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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  • Mahler measuring the genetic code of amoebae

    Algebraic geometry

    SCYHY. HeEHANAZ In Press Advances in Theoretical and Mathematical Physics

    Mahler measuring amoebae

    Genetic symbolic regression methods reveal the relationship between amoebae from tropical geometry and the Mahler measure from number theory.

  • Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces

    Algebraic geometry

    AAYHY. HeEHBA Arxiv

    Bundled Laplacians

    By approximating the basis of eigenfunctions, we computationally determine the harmonic modes of bundle-valued Laplacians on Calabi-Yau manifolds.

  • On a girth-free variant of the Bourgain–Gamburd machine

    Combinatorics

    ISI. Shkredov Finite Fields and Their Applications

    Ungrouped machines

    A new connection between continued fractions and the Bourgain–Gamburd machine reveals a girth-free variant of this widely-celebrated theorem.

  • The role of complexity for digital twins of cities

    Complex systems

    GCG. CaldarelliEAMBMBCG... Nature Computational Science

    Complex digital cities

    A complexity-science approach to digital twins of cities views them as interwoven self-organising phenomena, instead of machines or logistic systems.

  • Number theory

    Submitted

    Sum-product with few primes

    For a finite set of integers with few prime factors, improving the lower bound on its sum and product sets affirms the Erdös-Szemerédi conjecture.

  • Group theory

    Submitted

    On John McKay

    This obituary celebrates the life and work of John Keith Stuart McKay, highlighting the mathematical miracles for which he will be remembered.

  • Machine learning

    Arxiv

    BERT enhanced with recurrence

    The quadratic complexity of attention in transformers is tackled by combining token-based memory and segment-level recurrence, using RMT.

  • Number theory

    Geometric And Functional Analysis

    Random Chowla conjecture

    The distribution of partial sums of a Steinhaus random multiplicative function, of polynomials in a given form, converges to the standard complex Gaussian.

  • Statistical physics

    Submitted

    Landau meets Kauffman

    A new, simple approach to the critical Kauffman model with connectivity one sharpens the bounds on the number and length of attractors.

  • Statistical physics

    Submitted

    Single-input Boolean networks

    A new, simpler approach to the critical Kauffman model with connectivity one reveals that it has more attractors than previously believed.

  • Synthetic biology

    Submitted

    Cell soup in screens

    Bursting cells can introduce noise in transcription factor screens, but modelling this process allows us to discern true counts from false.

  • Gravity

    Arxiv

    Kerr black holes symmetry

    Effective field theories for Kerr black holes, showing the 3-point Kerr amplitudes are uniquely predicted using higher-spin gauge symmetry.

  • Number theory

    Submitted

    Multiplicativity of sets

    Expanding the known multiplicative properties of large difference sets yields a new, quantitative proof on the structure of product sets.

  • Statistical physics

    Nature Physics

    Network renormalization

    Applying diffusion-based graph operators to complex networks identifies the proper spatiotemporal scales by overcoming small-world effects.

  • AI-assisted maths

    In Press Advances in Theoretical and Mathematical Physics

    Clustered cluster algebras

    Cluster variables in Grassmannian cluster algebras can be classified with HPC by applying the tableaux method up to a fixed number of columns.

  • Number theory

    Submitted

    Bounding Zaremba’s conjecture

    Using methods related to the Bourgain–Gamburd machine refines the previous bound on Zaremba’s conjecture in the theory of continued fractions.

  • Neurocomputing

    Physical Review E

    Optimal electronic reservoirs

    Balancing memory from linear components with nonlinearities from memristors optimises the computational capacity of electronic reservoirs.

  • String theory

    Journal of High Energy Physics

    Gauge theory and integrability

    The algebra of a toric quiver gauge theory recovers the Bethe ansatz, revealing the relation between gauge theories and integrable systems.

  • 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

    Arxiv

    Structure of genetic computation

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

  • Gravity

    Physics Letters B

    AI classifies space-time

    A neural network learns to classify different types of spacetime in general relativity according to their algebraic Petrov classification.

  • String theory

    Journal of High Energy Physics

    Algebra of melting crystals

    Certain states in quantum field theories are described by the geometry and algebra of melting crystals via properties of partition functions.

  • Combinatorics, Number theory

    Submitted

    Set additivity and growth

    The additive dimension of a set, which is the size of a maximal dissociated subset, is closely connected to the rapid growth of higher sumsets.

  • AI-assisted maths

    Physics Letters B

    Machine learning Hilbert series

    Neural networks find efficient ways to compute the Hilbert series, an important counting function in algebraic geometry and gauge theory.

  • AI-assisted maths

    Submitted

    AI for cluster algebras

    Investigating cluster algebras through the lens of modern data science reveals an elegant symmetry in the quiver exchange graph embedding.

  • AI-assisted maths

    Physics Letters B

    Line bundle connections

    Neural networks find numerical solutions to Hermitian Yang-Mills equations, a difficult system of PDEs crucial to mathematics and physics.

  • AI-assisted maths

    Physical Review D

    Calabi-Yau anomalies

    Unsupervised machine-learning of the Hodge numbers of Calabi-Yau hypersurfaces detects new patterns with an unexpected linear dependence.

  • String theory

    Communications in Mathematical Physics

    Mahler measure for quivers

    Mahler measure from number theory is used for the first time in physics, yielding “Mahler flow” which extrapolates different phases in QFT.

  • Number theory

    Submitted

    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.

  • AI-assisted maths

    Journal of Symbolic Computation

    Learning the Sato–Tate conjecture

    Machine-learning methods can distinguish between Sato-Tate groups, promoting a data-driven approach for problems involving Euler factors.

  • Machine learning

    International Journal of Modern Physics A

    Universes as big data

    Machine-learning is a powerful tool for sifting through the landscape of possible Universes that could derive from Calabi-Yau manifolds.

  • Network theory

    Proceedings of the National Academy of Sciences of the USA

    True scale-free networks

    The underlying scale invariance properties of naturally occurring networks are often clouded by finite-size effects due to the sample data.

  • Number theory

    Submitted

    Reflexions on Mahler

    Unifying Mahler measure, dessins and gauge theory, Newton polynomials reveal a 1-to-1 correspondence between Mahler measure and dessins.

  • Graph theory

    Arxiv

    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.

  • Statistical physics

    Physical Review E

    Coexistence in diverse ecosystems

    Scale-invariant plant clusters explain the ability for a diverse range of plant species to coexist in ecosystems such as Barra Colorado.

  • Mathematical medicine

    European Urology Focus

    Cancer screening with MRI

    An ongoing study tests the feasibility of using MRI scans to screen men for prostate cancer in place of unreliable antigen blood tests.

  • Neural networks

    New Journal of Physics

    Quick quantum neural nets

    The notion of quantum superposition speeds up the training process for binary neural networks and ensures that their parameters are optimal.

  • Quantum physics

    New Journal of Physics

    Going, going, gone

    A solution to the information paradox uses standard quantum field theory to show that black holes can evaporate in a predictable way.

  • Mathematical medicine

    Journal of Mathematical Biology

    Tumour infiltration

    A delicate balance between white blood cell protein expression and the molecules on the surface of tumour cells determines cancer prognoses.

  • Neurocomputing

    Science Advances

    Breaking classical barriers

    Circuits of memristors, resistors with memory, can exhibit instabilities which allow classical tunnelling through potential energy barriers.

  • String theory

    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.

  • Machine learning

    Journal of Symbolic Computation

    Neurons on amoebae

    Machine-learning 2-dimensional amoeba in algebraic geometry and string theory is able to recover the complicated conditions from so-called lopsidedness.

  • Group theory

    ICCM

    New approaches to the Monster

    Editorial of the last set of lectures given by the founder, McKay, of Moonshine Conjectures, the proof of which got Borcherds the Fields Medal.

  • Network theory

    Nature Reviews Physics

    Physics of financial networks

    Statistical physics contributes to new models and metrics for the study of financial network structure, dynamics, stability and instability.

  • Economic complexity

    Journal of Financial Stability

    Channels of contagion

    Fire sales of common asset holdings can whip through a channel of contagion between banks, insurance companies and investments funds.

  • Financial risk

    Physical Review E

    Risky bank interactions

    Networks where risky banks are mostly exposed to other risky banks have higher levels of systemic risk than those with stable bank interactions.

  • Mathematical medicine

    Cancer Cell

    Cancer and coronavirus

    Cancer patients who contract and recover from Coronavirus-2 exhibit long-term immune system weaknesses, depending on the type of cancer.

  • Particle physics

    Arxiv

    Scale of non-locality

    The number of particles in a higher derivative theory of gravity relates to its effective mass scale, which signals the theory’s viability.

  • 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.

  • Inference

    Physical Review E

    Exact linear regression

    Exact methods supersede approximations used in high-dimensional linear regression to find correlations in statistical physics problems.

  • Combinatorics

    Arxiv

    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.

  • Combinatorics

    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.

  • Number theory

    Submitted

    Energy bounds for roots

    Bounds for additive energies of modular roots can be generalised and improved with tools from additive combinatorics and algebraic number theory.

  • 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.

  • Financial markets

    Mathematical Finance

    Network valuation in finance

    Consistent valuation of interbank claims within an interconnected financial system can be found with a recursive update of banks' equities.

  • Neural networks

    Physical Review Letters

    Deep layered machines

    The ability of deep neural networks to generalize can be unraveled using path integral methods to compute their typical Boolean functions.

  • Statistical physics

    Journal of Physics A

    Replica analysis of overfitting

    Statistical methods that normally fail for very high-dimensional data can be rescued via mathematical tools from statistical physics.

  • 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.

  • Inference, Statistical physics

    Journal of Physics A

    Replica clustering

    We optimize Bayesian data clustering by mapping the problem to the statistical physics of a gas and calculating the lowest entropy state.

  • 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.

  • Network theory

    Journal of Economic Interaction and Coordination

    Bursting dynamic networks

    A mathematical model captures the temporal and steady state behaviour of networks whose two sets of nodes either generate or destroy links.

  • Economic complexity

    Energy Policy

    Renewable resource management

    Modern portfolio theory inspires a strategy for allocating renewable energy sources which minimises the impact of production fluctuations.

  • Thermodynamics

    Scientific Reports

    Energy harvesting with AI

    Machine learning techniques enhance the efficiency of energy harvesters by implementing reversible energy-conserving operations.

  • 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.

  • Neurocomputing

    EPL

    Memristive networks

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

  • Statistical physics

    Nature Reviews Physics

    Physics of networks

    Statistical physics harnesses links between maximum entropy and information theory to capture null model and real-world network features.

  • 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.

  • Statistical physics, Thermodynamics

    Physical Review E

    One-shot statistic

    One-shot analogs of fluctuation-theorem results help unify these two approaches for small-scale, nonequilibrium statistical physics.

  • Complex networks

    Journal of Statistical Physics

    Information asymmetry

    Network users who have access to the network’s most informative node, as quantified by a novel index, the InfoRank, have a competitive edge.

  • Quantum physics

    Foundations of Physics

    A Hamiltonian recipe

    An explicit recipe for defining the Hamiltonian in general probabilistic theories, which have the potential to generalise quantum theory.

  • Neurocomputing

    European Physical Journal B

    Solvable memristive circuits

    Exact solutions for the dynamics of interacting memristors predict whether they relax to higher or lower resistance states given random initialisations.

  • Inference

    Physical Review Materials

    Grain shape inference

    The distributions of size and shape of a material’s grains can be constructed from a 2D slice of the material and electron diffraction data.

  • Baez theory

    ACM Transactions on Modeling and Computer Simulation

    Volunteer clouds

    A novel approach to volunteer clouds outperforms traditional distributed task scheduling algorithms in the presence of intensive workloads.

  • Financial networks

    Journal of Statistical Physics

    From ecology to finance

    Bipartite networks model the structures of ecological and economic real-world systems, enabling hypothesis testing and crisis forecasting.

  • Graph theory

    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.

  • Theory of innovation

    Technological Forecasting and Social Change

    Forecasting technology deployment

    Forecast errors for simple experience curve models facilitate more reliable estimates for the costs of technology deployment.

  • Financial networks

    PLoS ONE

    Hierarchies in directed networks

    An iterative version of a method to identify hierarchies and rankings of nodes in directed networks can partly overcome its resolution limit.

  • Graph theory

    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.

  • Financial networks

    Computational Management Science

    The interbank network

    The large-scale structure of the interbank network changes drastically in times of crisis due to the effect of measures from central banks.

  • 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 materials

    Physical Review B

    Dirac cones in 2D borane

    The structure of two-dimensional borane, a new semi-metallic single-layered material, has two Dirac cones that meet right at the Fermi energy.

  • Financial risk

    Journal of Computational Social Science

    Modelling financial systemic risk

    Complex networks model the links between financial institutions and how these channels can transition from diversifying to propagating risk.

  • Mathematical medicine

    Scientific Reports

    Bayesian analysis of medical data

    Bayesian networks describe the evolution of orthodontic features on patients receiving treatment versus no treatment for malocclusion.

  • 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.

  • Neural networks

    npj Quantum Information

    Quantum neural networks

    We generalise neural networks into a quantum framework, demonstrating the possibility of quantum auto-encoders and teleportation.

  • Network theory

    PLoS ONE

    Debunking in a world of tribes

    When people operate in echo chambers, they focus on information adhering to their system of beliefs. Debunking them is harder than it seems

  • Neurocomputing

    International Journal of Parallel, Emergent and Distributed Systems

    Memristive networks and learning

    Memristive networks preserve memory and have the ability to learn according to analysis of the network’s internal memory dynamics.

  • Neurocomputing

    Physical Review E

    Dynamics of memristors

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

  • Financial networks

    Physical Review E

    Bipartite trade network

    A new algorithm unveils complicated structures in the bipartite mapping between countries and products of the international trade network.

  • Sphere packing

    Mineralogical Magazine

    3d grains from 2d slices

    Moment-based methods provide a simple way to describe a population of spherical particles and extract 3d information from 2d measurements.

  • Complex systems

    Journal of Statistical Mechanics

    Disentangling links in networks

    Inference from single snapshots of temporal networks can misleadingly group communities if the links between snapshots are correlated.

  • Thermodynamics

    Proceedings of the Royal Society A

    Quantum thermodynamics

    Spectroscopy experiments show that energy shifts due to photon emission from individual molecules satisfy a fundamental quantum relation.

  • Financial markets

    Physical Review E

    Financial network reconstruction

    Statistical mechanics concepts reconstruct connections between financial institutions and the stock market, despite limited data disclosure.

  • Financial risk

    Nature Communications

    Pathways towards instability

    Processes believed to stabilize financial markets can drive them towards instability by creating cyclical structures that amplify distress.

  • Theormodynamics

    New Journal of Physics

    Worst-case work entropic equality

    A new equality which depends on the maximum entropy describes the worst-case amount of work done by finite-dimensional quantum systems.

  • 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

    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.

  • Complex networks, Financial risk

    PLoS ONE

    Non-linear distress propagation

    Non-linear models of distress propagation in financial networks characterise key regimes where shocks are either amplified or suppressed.

  • Financial risk

    Journal de Physique IV

    Immunisation of systemic risk

    Targeted immunisation policies limit distress propagation and prevent system-wide crises in financial networks according to sandpile models.

  • Complex networks

    Physical Review E

    Optimal growth rates

    An extension of the Kelly criterion maximises the growth rate of multiplicative stochastic processes when limited resources are available.

  • Quantum computing

    Physical Review A

    Tunnelling interpreted

    Quantum tunnelling only occurs if either the Wigner function is negative, or the tunnelling rate operator has a negative Wigner function.

  • Financial risk

    Proceedings of the National Academy of Sciences of the USA

    The price of complexity

    Increasing the complexity of the network of contracts between financial institutions decreases the accuracy of estimating systemic risk.

  • Thermodynamics

    Physical Review Letters

    Photonic Maxwell's demon

    With inspiration from Maxwell’s classic thought experiment, it is possible to extract macroscopic work from microscopic measurements of photons.

  • 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.

  • Network theory

    Physica D

    Cascades in flow networks

    Coupled distribution grids are more vulnerable to a cascading systemic failure but they have larger safe regions within their networks.

  • Percolation theory

    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.

  • Thermodynamics

    Physical Review E

    Optimal heat exchange networks

    Compact heat exchangers can be designed to run at low power if the exchange is concentrated in a crumpled surface fed by a fractal network.

  • Financial markets

    PLoS ONE

    Instability in complex ecosystems

    The community matrix of a complex ecosystem captures the population dynamics of interacting species and transitions to unstable abundances.

  • 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.

  • Financial risk, Percolation theory

    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.

  • Gravity

    Classical and Quantum Gravity

    Cyclic isotropic cosmologies

    In an infinitely bouncing Universe, the scalar field driving the cosmological expansion and contraction carries information between phases.

  • Theory of innovation

    Research Policy

    Predicting technological progress

    A formulation of Moore’s law estimates the probability that a given technology will outperform another at a certain point in the future.

  • Percolation theory

    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.

  • Financial markets

    PLoS ONE

    News sentiment and price dynamics

    News sentiment analysis and web browsing data are unilluminating alone, but inspected together, predict fluctuations in stock prices.

  • Network theory

    Physical Review E

    Communities in networks

    A new tool derived from information theory quantitatively identifies trees, hierarchies and community structures within complex networks.

  • Financial markets

    PLoS ONE

    Effect of Twitter on stock prices

    When the number of tweets about an event peaks, the sentiment of those tweets correlates strongly with abnormal stock market returns.

  • Complex networks

    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.

  • Biological networks

    Journal of the Royal Society Interface

    Protein interaction experiments

    Properties of protein interaction networks test the reliability of data and hint at the underlying mechanism with which proteins recruit each other.

  • Combinatorics, Graph theory

    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.

  • Complex networks

    PLoS ONE

    Collective attention to politics

    Tweet volume is a good indicator of political parties' success in elections when considered over an optimal time window so as to minimise noise.

  • Information theory

    New Journal of Physics

    A measure of majorization

    Single-shot information theory inspires a new formulation of statistical mechanics which measures the optimal guaranteed work of a system.

  • Financial risk

    PLoS ONE

    DebtRank and shock propagation

    A dynamical microscopic theory of instability for financial networks reformulates the DebtRank algorithm in terms of basic accounting principles.

  • Statistical physics

    Journal of Physics A

    Spin systems on Bethe lattices

    Exact equations for the thermodynamic quantities of lattices made of d-dimensional hypercubes are obtainable with the Bethe-Peierls approach.

  • Financial risk, Network theory

    Network Theory of Finance

    Fragility of the interbank network

    The speed of a financial crisis outbreak sets the maximum delay before intervention by central authorities is no longer effective.

  • Theory of materials

    Physical Review B

    Structure and stability of salts

    The stable structures of calcium and magnesium carbonate at high pressures are crucial for understanding the Earth's deep carbon cycle.

  • Economic complexity

    PLoS ONE

    Dynamics of economic complexity

    Dynamical systems theory predicts the growth potential of countries with heterogeneous patterns of evolution where regression methods fail.

  • Neurocomputing

    EPL

    From memory to scale-free

    A local model of preferential attachment with short-term memory generates scale-free networks, which can be readily computed by memristors.

  • Percolation theory

    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.

  • Graph theory

    ESAIM: Proceedings and surveys

    Random graphs with short loops

    The analysis of real networks which contain many short loops requires novel methods, because they break the assumptions of tree-like models.

  • Economic complexity

    PLoS ONE

    Taxonomy and economic growth

    Less developed countries have to learn simple capabilities in order to start a stable industrialization and development process.

  • Sphere packing

    Journal of Chemical Physics

    Viscosity of polydisperse spheres

    A fast and simple way to measure how polydisperse spheres crowd around each other, termed the packing fraction, agrees well with rheological data.

  • Financial risk

    Scientific Reports

    Networks of credit default swaps

    Time series data from networks of credit default swaps display no early warnings of financial crises without additional macroeconomic indicators.

  • Graph theory

    Journal of Physics A

    Entropies of graph ensembles

    Explicit formulae for the Shannon entropies of random graph ensembles provide measures to compare and reproduce their topological features.

  • 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.

  • Quantum theory

    Journal of Physics A

    Entanglement typicality

    A review of the achievements concerning typical bipartite entanglement for random quantum states involving a large number of particles.

  • Theory of materials

    Physical Review B

    Predicting interface structures

    Generating random structures in the vicinity of a material’s defect predicts the low and high energy atomic structure at the grain boundary.

  • Percolation theory

    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.

  • Financial risk

    Scientific Reports

    Memory effects in stock dynamics

    The likelihood of stock prices bouncing on specific values increases due to memory effects in the time series data of the price dynamics.

  • Network theory

    PLoS ONE

    Self-healing complex networks

    The interplay between redundancies and smart reconfiguration protocols can improve the resilience of networked infrastructures to failures.

  • Fractals

    Physical Review E

    Structural imperfections

    Fractal structures need very little mass to support a load; but for current designs, this makes them vulnerable to manufacturing errors.

  • Financial risk

    Scientific Reports

    Default cascades in networks

    The optimal architecture of a financial system is only dependent on its topology when the market is illiquid, and no topology is always superior.

  • Sphere packing

    Powder Technology

    Random close packing fractions

    Lognormal distributions (and mixtures of same) are a useful model for the size distribution in emulsions and sediments.

  • Biological networks

    Journal of Physics A

    Multitasking immune networks

    The immune system must simultaneously recall multiple defense strategies because many antigens can attack the host at the same time.

  • Economic complexity

    Journal of Economic Dynamics and Control

    Metrics for global competitiveness

    A new non-monetary metric captures diversification, a dominant effect on the globalised market, and the effective complexity of products.

  • Economic complexity

    PLoS ONE

    Measuring the intangibles

    Coupled non-linear maps extract information about the competitiveness of countries to the complexity of their products from trade data.

  • 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.

  • Mathematical medicine

    Journal of Physics A

    Multi-tasking in immune networks

    Associative networks with different loads model the ability of the immune system to respond simultaneously to multiple distinct antigen invasions.

  • Fractals

    Physical Review E

    Gentle loads

    The most efficient load-bearing fractals are designed as big structures under gentle loads, a common situation in aerospace applications.

  • Financial networks

    Scientific Reports

    Interbank controllability

    Complex networks detect the driver institutions of an interbank market and ascertain that intervention policies should be time-scale dependent.

  • Financial networks

    Nature Physics

    Reconstructing credit

    New mathematical tools can help infer financial networks from partial data to understand the propagation of distress through the network.

  • Financial networks

    Nature Physics

    Complex derivatives

    Network-based metrics to assess systemic risk and the importance of financial institutions can help tame the financial derivatives market.

  • Economic theory

    Journal of Economic Dynamics and Control

    Organized knowledge economies

    The Yule-Simon distribution describes the diffusion of knowledge and ideas in a social network which in turn influences economic growth.

  • Financial risk

    Journal of Statistical Physics

    Bootstrapping topology and risk

    Information about 10% of the links in a complex network is sufficient to reconstruct its main features and resilience with the fitness model.

  • Network theory

    Physical Review E

    Weighted network evolution

    A statistical procedure identifies dominant edges within weighted networks to determine whether a network has reached its steady state.

  • Fractals

    Physical Review Letters

    Ultralight fractal structures

    The transition from solid to hollow beams changes the scaling of stability versus loading analogously to increasing the hierarchical order by one.

  • Fractals

    Mechanics Research Communications

    Hierarchical space frames

    A systematic way to vary the power-law scaling relations between loading parameters and volume of material aids the hierarchical design process.

  • Economic complexity

    PLoS ONE

    Network analysis of export flows

    Network theory finds unexpected interactions between the number of products a country produces and the number of countries producing each product.

  • Economic complexity

    Scientific Reports

    Metric for fitness and complexity

    A quantitative assessment of the non-monetary advantage of diversification represents a country’s hidden potential for development and growth.

  • Mathematical medicine

    PLoS ONE

    Networks for medical data

    Network analysis of diagnostic data identifies combinations of the key factors which cause Class III malocclusion and how they evolve over time.

  • Financial markets

    PLoS ONE

    Search queries predict stocks

    Analysis of web search queries about a given stock, from the seemingly uncoordinated activity of many users, can anticipate the trading peak.

  • Graph theory

    Physical Review E

    Unbiased randomization

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

  • Network theory

    EPL

    Robust and assortative

    Spectral analysis shows that disassortative networks exhibit a higher epidemiological threshold and are therefore easier to immunize.

  • Network theory

    EPL

    Clustering inverted

    Edge multiplicity—the number of triangles attached to edges—is a powerful analytic tool to understand and generalize network properties.

  • Biological networks

    Interface Focus

    What you see is not what you get

    Methods from tailored random graph theory reveal the relation between true biological networks and the often-biased samples taken from them.

  • Fluid dynamics

    Food Biophysics

    Shear elastic deformation in cells

    Analysis of the linear elastic behaviour of plant cell dispersions improves our understanding of how to stabilise and texturise food products.

  • Statistical physics

    Philosophical Magazine

    Dynamics of Ising chains

    A transfer operator formalism solves the macroscopic dynamics of disordered Ising chain systems which are relevant for ageing phenomena.

  • Theory of materials

    Mathematics and Computers in Simulation

    Diffusional liquid-phase sintering

    A Monte Carlo model simulates the microstructural evolution of metallic and ceramic powders during the consolidation process liquid-phase sintering.

  • Graph theory

    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.

  • 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.

  • Sphere packing

    Physical Review E

    Ever-shrinking spheres

    Techniques from random sphere packing predict the dimension of the Apollonian gasket, a fractal made up of non-overlapping hyperspheres.

  • 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.