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

VennDiagramWeb: a web application for the generation of highly customizable Venn and Euler diagrams.

BackgroundVisualization of data generated by high-throughput, high-dimensionality experiments is rapidly becoming a rate-limiting step in computational biology. There is an ongoing need to quickly develop high-quality visualizations that can be easily customized or incorporated into automated pipelines. This often requires an interface for manual plot modification, rapid cycles of tweaking visualization parameters, and the generation of graphics code. To facilitate this process for the generation of highly-customizable, high-resolution Venn and Euler diagrams, we introduce VennDiagramWeb: a web application for the widely used VennDiagram R package. VennDiagramWeb is hosted at http://venndiagram.res.oicr.on.ca/ .ResultsVennDiagramWeb allows real-time modification of Venn and Euler diagrams, with parameter setting through a web interface and immediate visualization of results. It allows customization of essentially all aspects of figures, but also supports integration into computational pipelines via download of R code. Users can upload data and download figures in a range of formats, and there is exhaustive support documentation.ConclusionsVennDiagramWeb allows the easy creation of Venn and Euler diagrams for computational biologists, and indeed many other fields. Its ability to support real-time graphics changes that are linked to downloadable code that can be integrated into automated pipelines will greatly facilitate the improved visualization of complex datasets. For application support please contact [email protected]

Design of teaching materials informed by consideration of learning-impaired students

The general aim of this project is to fundamentally re-think the design of teaching materials in view of what is now known about cognitive deficits and about what Howard Gardner has termed ‘multiple intelligences’. The applicant has implemented this strategy in two distinct areas, the first involving the writing of an English language programme for Chinese speakers, the second involving the construction of specialized equipment for teaching elementary logic to blind students. The next phase (for which funding is sought) is to test the effectiveness of the logic device, because in theory – the one to be tested – materials the design of which is informed by the above rationale will provide a richer learning experience for non-impaired users

Formal logic: Classical problems and proofs

Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational

Prolegomena to a non-equilibrium quantum statistical mechanics

We suggest that the framework of quantum information theory, which has been developing rapidly in recent years due to intense activity in quantum computation and quantum communication, is a reasonable starting point to study non-equilibrium quantum statistical phenomena. As an application, we discuss the non-equilibrium quantum thermodynamics of black hole formation and evaporation.Comment: 20 pages, LaTeX with elsart.cls, 8 postscript figures. Special issue on quantum computation of Chaos, Solitons, and Fractal

A-Lister: a tool for analysis of differentially expressed omics entities across multiple pairwise comparisons.

BackgroundResearchers commonly analyze lists of differentially expressed entities (DEEs), such as differentially expressed genes (DEGs), differentially expressed proteins (DEPs), and differentially methylated positions/regions (DMPs/DMRs), across multiple pairwise comparisons. Large biological studies can involve multiple conditions, tissues, and timepoints that result in dozens of pairwise comparisons. Manually filtering and comparing lists of DEEs across multiple pairwise comparisons, typically done by writing custom code, is a cumbersome task that can be streamlined and standardized.ResultsA-Lister is a lightweight command line and graphical user interface tool written in Python. It can be executed in a differential expression mode or generic name list mode. In differential expression mode, A-Lister accepts as input delimited text files that are output by differential expression tools such as DESeq2, edgeR, Cuffdiff, and limma. To allow for the most flexibility in input ID types, to avoid database installation requirements, and to allow for secure offline use, A-Lister does not validate or impose restrictions on entity ID names. Users can specify thresholds to filter the input file(s) by column(s) such as p-value, q-value, and fold change. Additionally, users can filter the pairwise comparisons within the input files by fold change direction (sign). Queries composed of intersection, fuzzy intersection, difference, and union set operations can also be performed on any number of pairwise comparisons. Thus, the user can filter and compare any number of pairwise comparisons within a single A-Lister differential expression command. In generic name list mode, A-Lister accepts delimited text files containing lists of names as input. Queries composed of intersection, fuzzy intersection, difference, and union set operations can then be performed across these lists of names.ConclusionsA-Lister is a flexible tool that enables the user to rapidly narrow down large lists of DEEs to a small number of most significant entities. These entities can then be further analyzed using visualization, pathway analysis, and other bioinformatics tools

Entropic Bell inequalities

We derive entropic Bell inequalities from considering entropy Venn diagrams. These entropic inequalities, akin to the Braunstein-Caves inequalities, are violated for a quantum-mechanical Einstein-Podolsky-Rosen pair, which implies that the conditional entropies of Bell variables must be negative in this case. This suggests that the satisfaction of entropic Bell inequalities is equivalent to the non-negativity of conditional entropies as a necessary condition for separability