated in the periphery by diasporic peoples with general inferences on both Italian Diasporic culture in the United States, and specifically a cohort of Americans of Italian, mixed Italian descent that reside in Mahoning Valley in the state of Ohio, USA. I argue that using signs that arrived via memes i.e., non-biologically spread cultural data to the United States through migratory flows, American Italians have the ability to semiotically interpret Italian signs thereby maintaining an authentic and ephemeral connection to Italy while in the periphery. In the present study, signs found in the peripheries of Italy as centre that work in unison to create meaning or Memetic Codes Clusters have been identified and defined as interpretable and communicable cultural value systems. They are examples of multimodal structures operating as memes outside of an origination point connecting and maintaining perception to a core culture: cultures that have historically exerted influence due to hegemony, mass communication, and popular appeal. Multiple examples from a selection of targeted audiovisual and literary texts have been correlated with the aforementioned clusters serving as aesthetic markers. Preliminary findings suggest there are discernible semiotic attributes contained in both samples that illustrate the fecundity and hybridisation of Italian culture in the periphery. Keywords: culture, diaspora, Italian America, memes, semiotic