Linkage

The “you wouldn’t trust a floating point comparison” meme below, by David Amador (\(\mathbb{M}\)) is based on an anti-video-piracy “you wouldn’t steal a…” campaign. So, naturally, I stole the meme for my computational geometry lecture notes.

If you’ve been following recent posts on the fractal behavior of roots of polynomials with coefficients ±1 by John Baez or of the eigenvalues of matrices with coefficients ±1 by Dan Piponi (\(\mathbb{M}\)), or if you’ve been reading Baez’s recent exposition “The Beauty of Roots” with Christensen and Derbyshire in the Notices of the AMS, you might also like “A Murmuration of Zeros” by Jonathan Kujawa in 3 Quarks Daily, on the same constellation of topics. Name-checked in Kujawa’s post: Piponi, Christensen, Derbyshire, and Greg Egan (for his 2011 Littlewood applet). Unfortunately missed: Baez and the Notices article.

MDPI, Frontiers, and Hindawi banned in Malaysia (\(\mathbb{M}\), via). State funds cannot be used to pay for publications in their journals, and those publications will not count in research evaluations. This follows similar bans in Czechia and China. Article is in Vietnamese but readable through Google translate.

The three solutions of \(2^x=x^2\). Two are nice and easy to find. The third is irrational but “annoyingly close to \(-23/30\)”.

The emerging utility of graphons in applied math (\(\mathbb{M}\)) A graphon is just a symmetric measurable function from \([0,1]^2\) to \([0,1]\). It can be used to define a family of probability distributions on graphs, with any number of vertices, by choosing vertices uniformly at random from the unit interval and then using the function to define the probability of including each edge. Graphons can also describe certain limits of infinite sequences of dense graphs. This SIAM News post by Jason Bramburger describes at a high level applications of this formalism to the study of coupled oscillators, pattern formation, and neural networks. In the comments, though, Jeremy Kun points out that graphons have been “emerging” for years now and wonders what they have emerged into.

The University of California library system gives up on paying open-access fees for UC authors in IEEE publications (\(\mathbb{M}\)). The reason they give is that too few UC authors of IEEE publications are making their papers open-access, and too few of those are covering the charges with their own grants, making the libraries’ coverage of the charges expensive and insufficiently helpful. My own current NSF grant does not cover this sort of charge, so I rely on institutional support to pay this sort of fee, when possible. I realize that the “it’s too expensive” and “we’re only paying this for a small fraction of papers” arguments appear contradictory but that’s what the link says.

Nobel Prize winner Katalin Karikó on “how to support shunned scholars like her” (\(\mathbb{M}\), unpaywalled copy). Karikó was kicked out of Temple University and demoted at the University of Pennsylvania for following her unconventional research path. But the Chronicle article emphasizes Karikó’s preference not to point fingers of blame at the academic system for failing to support her. Instead, she wants to credit Penn researchers Elliot Barnathan and David Langer for fighting to continue her research program when she was in danger of having no way of doing so, and she is looking for ways to reward that kind of advocacy and provide similar support to future researchers.

Elastic-beam and stretchable fabric tensegrity surface by Alison Martin.

A new method of faking citation counts (\(\mathbb{M}\)): submit metadata to the citation-counting sites that list more citations than are actually present in the papers they describe. “It isn’t clear who is manipulating the metadata files or whether the issue is due to a technical glitch.” This apparently doesn’t affect Google Scholar because GS mines its own metadata from the papers themselves.

Quivers, a type of directed multigraph with a “powerquiver” construction analogous to powersets of sets. Oscar Cunningham for the “supergraph” Mathober prompt. Just like a set corresponds to a subset of a powerset (the subset of its singleton sets), any quiver corresponds to a subgraph of its powerquiver.

How to use SSE to transpose bit-packed binary matrices (\(\mathbb{M}\)). These are the “Streaming SIMD Extensions”, long part of the Intel x86 architecture. As for why you would want to transpose this kind of matrix: suppose, for instance, that you have a directed graph, with the set of outgoing neighbors of each vertex packed into a set represented in this way. Then a transpose gets you the incoming neighbors, represented in the same way. Or suppose you have an undirected graph, packed into a triangular matrix, like in graph6 format. It’s relatively easy to pad that out into a square matrix, but that gives you only the adjacencies in one direction between each pair of vertices. You want them in both directions, in one matrix? Transpose and do a bitwise binary or. I don’t know how to do this with anywhere near the same efficiency on a conventional random-access architecture with the C repertoire of bitwise operations. You could pack \(\sqrt{\log n}\times\sqrt{\log n}\) subarrays into words and do lookups in a table of size \(n\), but the \(n\) for which this is practical is significantly smaller than for SSE and I think the overhead of setting it up would be higher. I might have expected to find something about this problem in Arndt’s Matters Computational but I didn’t see it there.

At the latest Grace Hopper Celebration, “an event meant to be a career-builder for women and nonbinary tech workers turned into yet another symbol of the industry’s gender imbalance after self-identifying men showed up in droves” (\(\mathbb{M}\)). I had been hesitating to link this earlier this out of concern that it might be a stealth TERF narrative, but the NPR story makes clear that no, it was “men with he/him pronouns on their nametags” taking over an event intended to be a safe and inclusive space for women and non-binary people in tech. It’s not entirely clear whether future offerings of the event can legally ban men, or even whether they want to: an organizer is quoted as saying that “male allyship is necessary”. But the men described in the link don’t sound like allies, and forcing or allowing all events to be governed by the tyranny of the majority is itself harmful.

The insides of a paperfolded excavated dodecahedron, Paula Beardell Krieg.

A nowhere-neat tessellation of the hyperbolic plane modeled after the binary tiling but using golden-ratio rectangles in two orientations rather than horizontal dominos. “Nowhere neat” means that no two tiles meet edge-to-edge; the herringbone tiling of the Euclidean plane is a more familiar example.

Rubik’s cubes arranged to display a trefoil knot rather than the more familiar “solved” state with six blank faces.