Our papers are the official record of our discoveries. They allow others to build on and apply our work. Each one is the result of many months of research, so we make a special effort to make our papers clear, inspiring and beautiful, and publish them in leading journals.

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  • Citations
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  • A. EsterovA. Esterov
  • O. GamayunO. Gamayun
  • A. V. KosyakA. V. Kosyak
  • A. OchirovA. Ochirov
  • E. SobkoE. Sobko
  • Y. HeY. He
  • M. BurtsevM. Burtsev
  • M. ReevesM. Reeves
  • I. ShkredovI. Shkredov
  • T. FinkT. Fink
  • F. SheldonF. Sheldon
  • G. CaldarelliG. Caldarelli
  • R. HannamR. Hannam
  • F. CaravelliF. Caravelli
  • A. CoolenA. Coolen
  • O. DahlstenO. Dahlsten
  • A. MozeikaA. Mozeika
  • M. BardosciaM. Bardoscia
  • P. BaruccaP. Barucca
  • M. RowleyM. Rowley
  • I. TeimouriI. Teimouri
  • F. AntenucciF. Antenucci
  • A. ScalaA. Scala
  • R. FarrR. Farr
  • A. ZegaracA. Zegarac
  • S. SebastioS. Sebastio
  • B. BollobásB. Bollobás
  • F. LafondF. Lafond
  • D. FarmerD. Farmer
  • C. PickardC. Pickard
  • T. ReevesT. Reeves
  • J. BlundellJ. Blundell
  • A. GallagherA. Gallagher
  • M. PrzykuckiM. Przykucki
  • P. SmithP. Smith
  • L. PietroneroL. Pietronero
  • Number of ordered factorizations and recursive divisors

    Number theory

    TFT. Fink Submitted

    Counting recursive divisors

    Three new closed-form expressions give the number of recursive divisors and ordered factorisations, which were until now hard to compute.

  • Properties of the recursive divisor function and the number of ordered factorisations

    Number theory

    TFT. Fink Arxiv

    Recursive divisor properties

    The recursive divisor function has a simple Dirichlet series that relates it to the divisor function and other standard arithmetic functions.

  • Number of attractors in the critical Kauffman model is exponential

    Statistical physics

    TFT. FinkFSF. Sheldon Physical Review Letters

    Kauffman cracked

    Surprisingly, the number of attractors in the critical Kauffman model with connectivity one grows exponentially with the size of the network.

  • Biological logics are restricted

    Combinatorics

    TFT. FinkRHR. Hannam Submitted

    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.

  • Statistical physics

    Journal of Physics A

    Landau meets Kauffman

    Insights from number theory suggest a new way to solve the critical Kauffman model, giving new bounds on the number and length of attractors.

  • Statistical physics

    In press Physical Review Research

    Multiplicative loops

    The dynamics of the Kauffman network can be expressed as a product of the dynamics of its disjoint loops, revealing a new algebraic structure.

  • Evolvability

    Arxiv

    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.

  • Combinatorics

    Submitted

    Structure of genetic computation

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

  • Number theory

    Journal of Number Theory

    Recursively divisible numbers

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

  • Evolvability

    Submitted

    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.

  • Combinatorics

    Draft

    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.

  • Number theory

    Arxiv

    Ample and pristine numbers

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

  • Theory of innovation

    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.

  • Theory of innovation

    Arxiv

    Recursive structure of innovation

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

  • Geometry

    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.

  • Theory of innovation

    Science Advances

    The rate of innovation

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

  • Theory of innovation

    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.

  • Theory of innovation

    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.

  • Theory of innovation

    Nature Communications

    Serendipity and strategy

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

  • Graph theory

    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.

  • Discrete dynamics

    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.

  • Network theory

    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.

  • Network theory

    Entropy

    The temperature of networks

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

  • Network theory

    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.

  • Information theory

    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.

  • Discrete dynamics

    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.

  • Statistical physics

    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.