Category Archives: math

Any clues about this Newton iteration formula with Jacobian matrix?

A while ago I wrote about using Boltzmann sampling to generate random instances of algebraic data types, and mentioned that I have some code I inherited for doing the core computations. There is one part of the code that I … Continue reading

Posted in math | Tagged , , , , , , | 8 Comments

The network reliability problem and star semirings

In a previous post I defined the network reliability problem. Briefly, we are given a directed graph whose edges are labelled with probabilities, which we can think of as giving the likelihood of a message successfully traversing a link in … Continue reading

Posted in math | Tagged , , , , , | 9 Comments

Boltzmann sampling for generic Arbitrary instances

tl;dr: I know how to generate random instances of data types in a generic way, and even have some old code that already does all the hard work, but won’t have time to polish and package it until this summer. … Continue reading

Posted in combinatorics, haskell, math, species | Tagged , , , , , | 14 Comments

The network reliability problem

Let be a directed graph with vertices and edges . Multiple edges between the same pair of vertices are allowed. For concreteness’ sake, think of the vertices as routers, and the edges as (one-way) connections. Let denote the set of … Continue reading

Posted in math | Tagged , , , | 17 Comments

A strange representation of Z6

On my other blog I am writing about a proof of the Lucas-Lehmer test, and today in the course of working up some examples I stumbled across this little gem. Let be a monoid, and let denote the subset of … Continue reading

Posted in math | Tagged , , , | 11 Comments

Catsters guide is complete!

About a year and a half ago I announced that I had started creating a guide to the excellent series of category theory YouTube videos by the Catsters (aka Eugenia Cheng and Simon Willerton). I am happy to report that … Continue reading

Posted in haskell, math, teaching | Tagged | 2 Comments

The Species of Bracelets

Summary: The species package now has support for bracelets, i.e. equivalence classes of lists up to rotation and reversal. I show some examples of their use and then explain the (very interesting!) mathematics behind their implementation. I recently released a … Continue reading

Posted in combinatorics, haskell, math, species | Tagged , , | 5 Comments