Linkage

A tutorial on how to use Inkscape to make nice mathematical diagrams quickly enough for real-time note-taking in mathematical lectures (\(\mathbb{M}\), via). It’s from 2019, so doesn’t take advantage of newer features of Inkscape released since then. I use Illustrator, but without a site license it’s expensive; the other free program many of our students use is Ipe, more oriented to PDF than SVG but with good TeX integration.

Cop-win graph (\(\mathbb{M}\)), now a Wikipedia Good Article. It was the last of my current nominations, so it may be a while until the next. These are graphs on which a cop can catch a robber in a game where they alternate moving on edges or staying put, as I discussed in an earlier post. The GA reviewer made me take out as unsourced a statement that a recognition algorithm of Spinrad 2004 uses time \(O(mn/\log n)\), faster than the bound of \(O(n^3/\log n)\) from Spinrad’s paper. But I still think it’s true.

Lights out game on a grid (\(\mathbb{M}\)). This is the puzzle where you have to turn out all of a given set of lights on a grid graph using switches that flip the state of any grid cell and all of its neighbors. It’s just solving sparse systems of linear equations over \(\mathbb{F}_2\), but Gaussian elimination is slow and the usual form of nested dissection requires full-rank matrices. Instead Chao Xu describes an \(O(n^3)\)-time algorithm.

Stanford mathematics professor Brian Conrad takes a deeper look at the proposed revisions to the California Math Framework for high school mathematics (\(\mathbb{M}\), via), finding an “abundance of false or misleading citations”, “misrepresentations of facts and evidence”, “guidance lacking details essential for implementation or seeming to be opinions rather than evidence-based”, and “bias toward data science … based on misinformation and hype”.

A twisty mechanical puzzle with exponential solution length inspires Henry Segerman to ask: are superexponential puzzles possible?

Progress in polyhedral combinatorics (\(\mathbb{M}\), via): convex polytopes cannot have fewer intermediate-dimensional faces than the smaller of their numbers of facets or vertices.

Steven Clontz reviews Games for Your Mind (\(\mathbb{M}\)), by Jason Rosenhouse, in Notices of the AMS. It’s about logic puzzles in the style of Lewis Carroll and Raymond Smullyan, but the review has a broader focus on puzzles and metapuzzles more generally.

Digital marbling (\(\mathbb{M}\)). A recent physics-based simulation project for paper marbling, by Amanda Ghassaei, who was also responsible for an origami simulator that I linked with a different url a few years ago.

The information Elsevier tracks and resells about the scientists who access its journals (\(\mathbb{M}\), via). An EU GDPR personal information request reveals not just dates and times from journal paper reading, writing, and reviewing data but also user names, phone numbers, and bank account information, whether you read the emails from them, and a huge list of the spam newsletters that they subscribe you to.

Terry Tao tries to make mathematical sense of notations like \(\pm\) or \(O(\dots)\) (\(\mathbb{M}\)) that specify something partially rather than exactly. It’s a long post, but I think much less technical than most of Tao’s posts.

Pandemic at the conference (\(\mathbb{M}\)): ACM CHI, the annual conference in computer–human interaction, was held in a hybrid format with 1900 physical attendees in New Orleans a week ago. It became a coronavirus superspreader event, despite its vaccine and mask mandates.

The mystery of who wrote a mathematics paper in a special issue, heavily based on the work of the highly-cited special issue editor (\(\mathbb{M}\)). It’s by someone who doesn’t seem to exist at a college that doesn’t exist. But the special issue editor can show emails from the author, so that’s something. Searching MathSciNet for similarly-titled works produces confidence-inspiring journals like Chaos, Solitons, and Fractals and Fuzzy Sets and Systems, but this one isn’t indexed.

May 12th was chosen as a day to globally celebrate women in mathematics (\(\mathbb{M}\)). It was the birthday of Maryam Mirzakhani (1977–2017), the first and so far only woman to win the Fields Medal. The link lists celebration events continuing for a month or so.

Polyomino loops (\(\mathbb{M}\)). Matthew Yuan wonders, if you play billiards in a polyomino and try shooting a ball diagonally from the midpoint of each of the polyomino edges, how to count the number of loops that these billiard paths will link up into. It’s somewhat related to the African lusona drawings that I discussed in an earlier post.

Collecting sensitive survey responses privately (\(\mathbb{M}\)). This excerpt by Jeremy Kun from his book-in-progress on practical programming techniques is about randomized response, a method for collecting accurate information from survey respondents on whether they may have participated in an illegal activity (like, say, abortion in the US in the 1960s) without revealing the identities of the participants to the data collectors. Similar ideas of preventing inferences about individuals in data sets also led to the development of differential privacy.