Notes by Juan M. Bello-Rivas https://superadditive.com/notes/ Memoranda on various topics of interest en-us 1440 jmbr@superadditive.com (Juan M. Bello-Rivas) https://superadditive.com/images/favicon.png Notes by Juan M. Bello-Rivas https://superadditive.com/notes/ Diffusion on Penrose tilings https://superadditive.com/notes/diffusion-on-penrose-tilings https://superadditive.com/notes/diffusion-on-penrose-tilings Have you ever wondered what the wavefront of heat propagation on a Penrose tiling looks like? Wonder no more! jmbr@superadditive.com (Juan M. Bello-Rivas) Sun, 05 Apr 2026 08:59:22 -0700 Introduction to graph neural networks https://superadditive.com/notes/intro-to-gnns https://superadditive.com/notes/intro-to-gnns Introduction to graph neural networks. jmbr@superadditive.com (Juan M. Bello-Rivas) Thu, 24 Apr 2025 20:14:58 -0700 Slides on the original transformer paper https://superadditive.com/notes/review-of-attention-is-all-you-need https://superadditive.com/notes/review-of-attention-is-all-you-need Slides of a presentation on transformers. jmbr@superadditive.com (Juan M. Bello-Rivas) Sat, 30 Nov 2024 19:30:00 -0800 Visual proof of the arithmetic-geometric mean inequality https://superadditive.com/notes/arithmetic-geometric-mean-inequality https://superadditive.com/notes/arithmetic-geometric-mean-inequality Animation of a visual proof of the arithmetic-geometric mean inequality. jmbr@superadditive.com (Juan M. Bello-Rivas) Wed, 31 Jan 2024 22:29:26 -0800 Divergent mean first passage time https://superadditive.com/notes/divergent-mean-first-passage-time https://superadditive.com/notes/divergent-mean-first-passage-time An example of a first passage time without a mean. jmbr@superadditive.com (Juan M. Bello-Rivas) Wed, 23 Nov 2022 00:00:00 -0800 Computing π using atoms https://superadditive.com/notes/computing-pi-using-atoms https://superadditive.com/notes/computing-pi-using-atoms Everyone knows it's possible to compute π by throwing darts at random but it's not so well known that you can calculate it by simulating an atom in a periodic box. jmbr@superadditive.com (Juan M. Bello-Rivas) Tue, 15 Nov 2022 00:00:00 -0800 Expectation of non-negative random variables https://superadditive.com/notes/expectation-non-negative-random-variables https://superadditive.com/notes/expectation-non-negative-random-variables Some proofs of formulas for the expectation of non-negative random variables in the discrete and absolutely continuous case jmbr@superadditive.com (Juan M. Bello-Rivas) Mon, 14 Nov 2022 00:00:00 -0800 Linear least squares regression on graph cycles https://superadditive.com/notes/linear-least-squares-regression-on-graph-cycles https://superadditive.com/notes/linear-least-squares-regression-on-graph-cycles Estimation of the weights of a directed, weighted graph from samples, knowing that the true weights satisfy a set of linear constraints determined by the closed paths within the graph. jmbr@superadditive.com (Juan M. Bello-Rivas) Fri, 12 Jun 2020 00:00:00 -0700