Categorifications from planar diagrammatics

A diagrammatic presentation of functors and natural transformations and the virtues of biadjointness are discussed. We then review a graphical description of the category of Soergel bimodules and a diagrammatic categorification of positive halves of quantum groups. These notes are a write-up of Takagi lectures given by the author in Hokkaido University in June 2009.Comment: 30 pages, latex, ep

Graphics for relatedness research

Studies of relatedness have been crucial in molecular ecology over the last decades. Good evidence of this is the fact that studies of population structure, evolution of social behaviours, genetic diversity and quantitative genetics all involve relatedness research. The main aim of this article is to review the most common graphical methods used in allele sharing studies for detecting and identifying family relationships. Both IBS and IBD based allele sharing studies are considered. Furthermore, we propose two additional graphical methods from the field of compositional data analysis: the ternary diagram and scatterplots of isometric log-ratios of IBS and IBD probabilities. We illustrate all graphical tools with genetic data from the HGDP-CEPH diversity panel, using mainly 377 microsatellites genotyped for 25 individuals from the Maya population of this panel. We enhance all graphics with convex hulls obtained by simulation and use these to confirm the documented relationships. The proposed compositional graphics are shown to be useful in relatedness research, as they also single out the most prominent related pairs. The ternary diagram is advocated for its ability to display all three allele sharing probabilities simultaneously. The log-ratio plots are advocated as an attempt to overcome the problems with the Euclidean distance interpretation in the classical graphics.Peer ReviewedPostprint (published version

On network modeling of manufacturing and related processes using GERT Summary report

Network modeling of manufacturing and related processes using Graphical Evaluation and Review Techniqu

More on Keynes and the Classics

This paper provides a simple, graphical review of the Keynes versus the classics debate. It focuses on four key issues: the roles of ¡ãexible wages and the velocity of money as well as the determination interest rates and the nominal price level. Its aim is to improve upon the rather bland presentation of Keynes' model usually found in textbooks and to give students a sense of the point counterpoint of this important debate.

Four GERT views of planning R and D projects

Graphical evaluation and review technique for research and development planning proces