Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each paper is the result of many months of research, so we make a special effort to make them clear, beautiful and inspirational, and publish them in leading journals.
The principal eigenvalue of small neutral networks determines their robustness, and is bounded by the logarithm of the number of vertices.
A subset of bootstrap percolation models, which stabilise systems of cells on infinite lattices, exhibit non-trivial phase transitions.
A simple formula gives the maximum time for an n x n grid to become entirely infected having undergone a bootstrap percolation process.