This is a cool, short paper giving an intuitive proof of the correctness of Strassen's matrix multiplication algorithm. https://arxiv.org/pdf/1708.08083.pdf

It boils down to combining a rotation matrix with an associated non-eigenvector to construct two bases whose multiplication table only involves 7 matrices, due to the symmetries of the rotation. Hence the "7 multiplications suffice" trick.

Some notes math and gerrymandering.

https://jeremykun.com/2017/08/14/notes-on-math-and-gerrymandering/

Turns out, hard to visualize 1M polygonal lines with d3. Got something working, but now sorta not as interested in this particular representation. Maybe something more like a heatmap of random walks?

Like, doing this just feels weird: \( \bigcirc_{i=1}^nf_i := f_1 \circ f_2 \circ \dots \circ f_n \)

The restrictions to "tame distributions" generating the data is, of course, because even weakly learning threshold functions under adversarial noise is known to be NP-hard, and this recent paper extends this to all constant-degree polynomial threshold functions: https://eccc.weizmann.ac.il/report/2017/115

I recently read Michèle Audin's book Remembering Sofya Kovalevskaya. It was a really interesting book. Not exactly biography, not exactly memoir, not exactly math. Has anyone here read it? I'd be interested in your reactions. This is my review: https://blogs.scientificamerican.com/roots-of-unity/review-remembering-sofya-kovalevskaya/

Stable redistricting in road networks: https://11011110.github.io/blog/2017/06/29/stable-redistricting-in.html

A graphon is a limit sequence of (adjacency matrices of) finite graphs, pictured as a function on the unit square. This also works for graph distributions, such as Erdos-Renyi and preferential attachment graphs (pictured below).

Problems in extremal graph theory (eg. find the minimum number of 4 cycles occurring in a graph with \( \Omega(n^2) \) edges) translate nicely to graphons, and vice versa.

Time to justify my presence here...

The Heesch number of a shape is the maximum number of layers of copies of that shape by which you can surround it. Heesch's Problem asks which positive integers can be Heesch numbers. I'll show a few fun new results over a series of blog posts; today, I offer a basic introduction to the topic. http://isohedral.ca/heesch-numbers-part-1/

Author of Math ∩ Programming, PhD from UI Chicago.

Joined Jun 2017