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.

  • Eigenvalues of neutral networks: Interpolating between hypercubes

    TRT. ReevesRFR. FarrJBJ. BlundellAGA. GallagherTFT. Fink Discrete Mathematics

    Eigenvalues of neutral networks

    The principal eigenvalue of small neutral networks determines their robustness, and is bounded by the logarithm of the number of vertices.

  • Subcritical U-Bootstrap percolation models have non-trivial phase transitions

    PBBBB. BollobasMPM. PrzykuckiPSP. Smith Transactions of the American Mathematical Society

    Bootstrap percolation models

    A subset of bootstrap percolation models, which stabilise systems of cells on infinite lattices, exhibit non-trivial phase transitions.

  • Maximum percolation time in two-dimensional bootstrap percolation

    FBMPM. Przykucki SIAM Journal on Discrete Mathematics

    Maximum percolation time

    A simple formula gives the maximum time for an n x n grid to become entirely infected having undergone a bootstrap percolation process.