Occasionally I will post here about things I find interesting.
Why is my train always late? Do lightbulbs last longer than they should? These questions can be answered with the waiting time paradox and the inspection paradox.
Julia sets and the Mandelbrot set arise naturally in complex dynamics. We explore some of their properties and methods for plotting them.
A software package for motif-based spectral clustering of weighted directed networks.
To complement my earlier post on Goodstein sequences, I wrote a Python script to calculate them.
The Dirichlet problem is an important boundary value problem, with applications in physics. Although hard to solve analytically, we can construct probabilistic approximations using continuous local martingales.
Goodstein sequences grow fast and appear to diverge to infinity. But a neat application of ordinal arithmetic gives a surprising result.
The notion of modes of convergence is central to probability theory. This short article focuses on the relative strengths of these convergences, and includes a helpful diagram.