ԷՅԼԵՐԻ ՄԵԹՈԴՈՎ ՈՐՈՇ ՏԵՔՍՏԱՅԻՆ ԽՆԴԻՐՆԵՐԻ ԼՈՒԾՈՒՄԸ ՈՐՊԵՍ ՍՈՎՈՐՈՂՆԵՐԻ ՏԵՍՈՂԱԿԱՆ ՄՏԱԾՈՂՈՒԹՅԱՆ ԶԱՐԳԱՑՄԱՆ ԱՌԱՆՁՆԱՀԱՏՈՒԿ ՄԱԹԵՄԱՏԻԿԱԿԱՆ ՄԻՋՈՑ / SOLUTION OF SOME TEXT PROBLEMS BY EULER'S METHOD AS A UNIQUE MATHEMATICAL TOOL FOR DEVELOPING VISUAL THINKING OF STUDENTS

Հոդվածում դիտարկված է Էյլերի տրամագրերի (դիագրամների) միջոցով մաթեմատիկայի դասընթացից բազմություններին առնչվող որոշ խնդիրների լուծման նոր մեթոդական հնար, որը հնարավորություն է տալիս առավել դյուրացնել և ակնառու դարձնել տեքստային խնդիրների լուծումը՝ զարգացնելով սովորողների տեսողական մտածողությունըֈ:/ The article touches upon a new methodological approach to solving some textual mathematical tasks associated with sets using Euler diagrams, which facilitates the solution of mathematical tasks, developing the visual thinking of students.

Euler diagrams drawn with ellipses area-proportionally (Edeap)

BackgroundArea-proportional Euler diagrams are frequently used to visualize data from Microarray experiments, but are also applied to a wide variety of other data from biosciences, social networks and other domains.ResultsThis paper details Edeap, a new simple, scalable method for drawing area-proportional Euler diagrams with ellipses. We use a search-based technique optimizing a multi-criteria objective function that includes measures for both area accuracy and usability, and which can be extended to further user-defined criteria. The Edeap software is available for use on the web, and the code is open source. In addition to describing our system, we present the first extensive evaluation of software for producing area-proportional Euler diagrams, comparing Edeap to the current state-of-the-art; circle-based method, venneuler, and an alternative ellipse-based method, eulerr.ConclusionsOur evaluation—using data from the Gene Ontology database via GoMiner, Twitter data from the SNAP database, and randomly generated data sets—shows an ordering for accuracy (from best to worst) of eulerr, followed by Edeap and then venneuler. In terms of runtime, the results are reversed with venneuler being the fastest, followed by Edeap and finally eulerr. Regarding scalability, eulerr cannot draw non-trivial diagrams beyond 11 sets, whereas no such limitation is present in Edeap or venneuler, both of which draw diagrams up to the tested limit of 20 sets.

Set Visualisations with Euler and Hasse Diagrams

This paper discusses set visualisations with concept lattices in the sense of Formal Concept Analysis (FCA) in contrast to visualisations with Euler diagrams. Both types of visualisations have advantages and disadvantages. Because of the connection between both fields and the body of knowledge that exists in both fields it is of interest to investigate whether results from either field can contribute to the other.

DynaVenn: web-based computation of the most significant overlap between ordered sets

Background In many research disciplines, ordered lists are compared. One example is to compare a subset of all significant genes or proteins in a primary study to those in a replication study. Often, the top of the lists are compared using Venn diagrams, ore more precisely Euler diagrams (set diagrams showing logical relations between a finite collection of different sets). If different cohort sizes, different techniques or algorithms for evaluation were applied, a direct comparison of significant genes with a fixed threshold can however be misleading and approaches comparing lists would be more appropriate. Results We developed DynaVenn, a web-based tool that incrementally creates all possible subsets from two or three ordered lists and computes for each combination a p-value for the overlap. Respectively, dynamic Venn diagrams are generated as graphical representations. Additionally an animation is generated showing how the most significant overlap is reached by backtracking. We demonstrate the improved performance of DynaVenn over an arbitrary cut-off approach on an Alzheimer’s Disease biomarker set. Conclusion DynaVenn combines the calculation of the most significant overlap of different cohorts with an intuitive visualization of the results. It is freely available as a web service at http://www.ccb.uni-saarland.de/dynavenn.