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{"title"=>"euler APE: Drawing area-proportional 3-Venn diagrams using ellipses", "type"=>"journal", "authors"=>[{"first_name"=>"Luana", "last_name"=>"Micallef", "scopus_author_id"=>"55305680000"}, {"first_name"=>"Peter", "last_name"=>"Rodgers", "scopus_author_id"=>"7102858782"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"isbn"=>"1932-6203 (Electronic) 1932-6203 (Linking)", "sgr"=>"84902272773", "pui"=>"373567395", "doi"=>"10.1371/journal.pone.0101717", "pmid"=>"25032825", "issn"=>"19326203", "scopus"=>"2-s2.0-84902272773"}, "id"=>"34805686-64cd-3745-965f-e86d6edbdc39", "abstract"=>"Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.", "link"=>"http://www.mendeley.com/research/euler-ape-drawing-areaproportional-3venn-diagrams-using-ellipses", "reader_count"=>139, "reader_count_by_academic_status"=>{"Unspecified"=>4, "Professor > Associate Professor"=>4, "Researcher"=>38, "Student > Doctoral Student"=>6, "Student > Ph. D. Student"=>47, "Student > Postgraduate"=>10, "Student > Master"=>11, "Other"=>3, "Student > Bachelor"=>7, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>3, "Professor"=>4}, "reader_count_by_user_role"=>{"Unspecified"=>4, "Professor > Associate Professor"=>4, "Researcher"=>38, "Student > Doctoral Student"=>6, "Student > Ph. D. Student"=>47, "Student > Postgraduate"=>10, "Student > Master"=>11, "Other"=>3, "Student > Bachelor"=>7, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>3, "Professor"=>4}, "reader_count_by_subject_area"=>{"Unspecified"=>9, "Agricultural and Biological Sciences"=>60, "Arts and Humanities"=>1, "Business, Management and Accounting"=>2, "Chemistry"=>5, "Computer Science"=>7, "Engineering"=>4, "Environmental Science"=>2, "Biochemistry, Genetics and Molecular Biology"=>11, "Nursing and Health Professions"=>1, "Mathematics"=>1, "Medicine and Dentistry"=>19, "Neuroscience"=>5, "Pharmacology, Toxicology and Pharmaceutical Science"=>1, "Physics and Astronomy"=>1, "Psychology"=>3, "Social Sciences"=>2, "Immunology and Microbiology"=>3, "Linguistics"=>2}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>19}, "Social Sciences"=>{"Social Sciences"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Psychology"=>{"Psychology"=>3}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>9}, "Environmental Science"=>{"Environmental Science"=>2}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>1}, "Engineering"=>{"Engineering"=>4}, "Chemistry"=>{"Chemistry"=>5}, "Neuroscience"=>{"Neuroscience"=>5}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>3}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>60}, "Computer Science"=>{"Computer Science"=>7}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>2}, "Nursing and Health Professions"=>{"Nursing and Health Professions"=>1}, "Linguistics"=>{"Linguistics"=>2}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>11}}, "reader_count_by_country"=>{"New Zealand"=>1, "Canada"=>1, "Netherlands"=>1, "Sweden"=>1, "United States"=>3, "Brazil"=>1, "Denmark"=>1, "Mexico"=>1, "United Kingdom"=>2, "France"=>1, "Germany"=>3}, "group_count"=>5}

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• {"url"=>"http%3A%2F%2Fjournals.plos.org%2Fplosone%2Farticle%3Fid%3D10.1371%252Fjournal.pone.0101717", "share_count"=>0, "like_count"=>0, "comment_count"=>0, "click_count"=>0, "total_count"=>0}

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• {"id"=>"1263015496980369408", "text"=>"https://t.co/hymXjz3XU2\n\narea-proportional?????????????????????????????????????", "created_at"=>"2020-05-20T07:55:34Z", "user"=>"yamagu09", "user_name"=>"????????", "user_profile_image"=>"http://pbs.twimg.com/profile_images/481755432071884800/nkmXVv--_normal.jpeg"}
• {"id"=>"497016882084737024", "text"=>"Plotting Euler diagram of twitter #IPCC interactions. Great free software here: http://t.co/hsFpZ4ofR2 #eulerAPE http://t.co/p2pmiWxdT1", "created_at"=>"2014-08-06T13:50:33Z", "user"=>"SaffronJONeill", "user_name"=>"Saffron O'Neill", "user_profile_image"=>"http://pbs.twimg.com/profile_images/417708006843756544/ImdZKU9e_normal.jpeg"}
• {"id"=>"497021705559506944", "text"=>"RT @SaffronJONeill: Plotting Euler diagram of twitter #IPCC interactions. Great free software here: http://t.co/hsFpZ4ofR2 #eulerAPE http:/…", "created_at"=>"2014-08-06T14:09:43Z", "user"=>"ExeterGeography", "user_name"=>"ExeterGeography", "user_profile_image"=>"http://pbs.twimg.com/profile_images/468282191500177408/Rq3nkVXd_normal.jpeg"}
• {"id"=>"499501960333389824", "text"=>"RT @SaffronJONeill: Plotting Euler diagram of twitter #IPCC interactions. Great free software here: http://t.co/hsFpZ4ofR2 #eulerAPE http:/…", "created_at"=>"2014-08-13T10:25:22Z", "user"=>"GBNfree", "user_name"=>"DGfree", "user_profile_image"=>"http://pbs.twimg.com/profile_images/498764924135305216/Gr4FAwY4_normal.png"}
• {"id"=>"523802198824583168", "text"=>"#PLOSONE #methods #datavisualisation eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses http://t.co/cMuc4DIdZx", "created_at"=>"2014-10-19T11:45:50Z", "user"=>"frank_burdon", "user_name"=>"Francis J. Burdon", "user_profile_image"=>"http://pbs.twimg.com/profile_images/433334408188149761/YbK9_R3O_normal.jpeg"}
• {"id"=>"523811843249541120", "text"=>"RT @frank_burdon: #PLOSONE #methods #datavisualisation eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses http://t.co/cMuc4…", "created_at"=>"2014-10-19T12:24:10Z", "user"=>"Aquatic_world", "user_name"=>"Aquatic life world", "user_profile_image"=>"http://pbs.twimg.com/profile_images/506833784168132608/ervTgKxl_normal.jpeg"}
• {"id"=>"523852264474439680", "text"=>"RT @frank_burdon: #PLOSONE #methods #datavisualisation eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses http://t.co/cMuc4…", "created_at"=>"2014-10-19T15:04:47Z", "user"=>"_djli", "user_name"=>"Daijiang Li", "user_profile_image"=>"http://pbs.twimg.com/profile_images/459147858722029569/kRvq34C5_normal.jpeg"}

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• {"title"=>"File:Biographies in Armenian Wikipedia (a), English Wikipedia (b) and Russian Wikipedia (c) - August 2016.png", "url"=>"http://commons.wikimedia.org/wiki/File:Biographies_in_Armenian_Wikipedia_(a),_English_Wikipedia_(b)_and_Russian_Wikipedia_(c)_-_August_2016.png", "timestamp"=>"2016-11-23T21:01:54Z"}

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Figshare

• {"files"=>["https://ndownloader.figshare.com/files/1599146"], "description"=>"<p>(A) Comparing the cell-type of differentially regulated genes after an anti-cancer drug treatment <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Regenbrecht1\" target=\"_blank\">[11]</a>. The method used to draw the diagram has not been noted. This diagram is a reprint of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone-0101717-g003\" target=\"_blank\">Figure 3B</a> in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Regenbrecht1\" target=\"_blank\">[11]</a>, previously published under a CC BY license. (B) Summarizing prognostic indicators of severe malaria <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-DzeingElla1\" target=\"_blank\">[12]</a>. The method used to draw the diagram has not been noted. This diagram is a reprint of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone-0101717-g003\" target=\"_blank\">Figure 3</a> in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-DzeingElla1\" target=\"_blank\">[12]</a> (with the <i>N</i> value and the percentages in parenthesis removed), previously published under a CC BY license. (C) Analysing differences and similarities between identified chicken egg white proteome in three different studies <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Mann1\" target=\"_blank\">[13]</a>. Drawn using Venn Diagram Plotter [<a href=\"http://omics.pnl.gov/software/VennDiagramPlotter.php\" target=\"_blank\">http://omics.pnl.gov/software/VennDiagramPlotter.php</a>]. This diagram is a reprint of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone-0101717-g002\" target=\"_blank\">Figure 2A</a> in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Mann1\" target=\"_blank\">[13]</a>, previously published under a CC BY license. (D) Analysing overlaps between gene libraries <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Huber1\" target=\"_blank\">[14]</a>. Drawn using DrawVenn <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Chow1\" target=\"_blank\">[5]</a>. This diagram is a reprint of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone-0101717-g004\" target=\"_blank\">Figure 4B</a> in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Huber1\" target=\"_blank\">[14]</a> under a CC BY license, with permission from John Wiley and Sons, original copyright 2009. (E) Studying transcriptome variation of different tissue types of the male field cricket, namely testis, accessory gland and the rest of the body <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Bailey1\" target=\"_blank\">[15]</a>. Drawn using Convex Venn-3 <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Rodgers1\" target=\"_blank\">[51]</a>. This diagram is a reprint of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone-0101717-g001\" target=\"_blank\">Figure 1</a> (left) in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Bailey1\" target=\"_blank\">[15]</a> under a CC BY license, with permission from Nathan Bailey, original copyright 2013. (F) Summarizing genes affecting Top1-induced DNA damage identified in three different studies <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Reid1\" target=\"_blank\">[16]</a>. Drawn using DrawEuler <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Chow5\" target=\"_blank\">[55]</a>. This diagram is a reprint of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone-0101717-g003\" target=\"_blank\">Figure 3A</a> in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Reid1\" target=\"_blank\">[16]</a> (with added numeric labels indicating the quantitative data that according to the article each region in the diagram should represent), previously published under a CC BY license.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "area-proportional", "3-venn", "diagrams", "drawn", "circles", "polygons"], "article_id"=>1109129, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g001", "stats"=>{"downloads"=>0, "page_views"=>31, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Examples_of_area_proportional_3_Venn_diagrams_drawn_with_circles_A_8211_C_and_polygons_D_8211_F_in_literature_/1109129", "title"=>"Examples of area-proportional 3-Venn diagrams drawn with circles (A–C) and polygons (D–F) in literature.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599163"], "description"=>"<p>The <i>log₁₀</i> (<i>time in seconds</i>) and <i>log₁₀</i>(<i>total number of iterations</i>) taken to generate good diagrams for 9939 of the 10,000 data items in L1 during the first run (labelled as ‘<i>Run 1</i>’) and for 61 of the 10,000 data items in L1 during any of the one to a maximum of 10 reruns (labelled as ‘<i>Reruns</i>’).</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "iterations", "diagrams"], "article_id"=>1109146, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g008", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Time_and_total_number_of_iterations_to_generate_good_diagrams_for_data_in_L1_/1109146", "title"=>"Time and total number of iterations to generate good diagrams for data in L1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599158"], "description"=>"<p>At every iteration of the optimization algorithm, the (A) centre, (B) semi-axes and (C) angle of rotation of every ellipse are respectively modified by parameters <i>pγ</i>, <i>pαβ</i> and <i>pθ</i> in search for other solutions. (A) The grey points indicate the new centres that are obtained when one or both coordinates of the centre of an ellipse (solid black) are increasing or decreasing by <i>pγ</i>. (B) A label <i>+pαβ</i> means that that semi-axis was increased by the <i>pαβ</i> percentage, while -<i>pαβ</i> means that that semi-axis was decreased by the <i>pαβ</i> percentage. The dashed ellipses indicate how an ellipse (solid black) is changed when: (top, left) only the semi-major axis is increased or decreased by <i>pαβ</i>; (top, right) only the semi-minor is increased or decreased by <i>pαβ</i>; (bottom, left) the semi-axes are both increased or both decreased by <i>pαβ</i>; (bottom, right) one of the semi-axes is increased and the other is decreased by <i>pαβ</i>. (C) The dashed ellipses indicate how an ellipse (solid black) is changed when its angle of rotation is increased or decreased by <i>pθ</i>.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "ways", "modified", "optimization"], "article_id"=>1109141, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g006", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_different_ways_the_ellipses_properties_are_modified_during_the_optimization_search_process_/1109141", "title"=>"The different ways the ellipses' properties are modified during the optimization search process.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599174"], "description"=>"<p>(A) The figure with two Venn diagrams drawn with circles in a medical journal article <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Lenz1\" target=\"_blank\">[37]</a>. This is a redrawing of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone-0101717-g005\" target=\"_blank\">Figure 5</a> in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Lenz1\" target=\"_blank\">[37]</a>, previously published under a CC BY license. (B) The figure as it would have looked like if the diagrams were drawn with ellipses using euler<i>APE</i>. Labels for euler<i>APE</i>'s diagrams were added manually.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "recreated"], "article_id"=>1109155, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g013", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_figure_in_a_medical_journal_article_and_the_figure_recreated_with_euler_APE_/1109155", "title"=>"The figure in a medical journal article and the figure recreated with euler<i>APE</i>.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599156"], "description"=>"<p>The centre of ellipse <i>e</i>₃ is a point on the line <i>L</i> bisecting the angle <i>ψ</i> between the two tangents <i>T</i>₁ and <i>T</i>₂. The bisection method is applied in the interval indicated by the faded blue circles along <i>L</i>. The obtained centre should minimize the discrepancy of the required and the actual area of the region in exactly the three ellipses.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "diagram", "generator", "bisecting", "bisector"], "article_id"=>1109140, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g005", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_starting_diagram_generator_bisecting_the_interval_along_bisector_line_to_position_the_third_ellipse_/1109140", "title"=>"The starting diagram generator bisecting the interval along bisector line to position the third ellipse.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599173"], "description"=>"<p>The (A) <i>stress</i> and (B) <i>diagError</i> of all the diagrams generated with circles by venneuler, with circles by euler<i>APE</i> and with ellipses by euler<i>APE</i> for the 10,000 3-set data in L2. The 10,000 diagrams generated with circles by venneuler had <i>stress</i> in [3.77×10⁻⁵, 6.14×10⁻¹] with median 3.04×10⁻² and mean 6.41×10⁻², and <i>diagError</i> in [1.56×10⁻³, 2.46×10⁻¹] with median 4.56×10⁻² and mean 5.73×10⁻². The 10,000 diagrams generated with circles by euler<i>APE</i> had <i>stress</i> in [1.91×10⁻¹⁰, 7.79×10⁻¹] with median 7.00×10⁻² and mean 1.13×10⁻¹, and <i>diagError</i> in [3.30×10⁻⁶, 3.31×10⁻¹] with median 6.28×10⁻² and mean 6.73×10⁻². The 10,000 diagrams generated with ellipses by euler<i>APE</i> had <i>stress</i> in [3.98×10⁻¹⁴, 2.24×10⁻¹] with median 7.59×10⁻¹² and mean 1.17×10⁻¹⁰, and <i>diagError</i> in [6.00×10⁻⁸, 1.39×10⁻¹] with median 8.00×10⁻⁷ and mean 2.94×10⁻³.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "diagrams", "generated", "venneuler"], "article_id"=>1109154, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g012", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Stress_and_diagError_of_all_the_diagrams_generated_by_venneuler_and_euler_APE_circles_and_ellipses_/1109154", "title"=>"<i>Stress</i> and <i>diagError</i> of all the diagrams generated by venneuler and euler<i>APE</i> (circles and ellipses).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599152"], "description"=>"<p>All the diagrams are meant to depict <i>ω</i> = {<i>A</i> = 0.25, <i>B</i> = 0.01, <i>C</i> = 0.11, <i>AB</i> = 0.10, <i>AC</i> = 0.29, <i>BC</i> = 0.03, <i>ABC</i> = 0.15}, which represents the findings of a medical survey from a journal article <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Lenz1\" target=\"_blank\">[37]</a> that also included diagram D for <i>ω</i>. The diagrams generated for <i>ω</i> using circle-based drawing methods are marked as C, those of polygon-based methods are marked as P, and the only diagram with ellipses, that by euler<i>APE</i>, is E. Green indicates accurate diagrams with <i>diagError</i> ≤10⁻⁶. Red indicates diagrams with inaccurate or missing regions. D is a redrawing of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone-0101717-g005\" target=\"_blank\">Figure 5</a> (bottom) in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone.0101717-Lenz1\" target=\"_blank\">[37]</a>, previously published under a CC BY license.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "generated", "methods"], "article_id"=>1109135, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g003", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Diagrams_generated_by_various_drawing_methods_for_the_same_medical_data_from_a_journal_article_/1109135", "title"=>"Diagrams generated by various drawing methods for the same medical data from a journal article.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599153"], "description"=>"<p>(A) The quantitative values in each region indicate the required region areas, for which an area-proportional 3-Venn diagram should be drawn. (B) The first step of the construction whereby the three accurate 2-Venn diagrams are drawn. (C) The second step of the construction whereby the identical copies of the circle labelled <i>c</i> are rotated such that they overlap completely and only one circle labelled <i>c</i> is visible. (D) The instance when only three circles are visible, such that the regions of the 3-Venn diagram are obtained. (E) The actual area of the regions in the constructed diagram D, which, as in most cases when these diagrams are drawn with circles, do not correspond to the desired values in A. The numeric label in each region of this diagram indicates the regions' actual area.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "constructing", "area-proportional", "3-venn", "diagram"], "article_id"=>1109136, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g004", "stats"=>{"downloads"=>0, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_method_for_constructing_an_area_proportional_3_Venn_diagram_using_circles_/1109136", "title"=>"A method for constructing an area-proportional 3-Venn diagram using circles.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599148"], "description"=>"<p>Each of these diagrams depicts the sets and the quantitative data indicated by the numeric labels in the regions of the corresponding diagram in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101717#pone-0101717-g001\" target=\"_blank\">Figure 1</a>. These diagrams have been drawn with euler<i>APE</i>, but the labels have been added manually.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "area-proportional", "3-venn", "diagrams", "drawn", "ellipses"], "article_id"=>1109131, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g002", "stats"=>{"downloads"=>0, "page_views"=>37, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Accurate_area_proportional_3_Venn_diagrams_drawn_with_ellipses_and_euler_APE_for_the_data_in_Figure_1_/1109131", "title"=>"Accurate area-proportional 3-Venn diagrams drawn with ellipses and euler<i>APE</i> for the data in Figure 1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599167"], "description"=>"<p>(A) and (B) illustrate (<i>i</i>) the good diagram that was found using (<i>ii</i>) the starting diagram generated for the data item in L1 ({<i>a</i> = 2273, <i>b</i> = 24458, <i>c</i> = 44454, <i>ab</i> = 7116, <i>ac</i> = 740, <i>bc</i> = 18807, <i>abc</i> = 12092} for A and {<i>a</i> = 17033, <i>b</i> = 6248, <i>c</i> = 16230, <i>ab</i> = 615, <i>ac</i> = 289, <i>bc</i> = 840, <i>abc</i> = 922} for B) that was equal to the set of region areas of (<i>iii</i>) a randomly generated 3-Venn diagram.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "diagrams", "generated"], "article_id"=>1109148, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g009", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Examples_of_good_diagrams_generated_after_the_first_run_for_data_in_L1_/1109148", "title"=>"Examples of good diagrams generated after the first run for data in L1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599162"], "description"=>"<p>The number of reruns (1–10) that were required for euler<i>APE</i> to generate a good diagram for the 61 data items in L1 for which a non-good diagram was generated during the first run.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "reruns", "diagram", "61", "items"], "article_id"=>1109145, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g007", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_number_of_reruns_to_generate_a_good_diagram_for_61_data_items_in_L1_/1109145", "title"=>"The number of reruns to generate a good diagram for 61 data items in L1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599172"], "description"=>"<p>Examples of diagrams generated with (<i>i</i>) circles by venneuler, (<i>ii</i>) circles by euler<i>APE</i>, and (<i>iii</i>) ellipses by euler<i>APE</i> for random 3-set data in L2. (A) Diagrams generated for data {<i>a</i> = 3491, <i>b</i> = 3409, <i>c</i> = 3503, <i>ab</i> = 120, <i>ac</i> = 114, <i>bc</i> = 132, <i>abc</i> = 126}. A<i>i</i> is missing region <i>abc</i> and has <i>stress</i>  = 5.69×10⁻⁴ and <i>diagError</i>  = 1.16×10⁻². A<i>ii</i> and A<i>iii</i> have the required regions, one for every data set relation. A<i>ii</i> has <i>stress</i>  = 8.36×10⁻³ and <i>diagError</i>  = 2.63×10⁻². A<i>iii</i> has <i>stress</i>  = 3.96×10⁻¹² and <i>diagError</i>  = 6.55×10⁻⁷. (B) Diagrams generated for data {<i>a</i> = 45910, <i>b</i> = 3261, <i>c</i> = 45467, <i>ab</i> = 58845, <i>ac</i> = 3028, <i>bc</i> = 16406, <i>abc</i> = 18496}. B<i>i</i> is missing region <i>ac</i> and has <i>stress</i>  = 3.17×10⁻³ and <i>diagError</i>  = 2.07×10⁻². There are two regions in B<i>i</i> depicting only <i>b</i>. B<i>ii</i> and B<i>iii</i> have the required regions, one for every data set relation. B<i>ii</i> has <i>stress</i>  = 2.13×10⁻² and <i>diagError</i>  = 4.36×10⁻². B<i>iii</i> has <i>stress</i>  = 3.43×10⁻¹² and <i>diagError</i>  = 6.85×10⁻⁷. (C) Diagrams generated for data {<i>a</i> = 3664, <i>b</i> = 46743, <i>c</i> = 59811, <i>ab</i> = 1742, <i>ac</i> = 2099, <i>bc</i> = 17210, <i>abc</i> = 24504}. C<i>i</i>, C<i>ii</i> and C<i>iii</i> have the required regions, one for every data set relation. C<i>i</i> has <i>stress</i>  = 4.27×10⁻³ and <i>diagError</i>  = 2.30×10⁻². C<i>ii</i> has <i>stress</i>  = 8.31×10⁻³ and <i>diagError</i>  = 2.44×10⁻². C<i>iii</i> has <i>stress</i>  = 1.13×10⁻¹² and <i>diagError</i>  = 4.03×10⁻⁷.</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "diagrams", "generated", "venneuler"], "article_id"=>1109153, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g011", "stats"=>{"downloads"=>2, "page_views"=>110, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Examples_of_diagrams_generated_by_venneuler_and_euler_APE_circles_and_ellipses_for_data_in_L2_/1109153", "title"=>"Examples of diagrams generated by venneuler and euler<i>APE</i> (circles and ellipses) for data in L2.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}
• {"files"=>["https://ndownloader.figshare.com/files/1599170"], "description"=>"<p>(A) An example of (<i>i</i>) a non-good diagram with a very low <i>diagError</i> (6.51×10⁻⁴) generated during the first run and (<i>ii</i>) the good diagram generated during the first rerun for the data ({<i>a</i> = 10018, <i>b</i> = 27132, <i>c</i> = 39737, <i>ab</i> = 9567, <i>ac</i> = 11454, <i>bc</i> = 3, <i>abc</i> = 668}) in L1 obtained from (<i>iii</i>) a random diagram. The good diagram in <i>ii</i> was generated in 1.2 seconds and 86 iterations (including the first run and the one rerun). (B) An example of (<i>i</i>) a non-good diagram with a low <i>diagError</i> (8.38×10⁻³) generated during the first run and (<i>ii</i>) the good diagram generated during the first rerun for the data ({<i>a</i> = 53804, <i>b</i> = 39550, <i>c</i> = 1256, <i>ab</i> = 15606, <i>ac</i> = 15, <i>bc</i> = 29904, <i>abc</i> = 3597}) in L1 obtained from (<i>iii</i>) a random diagram. The good diagram in <i>ii</i> was generated in 2.9 seconds and 367 iterations (including the first run and the one rerun).</p>", "links"=>[], "tags"=>["Computer applications", "software engineering", "Software design", "Software tools", "mathematics", "Applied mathematics", "algorithms", "calculus", "geometry", "diagrams", "generated", "rerun"], "article_id"=>1109151, "categories"=>["Biological Sciences"], "users"=>["Luana Micallef", "Peter Rodgers"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0101717.g010", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Examples_of_good_diagrams_generated_after_the_first_rerun_for_data_in_L1_/1109151", "title"=>"Examples of good diagrams generated after the first rerun for data in L1.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-17 03:45:31"}

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Relative Metric

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F1000Prime