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.

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  • Concurrent enhancement of percolation and synchronization in adaptive networks

    YESBGCG. Caldarelli Scientific Reports

    Self-organising adaptive networks

    An adaptive network of oscillators in fragmented and incoherent states can re-organise itself into connected and synchronized states.

  • Emergence of strongly connected components in continuum disk-spin percolation

    FCF. CaravelliMBM. BardosciaFC Journal of Statistical Mechanics

    Clusters of neurons

    Percolation theory shows that the formation of giant clusters of neurons relies on a few parameters that could be measured experimentally.

  • 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.

  • Electronic Journal of Probability

    Percolation on Galton-Watson trees

    The critical probability for bootstrap percolation, a process which mimics the spread of an infection in a graph, is bounded for Galton-Watson trees.