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Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams
, 2013
"... All rights reserved. This dissertation may not be reproduced in whole or in part, by photocopying or other means, without the permission of the author. In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities ..."
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Cited by 1 (1 self)
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All rights reserved. This dissertation may not be reproduced in whole or in part, by photocopying or other means, without the permission of the author. In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations
Visualizations with Venn and Euler Diagrams
"... Venn and Euler diagrams intuitively visualize relationships and relative cardinalities of data sets. They are used extensively in areas as biosciences, business and criminology to facilitate data reasoning and analysis. However, current automatic drawing techniques do not always produce desirable di ..."
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Venn and Euler diagrams intuitively visualize relationships and relative cardinalities of data sets. They are used extensively in areas as biosciences, business and criminology to facilitate data reasoning and analysis. However, current automatic drawing techniques do not always produce desirable
Venn and Euler Data Diagrams
"... Scientists conducting microarray and other experiments use Venn and Euler diagrams to analyze and illustrate their results. Most existing computer programs that implement Venn and Euler diagrams are limited to three sets. The few programs that plot more than three sets rest on adhoc methods, such a ..."
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Scientists conducting microarray and other experiments use Venn and Euler diagrams to analyze and illustrate their results. Most existing computer programs that implement Venn and Euler diagrams are limited to three sets. The few programs that plot more than three sets rest on adhoc methods
Drawing areaproportional Venn and Euler diagrams
 In Proceedings of Graph Drawing 2003
, 2003
"... Abstract. We consider the problem of drawing Venn diagrams for which each region’s area is proportional to some weight (e.g., population or percentage) assigned to that region. These areaproportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey informatio ..."
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Cited by 56 (1 self)
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information about data sets with interacting characteristics. We develop algorithms for drawing areaproportional Venn diagrams for any population distribution over two characteristics using circles and over three characteristics using rectangles and nearrectangular polygons; modifications
Exact and Approximate Areaproportional Circular Venn and Euler Diagrams
 IEEE Trans Vis Comput Graph
"... Abstract — Scientists conducting microarray and other experiments use circular Venn and Euler diagrams to analyze and illustrate their results. As one solution to this problem, this article introduces a statistical model for fitting areaproportional Venn and Euler diagrams to observed data. The sta ..."
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Cited by 22 (0 self)
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Abstract — Scientists conducting microarray and other experiments use circular Venn and Euler diagrams to analyze and illustrate their results. As one solution to this problem, this article introduces a statistical model for fitting areaproportional Venn and Euler diagrams to observed data
Venn Diagrams with Few Vertices
 ELECTRON. J. COMBIN.
, 1998
"... An nVenn diagram is a collection of n finitelyintersecting simple closed curves in the plane, such that each of the 2 n sets X 1 #X 2 # #X n , where each X i is the open interior or exterior of the ith curve, is a nonempty connected region. The weight of a region is the number of curve ..."
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Cited by 6 (3 self)
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An nVenn diagram is a collection of n finitelyintersecting simple closed curves in the plane, such that each of the 2 n sets X 1 #X 2 # #X n , where each X i is the open interior or exterior of the ith curve, is a nonempty connected region. The weight of a region is the number
Conservativity for a hierarchy of Euler and Venn reasoning systems
 Proc. of Visual Languages and Logic 2009, CEUR Series
, 2009
"... This paper introduces a hierarchy of Euler and Venn diagrammatic reasoning systems in terms of their expressive powers in topologicalrelationbased formalization. At the bottom of the hierarchy is the Euler diagrammatic system introduced in MineshimaOkadaSatoTakemura [13, 12], which is expressiv ..."
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Cited by 2 (1 self)
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of S and S ’ are equivalent for diagrams of S. Furthermore, we prove that a regionbased Venn diagrammatic system is conservative over our topologicalrelationbased Euler diagrammatic system with respect to provability. 1
Generating euler diagrams
 In Proceedings of Diagrams 2002
, 2002
"... Abstract. This article describes an algorithm for the automated generation of any Euler diagram starting with an abstract description of the diagram. An automated generation mechanism for Euler diagrams forms the foundations of a generation algorithm for notations such as Harel’s higraphs, constrain ..."
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Cited by 66 (24 self)
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Abstract. This article describes an algorithm for the automated generation of any Euler diagram starting with an abstract description of the diagram. An automated generation mechanism for Euler diagrams forms the foundations of a generation algorithm for notations such as Harel’s higraphs
Picturing Probability: the poverty of Venn diagrams, the richness of
, 2006
"... Diagrams convey information, some intended some not. A history of ringed diagrams including their use by Euler and Venn shows that the information interrelations between different entities. This historical consistency predates and would have been known to both Euler and Venn. Venn’s use was a true i ..."
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innovation over Euler’s and, contrary to what some have recently suggested, Venn’s name deserves to be attached to these diagrams. Venn diagrams visually ground symbolic logic and abstract set operations. They do not ground probability. Their common overuse in introducing probability, especially in teaching
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