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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  • Flowers of immortality

    TFT. FinkYHY. He Draft for Journal of Physics A

    Flowers of immortality

    The eigenvalues of the mortality equation fall into two classes—the flower and the stem—but only the stem eigenvalues control the dynamics.

  • Regulatory motifs: structural and functional building blocks of genetic computation

    TFT. Fink Draft for Proceedings of the National Academy of Sciences of the USA

    Structure of genetic computation

    The structural and functional building blocks of gene regulatory networks correspond, which tell us how genetic computation is organised.

  • Biological logics are restricted

    TFT. FinkRHR. Hannam Sub. to Proceedings of the National Academy of Sciences of the USA

    In life, there are few rules

    The bipartite nature of regulatory networks means gene-gene logics are composed, which severely restricts which ones can show up in life.

  • Mortality equation offers a theory for programmed aging

    TFT. Fink Draft for Physical Review X

    I want to be forever young

    The mortality equation governs the dynamics of an evolving population with a given maximum age, offering a theory for programmed ageing.

  • Draft for Physical Review E

    Biological logics are restricted

    The fraction of logics that are biologically permitted can be bounded and shown to be tiny, which makes inferring them from experiments easier.

  • Draft for Proceedings of the London Mathematical Society

    Ample and pristine numbers

    Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.

  • Harvard Business Review

    Taming complexity

    Insights from biology, physics and business shed light on the nature and costs of complexity and how to manage it in business organizations.

  • Draft for Nature Communications

    Recursive structure of innovation

    A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.

  • Physical Review E

    Geometry of discrete space

    A phase transition creates the geometry of the continuum from discrete space, but it needs disorder if it is to have the right metric.

  • Science Advances

    The rate of innovation

    The distribution of product complexity helps explain why some technology sectors tend to exhibit faster innovation rates than others.

  • Strategy Science

    The science of strategy

    The usefulness of components and the complexity of products inform the best strategy for innovation at different stages of the process.

  • Nature Communications

    Serendipity and strategy

    In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.

  • MIT Sloan Management Review

    The secret structure of innovation

    Firms can harness the shifting importance of component building blocks to build better products and services and hence increase their chances of sustained success.

  • Interface Focus

    Form and function in gene networks

    The structural properties of a network motif predict its functional versatility and relate to gene regulatory networks.

  • 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.

  • 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.

  • Entropy

    The temperature of networks

    A new concept, graph temperature, enables the prediction of distinct topological properties of real-world networks simultaneously.

  • 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

    Assessing self-assembly

    The information needed to self-assemble a structure quantifies its modularity and explains the prevalence of certain structures over others.

  • Physica A

    Tie knots and topology

    The topological structure of tie knots categorises them by shape, size and aesthetic appeal and defines the sequence of knots to produce them.

  • EPL

    Random cellular automata

    Of the 256 elementary cellular automata, 28 of them exhibit random behavior over time, but spatio-temporal currents still lurk underneath.

  • EPL

    Single elimination competition

    In single elimination competition the best indicator of success is a player's wealth: the accumulated wealth of all defeated players.

  • The American Mathematical Monthly

    Recursively divisible numbers

    Recursively divisible numbers are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on.