Online region computations for Euler Diagrams with relaxed drawing conventions

AbstractEuler diagrams are an accessible and effective visualisation of data involving simple set-theoretic relationships. Efficient algorithms to quickly compute the abstract regions of an Euler diagram upon curve addition and removal have previously been developed (the single marked point approach, SMPA), but a strict set of drawing conventions (called well-formedness conditions) were enforced, meaning that some abstract diagrams are not representable as concrete diagrams. We present a new methodology (the multiple marked point approach, MMPA) enabling online region computation for Euler diagrams under the relaxation of the drawing convention that zones must be connected regions. Furthermore, we indicate how to extend the methods to deal with the relaxation of any of the drawing conventions, with the use of concurrent line segments case being of particular importance. We provide complexity analysis and compare the MMPA with the SMPA. We show that these methods are theoretically no worse than other comparators, whilst our methods apply to any case, and are likely to be faster in practise due to their online nature. The machinery developed for the concurrency case could be of use in Euler diagram drawing techniques (in the context of the Euler Graph), and in computer graphics (e.g. the development of an advanced variation of a winged edge data structure that deals with concurrency). The algorithms are presented for generic curves; specialisations such as utilising fixed geometric shapes for curves may occur in applications which can enhance capabilities for fast computations of the algorithms' input structures. We provide an implementation of these algorithms, utilising ellipses, and provide time-based experimental data for benchmarking purposes

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

Generating Simple Convex Venn Diagrams

In this paper we are concerned with producing exhaustive lists of simple monotone Venn diagrams that have some symmetry (non-trivial isometry) when drawn on the sphere. A diagram is simple if at most two curves intersect at any point, and it is monotone if it has some embedding on the plane in which all curves are convex. We show that there are 23 such 7-Venn diagrams with a 7-fold rotational symmetry about the polar axis, and that 6 of these have an additional 2-fold rotational symmetry about an equatorial axis. In the case of simple monotone 6-Venn diagrams, we show that there are 39020 non-isomorphic planar diagrams in total, and that 375 of them have a 2-fold symmetry by rotation about an equatorial axis, and amongst these we determine all those that have a richer isometry group on the sphere. Additionally, 270 of the 6-Venn diagrams also have the 2-fold symmetry induced by reflection about the center of the sphere. Since such exhaustive searches are prone to error, we have implemented the search in a couple of ways, and with independent programs. These distinct algorithms are described. We also prove that the Grünbaum encoding can be used to efficiently identify any monotone Venn diagram