Notes on software engineering, distributed systems, probability, and mathematics, with the occasional production war story and proof worked out in the open.https://julian.bayardo.info/https://julian.bayardo.info/post/using-scripts-windows/https://julian.bayardo.info/post/using-scripts-windows/Windows has no shebang line, so running C# and Python scripts is clunky. Here is how I make them feel native in PowerShell using dotnet-script and uv.Sun, 23 Feb 2025 15:53:00 GMThttps://julian.bayardo.info/post/the-effect-of-barriers/https://julian.bayardo.info/post/the-effect-of-barriers/When you fan out work and wait for all of it, the slowest sub-task sets your latency. Working out how badly that scales with k, and what you can do about it.Thu, 03 Oct 2024 07:00:00 GMThttps://julian.bayardo.info/post/pacemaker/https://julian.bayardo.info/post/pacemaker/Working out a probabilistic scheme to spread P2P downloads over time so thousands of machines do not stampede one producer whenever a fresh 200GB file appears.Mon, 19 Aug 2024 03:53:00 GMThttps://julian.bayardo.info/post/sketching-lru/https://julian.bayardo.info/post/sketching-lru/Approximating LRU eviction on a disk-resident key-value store with a quantile sketch over last-access times, instead of keeping an in-memory ordered list.Mon, 01 Apr 2024 03:53:00 GMThttps://julian.bayardo.info/post/fun-bugs-part-1/https://julian.bayardo.info/post/fun-bugs-part-1/A fun production race condition from the CloudBuild Cache, where disposing a StackExchange.Redis connection at the wrong moment quietly broke our fast path.Mon, 14 Sep 2020 08:41:00 GMThttps://julian.bayardo.info/post/emacs-on-windows-in-2020/https://julian.bayardo.info/post/emacs-on-windows-in-2020/Running emacs natively on Windows is painful. Here is how I got a fast, HiDPI-friendly setup using WSL and X410 with X11 forwarding in about five minutes.Sun, 13 Sep 2020 06:02:00 GMThttps://julian.bayardo.info/post/a-year-at-microsoft/https://julian.bayardo.info/post/a-year-at-microsoft/A lot has changed in the last couple of years for me. I did my first internship at Microsoft in 2016, which led to two more internships at Microsoft and one at Google. After that, roughly in mid 2018, I received my full…Sat, 02 May 2020 18:35:00 GMThttps://julian.bayardo.info/post/nch-closing-the-gap/https://julian.bayardo.info/post/nch-closing-the-gap/Filling the gaps the brief Non-Convex Hull paper leaves out: why its two formulations are equivalent, and where the per-point radii actually come from.Tue, 21 Aug 2018 04:10:11 GMThttps://julian.bayardo.info/post/nch-roto-translation-invariant/https://julian.bayardo.info/post/nch-roto-translation-invariant/The first proof from my surface-reconstruction thesis, showing the Non-Convex Hull implicit function is invariant to rotation and translation of the input points.Mon, 20 Aug 2018 22:23:28 GMThttps://julian.bayardo.info/post/processing-trees-recursion-schemes/https://julian.bayardo.info/post/processing-trees-recursion-schemes/Rebuilding a production decision-tree engine in Haskell using recursion schemes and Edward Kmett's recursion-schemes library, instead of an ad-hoc scripting language.Sat, 02 Jun 2018 23:51:15 GMThttps://julian.bayardo.info/post/understanding-modulo-bias/https://julian.bayardo.info/post/understanding-modulo-bias/A formal look at why rand() % k skews away from a uniform distribution, how large the bias actually gets, and how to sample a range without it.Wed, 02 May 2018 23:26:06 GMThttps://julian.bayardo.info/post/yet-another-proof-of-brookes-theorem/https://julian.bayardo.info/post/yet-another-proof-of-brookes-theorem/An alternative proof of the classic graph-coloring bound that any graph needs at most maximum-degree plus one colors, avoiding the usual greedy argument.Sat, 30 Apr 2016 23:28:23 GMThttps://julian.bayardo.info/post/matrix-trace-characterization/https://julian.bayardo.info/post/matrix-trace-characterization/A study-break proof working through the trace of a matrix: linearity, invariance under transpose and similarity, and why tr(AB) equals tr(BA).Fri, 24 Jul 2015 23:09:13 GMT