Venn Diagram

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Frank Ruskey - One of the best experts on this subject based on the ideXlab platform.

  • New Roses: Simple Symmetric Venn Diagrams with 11 and 13 Curves
    Discrete & Computational Geometry, 2014
    Co-Authors: Khalegh Mamakani, Frank Ruskey
    Abstract:

    A symmetric $$n$$ n -Venn Diagram is one that is invariant under $$n$$ n -fold rotation, up to a relabeling of curves. A simple $$n$$ n -Venn Diagram is an $$n$$ n -Venn Diagram in which at most two curves intersect at any point. In this paper, we introduce a new property of Venn Diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to Diagrams with crosscut symmetry, we found many simple symmetric Venn Diagrams with 11 curves. The question of the existence of a simple 11-Venn Diagram has been open since the 1960s. The technique used to find the 11-Venn Diagram is extended and a symmetric 13-Venn Diagram is also demonstrated.

  • Graph Drawing - The first simple symmetric 11-Venn Diagram
    Graph Drawing, 2013
    Co-Authors: Khalegh Mamakani, Frank Ruskey
    Abstract:

    An n-Venn Diagram is a collection of n simple closed curves in the plane with the following properties: (a) Each of the $2^n$ different intersections of the open interiors or exteriors of the curves is a non-empty connected region; (b) there are only finitely many points where the curves intersect. If each of the intersections is of only two curves, then the Diagram is said to be simple. The purpose of this poster is to highlight how we discovered the first simple symmetric 11-Venn Diagram.\ud \ud \ud \u

  • the first simple symmetric 11 Venn Diagram
    Graph Drawing, 2012
    Co-Authors: Khalegh Mamakani, Frank Ruskey
    Abstract:

    An n-Venn Diagram is a collection of n simple closed curves in the plane with the following properties: (a) Each of the 2n different intersections of the open interiors or exteriors of the curves is a non-empty connected region; (b) there are only finitely many points where the curves intersect. If each of the intersections is of only two curves, then the Diagram is said to be simple. The purpose of this poster is to highlight how we discovered the first simple symmetric 11-Venn Diagram.

  • a new rose the first simple symmetric 11 Venn Diagram
    arXiv: Computational Geometry, 2012
    Co-Authors: Khalegh Mamakani, Frank Ruskey
    Abstract:

    A symmetric Venn Diagram is one that is invariant under rotation, up to a relabeling of curves. A simple Venn Diagram is one in which at most two curves intersect at any point. In this paper we introduce a new property of Venn Diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to crosscut symmetry we found many simple symmetric Venn Diagrams with 11 curves. This answers an existence question that has been open since the 1960's. The first such Diagram that was discovered is shown here.

  • Spherical Venn Diagrams with Involutory Isometries
    The Electronic Journal of Combinatorics, 2011
    Co-Authors: Frank Ruskey, Mark Weston
    Abstract:

    In this paper we give a construction, for any $n$, of an $n$-Venn Diagram on the sphere that has antipodal symmetry; that is, the Diagram is fixed by the map that takes a point on the sphere to the corresponding antipodal point. Thus, along with certain Diagrams due to Anthony Edwards which can be drawn with rotational and reflective symmetry, for any isometry of the sphere that is an involution, there exists an $n$-Venn Diagram on the sphere invariant under that involution. Our construction uses a recursively defined chain decomposition of the Boolean lattice.

Khalegh Mamakani - One of the best experts on this subject based on the ideXlab platform.

  • New Roses: Simple Symmetric Venn Diagrams with 11 and 13 Curves
    Discrete & Computational Geometry, 2014
    Co-Authors: Khalegh Mamakani, Frank Ruskey
    Abstract:

    A symmetric $$n$$ n -Venn Diagram is one that is invariant under $$n$$ n -fold rotation, up to a relabeling of curves. A simple $$n$$ n -Venn Diagram is an $$n$$ n -Venn Diagram in which at most two curves intersect at any point. In this paper, we introduce a new property of Venn Diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to Diagrams with crosscut symmetry, we found many simple symmetric Venn Diagrams with 11 curves. The question of the existence of a simple 11-Venn Diagram has been open since the 1960s. The technique used to find the 11-Venn Diagram is extended and a symmetric 13-Venn Diagram is also demonstrated.

  • Graph Drawing - The first simple symmetric 11-Venn Diagram
    Graph Drawing, 2013
    Co-Authors: Khalegh Mamakani, Frank Ruskey
    Abstract:

    An n-Venn Diagram is a collection of n simple closed curves in the plane with the following properties: (a) Each of the $2^n$ different intersections of the open interiors or exteriors of the curves is a non-empty connected region; (b) there are only finitely many points where the curves intersect. If each of the intersections is of only two curves, then the Diagram is said to be simple. The purpose of this poster is to highlight how we discovered the first simple symmetric 11-Venn Diagram.\ud \ud \ud \u

  • the first simple symmetric 11 Venn Diagram
    Graph Drawing, 2012
    Co-Authors: Khalegh Mamakani, Frank Ruskey
    Abstract:

    An n-Venn Diagram is a collection of n simple closed curves in the plane with the following properties: (a) Each of the 2n different intersections of the open interiors or exteriors of the curves is a non-empty connected region; (b) there are only finitely many points where the curves intersect. If each of the intersections is of only two curves, then the Diagram is said to be simple. The purpose of this poster is to highlight how we discovered the first simple symmetric 11-Venn Diagram.

  • a new rose the first simple symmetric 11 Venn Diagram
    arXiv: Computational Geometry, 2012
    Co-Authors: Khalegh Mamakani, Frank Ruskey
    Abstract:

    A symmetric Venn Diagram is one that is invariant under rotation, up to a relabeling of curves. A simple Venn Diagram is one in which at most two curves intersect at any point. In this paper we introduce a new property of Venn Diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to crosscut symmetry we found many simple symmetric Venn Diagrams with 11 curves. This answers an existence question that has been open since the 1960's. The first such Diagram that was discovered is shown here.

  • IWOCA - Generating all simple convexly-drawable polar symmetric 6-Venn Diagrams
    Lecture Notes in Computer Science, 2011
    Co-Authors: Khalegh Mamakani, Wendy Myrvold, Frank Ruskey
    Abstract:

    An n-Venn Diagram consists of n curves drawn in the plane in such a way that each of the 2n possible intersections of the interiors and exteriors of the curves forms a connected non-empty region. A Venn Diagram is convexly-drawable if it can be drawn with all curves convex and it is simple if at most two curves intersect at any point. A Venn Diagram is called polar symmetric if its stereographic projection about the infinite outer face is isomorphic to the projection about the innermost face. We outline an algorithm that shows there are exactly 375 simple convexly drawable polar-symmetric 6-Venn Diagrams.

Sun Kim - One of the best experts on this subject based on the ideXlab platform.

  • Venn-diaNet : Venn Diagram based network propagation analysis framework for comparing multiple biological experiments.
    BMC bioinformatics, 2019
    Co-Authors: Benjamin Hur, Dongwon Kang, Sangseon Lee, Ji Hwan Moon, Gung Lee, Sun Kim
    Abstract:

    The main research topic in this paper is how to compare multiple biological experiments using transcriptome data, where each experiment is measured and designed to compare control and treated samples. Comparison of multiple biological experiments is usually performed in terms of the number of DEGs in an arbitrary combination of biological experiments. This process is usually facilitated with Venn Diagram but there are several issues when Venn Diagram is used to compare and analyze multiple experiments in terms of DEGs. First, current Venn Diagram tools do not provide systematic analysis to prioritize genes. Because that current tools generally do not fully focus to prioritize genes, genes that are located in the segments in the Venn Diagram (especially, intersection) is usually difficult to rank. Second, elucidating the phenotypic difference only with the lists of DEGs and expression values is challenging when the experimental designs have the combination of treatments. Experiment designs that aim to find the synergistic effect of the combination of treatments are very difficult to find without an informative system. We introduce Venn-diaNet, a Venn Diagram based analysis framework that uses network propagation upon protein-protein interaction network to prioritizes genes from experiments that have multiple DEG lists. We suggest that the two issues can be effectively handled by ranking or prioritizing genes with segments of a Venn Diagram. The user can easily compare multiple DEG lists with gene rankings, which is easy to understand and also can be coupled with additional analysis for their purposes. Our system provides a web-based interface to select seed genes in any of areas in a Venn Diagram and then perform network propagation analysis to measure the influence of the selected seed genes in terms of ranked list of DEGs. We suggest that our system can logically guide to select seed genes without additional prior knowledge that makes us free from the seed selection of network propagation issues. We showed that Venn-diaNet can reproduce the research findings reported in the original papers that have experiments that compare two, three and eight experiments. Venn-diaNet is freely available at: http://biohealth.snu.ac.kr/software/Venndianet.

  • Venn-diaNet : Venn Diagram based network propagation analysis framework for comparing multiple biological experiments
    BMC Bioinformatics, 2019
    Co-Authors: Benjamin Hur, Dongwon Kang, Sangseon Lee, Ji Hwan Moon, Gung Lee, Sun Kim
    Abstract:

    Abstract Background The main research topic in this paper is how to compare multiple biological experiments using transcriptome data, where each experiment is measured and designed to compare control and treated samples. Comparison of multiple biological experiments is usually performed in terms of the number of DEGs in an arbitrary combination of biological experiments. This process is usually facilitated with Venn Diagram but there are several issues when Venn Diagram is used to compare and analyze multiple experiments in terms of DEGs. First, current Venn Diagram tools do not provide systematic analysis to prioritize genes. Because that current tools generally do not fully focus to prioritize genes, genes that are located in the segments in the Venn Diagram (especially, intersection) is usually difficult to rank. Second, elucidating the phenotypic difference only with the lists of DEGs and expression values is challenging when the experimental designs have the combination of treatments. Experiment designs that aim to find the synergistic effect of the combination of treatments are very difficult to find without an informative system. Results We introduce Venn-diaNet, a Venn Diagram based analysis framework that uses network propagation upon protein-protein interaction network to prioritizes genes from experiments that have multiple DEG lists. We suggest that the two issues can be effectively handled by ranking or prioritizing genes with segments of a Venn Diagram. The user can easily compare multiple DEG lists with gene rankings, which is easy to understand and also can be coupled with additional analysis for their purposes. Our system provides a web-based interface to select seed genes in any of areas in a Venn Diagram and then perform network propagation analysis to measure the influence of the selected seed genes in terms of ranked list of DEGs. Conclusions We suggest that our system can logically guide to select seed genes without additional prior knowledge that makes us free from the seed selection of network propagation issues. We showed that Venn-diaNet can reproduce the research findings reported in the original papers that have experiments that compare two, three and eight experiments. Venn-diaNet is freely available at: http://biohealth.snu.ac.kr/software/Venndianet

Benjamin Hur - One of the best experts on this subject based on the ideXlab platform.

  • Venn-diaNet : Venn Diagram based network propagation analysis framework for comparing multiple biological experiments.
    BMC bioinformatics, 2019
    Co-Authors: Benjamin Hur, Dongwon Kang, Sangseon Lee, Ji Hwan Moon, Gung Lee, Sun Kim
    Abstract:

    The main research topic in this paper is how to compare multiple biological experiments using transcriptome data, where each experiment is measured and designed to compare control and treated samples. Comparison of multiple biological experiments is usually performed in terms of the number of DEGs in an arbitrary combination of biological experiments. This process is usually facilitated with Venn Diagram but there are several issues when Venn Diagram is used to compare and analyze multiple experiments in terms of DEGs. First, current Venn Diagram tools do not provide systematic analysis to prioritize genes. Because that current tools generally do not fully focus to prioritize genes, genes that are located in the segments in the Venn Diagram (especially, intersection) is usually difficult to rank. Second, elucidating the phenotypic difference only with the lists of DEGs and expression values is challenging when the experimental designs have the combination of treatments. Experiment designs that aim to find the synergistic effect of the combination of treatments are very difficult to find without an informative system. We introduce Venn-diaNet, a Venn Diagram based analysis framework that uses network propagation upon protein-protein interaction network to prioritizes genes from experiments that have multiple DEG lists. We suggest that the two issues can be effectively handled by ranking or prioritizing genes with segments of a Venn Diagram. The user can easily compare multiple DEG lists with gene rankings, which is easy to understand and also can be coupled with additional analysis for their purposes. Our system provides a web-based interface to select seed genes in any of areas in a Venn Diagram and then perform network propagation analysis to measure the influence of the selected seed genes in terms of ranked list of DEGs. We suggest that our system can logically guide to select seed genes without additional prior knowledge that makes us free from the seed selection of network propagation issues. We showed that Venn-diaNet can reproduce the research findings reported in the original papers that have experiments that compare two, three and eight experiments. Venn-diaNet is freely available at: http://biohealth.snu.ac.kr/software/Venndianet.

  • Venn-diaNet : Venn Diagram based network propagation analysis framework for comparing multiple biological experiments
    BMC Bioinformatics, 2019
    Co-Authors: Benjamin Hur, Dongwon Kang, Sangseon Lee, Ji Hwan Moon, Gung Lee, Sun Kim
    Abstract:

    Abstract Background The main research topic in this paper is how to compare multiple biological experiments using transcriptome data, where each experiment is measured and designed to compare control and treated samples. Comparison of multiple biological experiments is usually performed in terms of the number of DEGs in an arbitrary combination of biological experiments. This process is usually facilitated with Venn Diagram but there are several issues when Venn Diagram is used to compare and analyze multiple experiments in terms of DEGs. First, current Venn Diagram tools do not provide systematic analysis to prioritize genes. Because that current tools generally do not fully focus to prioritize genes, genes that are located in the segments in the Venn Diagram (especially, intersection) is usually difficult to rank. Second, elucidating the phenotypic difference only with the lists of DEGs and expression values is challenging when the experimental designs have the combination of treatments. Experiment designs that aim to find the synergistic effect of the combination of treatments are very difficult to find without an informative system. Results We introduce Venn-diaNet, a Venn Diagram based analysis framework that uses network propagation upon protein-protein interaction network to prioritizes genes from experiments that have multiple DEG lists. We suggest that the two issues can be effectively handled by ranking or prioritizing genes with segments of a Venn Diagram. The user can easily compare multiple DEG lists with gene rankings, which is easy to understand and also can be coupled with additional analysis for their purposes. Our system provides a web-based interface to select seed genes in any of areas in a Venn Diagram and then perform network propagation analysis to measure the influence of the selected seed genes in terms of ranked list of DEGs. Conclusions We suggest that our system can logically guide to select seed genes without additional prior knowledge that makes us free from the seed selection of network propagation issues. We showed that Venn-diaNet can reproduce the research findings reported in the original papers that have experiments that compare two, three and eight experiments. Venn-diaNet is freely available at: http://biohealth.snu.ac.kr/software/Venndianet

Neil B. Pride - One of the best experts on this subject based on the ideXlab platform.

  • the proportional Venn Diagram of obstructive lung disease two approximations from the united states and the united kingdom
    Chest, 2003
    Co-Authors: Joan B. Soriano, Kourtney J. Davis, Bobbie Coleman, George Visick, David M. Mannino, Neil B. Pride
    Abstract:

    Study objectives The nonproportional Venn Diagram of obstructive lung disease (OLD) produced for the 1995 American Thoracic Society guidelines has not been quantified. We aim to quantify the proportion of the general population with OLD and the intersections of physician-diagnosed asthma, chronic bronchitis, and emphysema in the United States and the United Kingdom, and to examine the relationship to obstructive spirometry. Design and participants We analyzed data from the US National Health and Nutrition Examination (NHANES) III survey (1988 to 1994) and the UK General Practice Research Database for the year 1998. Results The areas of intersection among the three OLD conditions produced seven mutually exclusive disease groups. The asthma-only group was the largest proportion of OLD patients, accounting for 50.3% and 79.4% of all OLD patients in the United States and the United Kingdom, respectively, and decreased with increasing age. Overall, 17% and 19% of OLD patients in the United States and in the United Kingdom, respectively, reported more than one OLD condition, and this percentage increased with age. According to the spirometry data from NHANES III, only 37.4% of emphysema-only patients had objective airflow obstruction. The prevalence of airflow obstruction was significantly higher among participants with combinations of emphysema and chronic bronchitis (57.7%), with emphysema and asthma (51.9%), and with all three OLD diseases concomitantly (52.0%). Conclusion Concomitant diagnosis of asthma, chronic bronchitis, or emphysema is common among OLD patients from the general population, particularly in adults aged ≥ 50 years.

  • The Proportional Venn Diagram of Obstructive Lung Disease*: Two Approximations From the United States and the United Kingdom
    Chest, 2003
    Co-Authors: Joan B. Soriano, Kourtney J. Davis, Bobbie Coleman, George Visick, David M. Mannino, Neil B. Pride
    Abstract:

    The nonproportional Venn Diagram of obstructive lung disease (OLD) produced for the 1995 American Thoracic Society guidelines has not been quantified. We aim to quantify the proportion of the general population with OLD and the intersections of physician-diagnosed asthma, chronic bronchitis, and emphysema in the United States and the United Kingdom, and to examine the relationship to obstructive spirometry. We analyzed data from the US National Health and Nutrition Examination (NHANES) III survey (1988 to 1994) and the UK General Practice Research Database for the year 1998. The areas of intersection among the three OLD conditions produced seven mutually exclusive disease groups. The asthma-only group was the largest proportion of OLD patients, accounting for 50.3% and 79.4% of all OLD patients in the United States and the United Kingdom, respectively, and decreased with increasing age. Overall, 17% and 19% of OLD patients in the United States and in the United Kingdom, respectively, reported more than one OLD condition, and this percentage increased with age. According to the spirometry data from NHANES III, only 37.4% of emphysema-only patients had objective airflow obstruction. The prevalence of airflow obstruction was significantly higher among participants with combinations of emphysema and chronic bronchitis (57.7%), with emphysema and asthma (51.9%), and with all three OLD diseases concomitantly (52.0%). Concomitant diagnosis of asthma, chronic bronchitis, or emphysema is common among OLD patients from the general population, particularly in adults aged > or = 50 years.