With the recent explosion in the amount, the variety, and the dimensionality of available data, identifying, extracting, and exploiting their underlying structure has become a problem of fundamental ...

Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland National Centre for Computational Design and Discovery of Novel Materials ...

Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks.

Last summer in Barcelona, Joachim Kock floated the idea that there might be a connection between two invariants of graphs: the Tutte polynomial and the magnitude function. Here I’ll explain what these ...

A geometric torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. The standard parametrization of a geometric torus maps ...

A few of us here at the Café decided that it would be good to have a short series of posts in which each of us (at least, each of us who wants to) says something about his overall take on higher ...