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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  • Dessins d’enfants, Seiberg-Witten curves and conformal blocks

    JBJ. BaoOFYHY. HeEHE. HirstJR... Journal of High Energy Physics

    QFT and kids’ drawings

    Groethendieck's “children’s drawings”, a type of bipartite graph, link number theory, geometry, and the physics of conformal field theory.

  • Transitions in loopy random graphs with fixed degrees and arbitrary degree distributions

    FAACA. Coolen Sub. to JPhys Complexity

    Transitions in loopy graphs

    The generation of large graphs with a controllable number of short loops paves the way for building more realistic random networks.

  • Memristive networks: from graph theory to statistical physics

    AZA. ZegaracFCF. Caravelli EPL

    Memristive networks

    A simple solvable model of memristive networks suggests a correspondence between the asymptotic states of memristors and the Ising model.

  • Eigenvalues of subgraphs of the cube

    BBJLSL European Journal of Combinatorics

    Hypercube eigenvalues

    Hamming balls, subgraphs of the hypercube, maximise the graph’s largest eigenvalue exactly when the dimension of the cube is large enough.

  • Journal of Physics A

    Exactly solvable random graphs

    An explicit analytical solution reproduces the main features of random graph ensembles with many short cycles under strict degree constraints.

  • Physical Review E

    Spectral partitioning

    The spectral density of graph ensembles provides an exact solution to the graph partitioning problem and helps detect community structure.

  • Physical Review E

    Dynamics of memristors

    Exact equations of motion provide an analytical description of the evolution and relaxation properties of complex memristive circuits.

  • Physical Review E

    Democracy in networks

    Analysis of the hyperbolicity of real-world networks distinguishes between those which are aristocratic and those which are democratic.

  • Forum of Mathematics, Sigma

    Erdős-Ko-Rado theorem analogue

    A random analogue of the Erdős-Ko-Rado theorem sheds light on its stability in an area of parameter space which has not yet been explored.

  • 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.

  • Physical Review Letters

    Easily repairable networks

    When networks come under attack, a repairable architecture is superior to, and globally distinct from, an architecture that is robust.

  • 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.

  • Social Informatics

    Scales in weighted networks

    Information theory fixes weighted networks’ degeneracy issues with a generalisation of binary graphs and an optimal scale of link intensities.

  • Physical Review E

    Unbiased randomization

    Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks.

  • Journal of Physics A

    Tailored random graph ensembles

    New mathematical tools quantify the topological structure of large directed networks which describe how genes interact within a cell.