11011110
About All posts
« Five-arc fractal

Linkage

Aug 31, 2025

  • 3d and layered QR codes (\(\mathbb{M}\)). The QR code spec only measures the darkness of image pixels near the centers of grid points, allowing a lot of freedom to use the rest for decorative purposes.

  • AI slop and the destruction of knowledge (\(\mathbb{M}\)). Elsevier caught adding incorrect AI-generated definitions of technical terms both to its own web sites and as links embedded within published journal articles.

  • Elegant mathematics bending the future of design (\(\mathbb{M}\), via ACM TechNews): a team involving Klara Mundilova at EPFL develops a system to design rigid curved beams bent into developable surfaces from flat strips.

  • Here’s a photo from the Palais des Congrès de Montréal (\(\mathbb{M}\)), where the SIAM/CAIMS joint meeting was held two weeks ago. The convention center is filled with large-scale artworks, but I found most of them kind of cold and impersonal and corporate. This one usually doesn’t even look like art, just a part of the architecture. But caught in the right light and by surprise, it could take you to another space. I hope I managed to convey some of that transformational effect in the image. It’s called “Translucide” (2002), by Jean-François Cantin, Michel Lemieux, and Victor Pilon.

    In the west foyer of the Palais des Congrès de Montréal, sunlight streams through a wall of rectangular stained glass panels, tiling the floor with trapezoids of color. Through the panels can be seen the trees of Jean-Paul-Riopelle Place, people among the trees, and more buildings behind the trees. A man walks through the foreground in business casual clothes, a tote bag over his shoulder, face turned towards the stained glass wall behind him; his shoes, shoulders, and the top of his head are colored red like the floor below him.

  • An AI-generated bifurcation plot for a dynamical system, in an AI-generated arXiv preprint, would be pretty enough as an artistic impression of a plot rather than something mathematically meaningful, if it weren’t for the mangled and misplaced axis labels.

  • Sergey Avvakumov and Alfredo Hubard construct cubical spheres with many facets (\(\mathbb{M}\)), blog post by Gil Kalai based on “Cubulating the sphere with many facets”, arXiv:2503.18047.

  • Another newly passed Wikipedia Good Article: Matroid parity problem (\(\mathbb{M}\)). Matroids generalize independence in linear algebra. If you have any matrix, you can find a basis for its column space by choosing columns greedily, checking only that each chosen column is independent of the others you have already chosen. But in the matroid parity problem, the columns come in pairs and you want to find a maximum independent set of paired columns. Another way to think about this is that each pair of columns defines a two-dimensional space, a plane, and you are trying to find a family of \(k\) of these planes that spans a full \(2k\)-dimensional space, for \(k\) as large as possible.

    Why? See the article for details, but algorithms for this problem have applications including approximating the largest planar subgraph of a given graph, in finding the highest-genus surface on which a given graph can be embedded, and in pinning into place two-dimensional bar-and-hinge linkages.

  • Numberphile with Richard Elwes on subcubic graph numbers (\(\mathbb{M}\)). Beyond the mystique of big numbers, this connects to some central topics in graph minor theory; a second video gets more into that.

  • Three-page topological book embeddings of knots and links. This allows each knot or link to be specified by a constant number of bits per spine crossing, specifying which pages the two arcs at that crossing belong to and whether they go up or down in those pages.

  • Non-periodic tilings of rectangles with aspect ratio \(\sqrt[4]2\), generated recursively from a partition of one of these nearly-square rectangles into five similar rectangles.

  • Call for papers: 17th Latin American Theoretical Informatics Symposium (LATIN) (\(\mathbb{M}\)), to be held next April in Florianópolis, Brazil. The submission deadline is October 6 for abstracts and October 13 for the full papers. I’ve enjoyed the past LATIN conferences I’ve gone to; it takes papers from a wide variety of topics in theoretical computer science, and more than many other theory conferences I get the impression that the audience is paying attention and interested.

  • Default search engine: Wikipedia (\(\mathbb{M}\), via). It used to be the case that Wikipedia’s search engine was so weak that I would use Google when I knew that the result I was looking for was a Wikipedia article, and Google would find it. But now the search powers of Google and the like have deteriorated so much (and been taken over by so much AI slop) that, according to Awal, it works better to make your default (not only) search engine be Wikipedia. Which of course leads to the question quis pro quaerentes quaerit: if one is using search to find content to edit Wikipedia, it’s not going to work to search for that content on Wikipedia. So in the face of the deterioration of other search engines, where do we go?

  • US plans to limit international students to a fixed-length stay of four years, shorter than the length of many doctorates (\(\mathbb{M}\), via).

  • The Noperthedron: A convex polyhedron without Rupert’s property (\(\mathbb{M}\)). New preprint by Jakob Steininger and Sergey Yurkevich. The name is from “Some upsetting things about shapes that we already knew” by Tom Murphy.

  • David Eppstein

Geometry, graphs, algorithms, and more