Linkage

Simplicial depth. Measuring how central a point is within a cloud of points by how many other triangles surround it. New Wikipedia article on an important topic in robust statistics.

Catholic outrage at giant robot spider (G+). The semi-official CCCG excursion to see this show made for a fun and memorable evening.

Why automatic citation-counting can be difficult (G+), why it’s important to read and check your references yourself rather than just copying them from earlier publications, and why it’s a good idea to get your bibtex data from a high-quality source like MathSciNet (whose blog the linked post is from).

Graph Drawing accepted papers and IPEC accepted papers. I have two at GD (about which more later) and one at IPEC (previously).

Deep math in the solution to a simple-looking equation (G+, via): find positive integers \(x\), \(y\), and \(z\) with

Arrow’s impossibility theorem for infinitely many voters (G+). In this case, one can construct election decision rules that are unexpectedly nice: every election has an outcome, which matches the preferences of at least one voter, can’t be changed by any finite subset of voters, and behaves monotonically. But they can’t be implemented by any recursive algorithm, and require weak forms of the axiom of choice to even exist.

Rick Anderson reviews Cabell’s List (G+), planned as a replacement for the now-defunct Beall’s List of predatory open-access journals. But it doesn’t distinguish low standards from predatory behavior, and its subscription-only and non-transparent nature are also problematic.

Shapes with the property that every billiard path either repeats or eventually covers the whole shape, rather than chaotically filling some part of the shape and then completely bypassing some other part (G+). Not many are known, but now there are two new ones, both non-convex quadrilaterals with rational angles.

Bubble-blowing clip from BBC’s The Code (G+), with near-polyhedral shapes in the center of clusters of bubbles.

Problem: US is way behind many other countries in connecting individual homes to high-speed internet. Solution: Who needs fast internet when you have cell phones that are only 5x slower? (G+)

What NYC subway stations actually look like. Or would, if we had X-ray vision.

The phenomenon of “crown shyness” where trees avoid touching (G+). Still with no definitive explanation of how or why.

Notes on math and gerrymandering (G+). Jeremy Kun’s notes from the Geometry of Redistricting workshop in Boston, with explanations of why a tangle of legal and political issues make it very difficult to impose simple mathematical solutions.