Linkage

Lee Bollinger, president of Columbia University: “No, I won’t start spying on my foreign-born students” (\(\mathbb{M}\)).

Update on the Safe ToC initiative (\(\mathbb{M}\)). Sandy Irani describes progress in combatting harassment and discrimination at theoretical computer science conferences, and calls for volunteer advocates to serve as contact points at conferences.

Escher-like spiral tilings, by Craig Kaplan (\(\mathbb{M}\), via). Sadly with no angels, devils, fish, or geese, but maybe some talented artist will take up that challenge.

How to peel self-intersecting onions (\(\mathbb{M}\)). Gabriel Nivasch extends the conjectured equivalence between convex layers and the affine curve-shortening flow to non-convex and self-intersecting curves. The generalized onion-peeling process alternates between steps that jump over grid points and steps that shrink curves to the shortest curve that passes between the same grid points. See also Gabriel’s animations of this process for grid points and for random points.

New stick number bounds from random sampling of confined polygons (\(\mathbb{M}\)). Tom Eddy and Clayton Shonkwiler do knot theory on large numbers of random 3d polygons, in the process finding polygonal representations of many knots with fewer segments than were known before.

42 is the answer. The question is: What is \((-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3\)?

Who Counts as a Notable Sociologist on Wikipedia? Gender, Race, and the “Professor Test” (\(\mathbb{M}\), via). After authors Adams, Brückner, and Naslund factored out seniority and impact of sociologists, white men remained more likely than others to have Wikipedia articles. Surprisingly to me, the disparity happens at article creation, not deletion. So we should create more articles about women! Or be less quick to create them on borderline-notable men…

Permutations in the real world: 12784563 (\(\mathbb{M}\)). Actually I have sentimental reasons to prefer 15426378, but I couldn’t find a nice photo of that one.

The history of Tetris randomizers (\(\mathbb{M}\), via). Truly uniformly random distributions tend to be more clustered than people expect (having runs of the same piece or of mostly the same piece). So later versions took measures to make the piece distribution less random and more non-clustered.

An \(\Omega(n^2)\) lower bound for random universal sets for planar graphs (\(\mathbb{M}\)). Random subsets of a square act like grids in lots of ways. Here’s one, from the linked preprint: to draw all \(n\)-vertex planar graphs with chosen points as vertices, you need either a grid or a random point set of \(\Theta(n^2)\) points. The reason is that drawings of the nested triangles graph contain a sequence of \(\Omega(n)\) points (corners of bounding boxes of triangles) that’s monotone in both coordinate directions, and smaller random sets (or grids) don’t have such sequences.

CSS polyhedra (\(\mathbb{M}\)). Visualizations of 3d rotating polyhedra, coded entirely in html/css and embeddable in other web pages.

Random minimum spanning trees (\(\mathbb{M}\)). Did you know that in random graphs with edge probability \(1/n\) (just below the appearance of the giant component) there are lots of components of size \(n^{3/2}\) that all look nearly the same as uniformly random spanning trees of a complete graph? And that the minimum spanning tree of a randomly-weighted complete graph, instead, looks like one of these components with a lot of others all glued onto it? Christina Goldschmidt describes her work in this area.

A big list of unlikely or surprising Turing-complete systems (\(\mathbb{M}\), via). My favorite: SVG is Turing-complete because it can be used to (slowly) simulate Rule 110 (and one hopes also simulate the weird boundary conditions needed to make Rule 110 Turing complete).

Milton’s hand-annotated volume of Shakespeare’s plays discovered sitting on a library shelf in Philly (\(\mathbb{M}\), via).

Vojtěch Jarník, now a good article on Wikipedia (\(\mathbb{M}\)). I teach his algorithm for minimum spanning trees in my classes, but lately in my research I’ve been citing him more for his work on the number of integer grid points on convex curves. He also did important work on Diophantine approximation and nowhere-differentiable functions.