# Notes

Here is a collection of miscellaneous notes:

**Learning information theory with hangman.** For a game of hangman with a
three-letter word, in which X is the probability space of the first letter (26
elements) and Y is the probability space of the last two leters (26^2
elements), I consider various information theoretic quantities (e.g. joint
entropy H(X,Y), conditional entropy H(Y|X), and the mutual information I(X;Y)).
Updated 11/26/20.

**Implementation of artificial boundary conditions in simulations of the 1D and 2D Fokker-Planck equations.**
The Fokker-Planck equation (FPE) describes the time-evolution of a probability
distribution subject to deterministic drift and stochastic diffusion.
Simulating this partial differential equation on a grid requires some care,
especially at the boundaries, to ensure no probability “leaks out.” Here I
explicitly report how to properly implement boundary conditions to ensure that
no leakage occurs with matrix equations for a 1D FPE equation, and
qualitatively explain how this approach may be extended to 2D (and
higher-dimensional) FPE equations. Updated 10/6/20.