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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  • True scale-free networks hidden by finite size effects

    MMGCAMARSSJRGCG. Caldarelli Proceedings of the National Academy of Sciences of the USA

    True scale-free networks

    Naturally occurring networks have an underlying scale-free structure that is often clouded by finite-size effects in the sample data.

  • The physics of financial networks

    MBM. BardosciaPBP. BaruccaSBFCGCDGFSTSGCG. Caldarelli Sub. to Nature Physics

    The physics of financial networks

    Complex network theory unlocks systematic understanding of financial stability and climate finance in pursuit of a more sustainable society.

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

    FAACA. Coolen Sub. to JPhys Complexity

    Transitions in loopy random graphs

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

  • Coarsening without interfacial energy

    RFR. Farr Sub. to Physical Review Letters

    Microstructural coarsening

    Rapid temperature cycling from one extreme to another affects the rate at which the mean particle size in solid or liquid solutions changes.

  • Arxiv

    Exact linear regression

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

  • 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.

  • Arxiv

    Ample & pristine numbers

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

  • 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.

  • Mathematical Finance

    Network valuation in financial systems

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

  • 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.

  • Arxiv

    Recursively divisible numbers

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

  • 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.

  • 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.

  • 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.

  • 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.

  • Scientific Reports

    Energy harvesting with AI

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

  • Sub. to Physical Review D

    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.

  • Energy Policy

    Renewable resource management

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

  • 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.

  • EPL

    Memristive networks

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

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • Physical Review E

    One-shot statistic

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

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • Scientific Reports

    Bayesian analysis of medical data

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

  • Physical Review B

    Dirac cones in 2D borane

    Theoretical searches propose 2D borane as a new graphene-like material which is stable and semi-metallic with Dirac cone structure.

  • npj Quantum Information

    Quantum neural networks

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

  • Physical Review E

    Enhanced capital-asset pricing model for bipartite financial networks reconstruction

    The challenge of statistical reconstruction is using the limited available information to predict stock holdings.

  • 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.

  • 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.

  • 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

  • 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.

  • 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.

  • International Journal of Parallel, Emergent and Distributed Systems

    Memristive networks

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

  • 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.

  • 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.

  • Physical Review E

    Dynamics of memristors

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

  • Nature Communications

    Pathways towards instability

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

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • Physical Review Letters

    Tunnelling interpreted

    In quantum tunnelling, a particle tunnels through a barrier that it classically could not surmount.

  • Royal Society

    Form and function in gene networks

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

  • Physica D Nonlinear Phenomena

    Cascades in flow networks

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

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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

    Photonic Maxwell's demon

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

  • 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.

  • 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.

  • Physical Review E

    Communities in networks

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

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • PLOS ONE

    Dynamics of economic complexity

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

  • 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.

  • PLOS ONE

    Taxonomy and economic growth

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

  • ESAIM: Proceedings and surveys

    Random graph ensembles with many short loops

    Short loops (cycles) in real networks are a theoretical challenge for modeling.

  • Journal of Chemical Physics

    Simple heuristic for the viscosity of polydisperse hard spheres

    Spheres crowd around each other in a manner that depends on their size distribution. We give a simple way to estimate the packing fraction.

  • Scientific Reports

    Credit default swaps networks and systemic risk

    CDS spreads over time for the selected institutions

  • Journal of Physics A

    Entropies of tailored random graph ensembles: bipartite graphs, generalized degrees, and node neighbourhoods

    Ensembles of tailored random graphs allow us to reason quantitatively about the complexity of system.

  • 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.

  • 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.

  • 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.

  • Electronic Journal of Probability

    Bootstrap percolation on Galton–Watson trees

    In bootstrap percolation, a node is infected when a sufficient number of neighbours are infected.

  • Scientific Reports

    Memory effects in stock price dynamics: evidences of technical trading

    Price dynamics incorporates the strategies of traders and investors in the market.

  • PLOS ONE

    Self-healing networks: redundancy and structure

    Infrastructure networks are very well engineered systems characterized by fluxes of commodities, from electric power to drinking water.

  • 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.

  • Scientific Reports

    Default cascades in complex networks: topology and systemic risk

    Frontier of large cascades evolution of the e-MID market in the period between January 1999 and January 2011.

  • Journal of Physics A

    Immune networks: multitasking capabilities near saturation

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

  • Powder Technology

    Random close packing fractions of lognormal distributions of hard spheres

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

  • Journal of Economic Dynamics and Control

    Economic complexity: conceptual grounding of a new metrics for global competitiveness

    We introduce a novel method to define a self-consistent and non-monetary metrics for the competitiveness of countries.

  • PLOS ONE

    Measuring the intangibles: a metric for the economic complexity of countries and products

    We present a framework to define a data-driven metrics to assess the level of competitiveness of a country.

  • Entropy

    Low-temperature behaviour of social and economic networks

    We define a generalized ensemble of graphs by introducing the concept of graph temperature.

  • 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.

  • Journal of Physics A

    Immune networks: multi-tasking capabilities at medium load

    An intriguing analogy exists between neural networks and immune networks.

  • Physics World

    Towers of strength

    The Eiffel Tower was never intended to be a permanent feature of the Parisian landscape.

  • Physical Review E

    Hierarchical structures

    We show that self-similar fractal structures exhibit new strength-to-mass scaling relations, offering unprecedented mechanical efficiency.

  • Scientific Reports

    Interbank controllability

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

  • Nature Physics

    Reconstructing a credit network

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

  • Nature Physics

    Complex derivatives

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

  • Journal of Statistical Physics

    Bootstrapping topology and systemic risk of complex network using the fitness model

    Vulnerability and systemicity do not depend only on GDP but also on the complex network of financial relations.

  • 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.

  • Physical Review Letters

    Ultralight fractal structures from hollow tubes

    A material’s architecture can be controlled over an ever increasing set of length scales.

  • 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.

  • Scientific Reports

    A new metric for countries’ fitness and products’ complexity

    A snapshot of the bipartite network for the most important countries; size of vertices is the fitness and the complexity

  • 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.

  • PLoS ONE

    Web search queries can predict stock market volumes

    Graphical illustration of the analysis presented in this paper.

  • Physical Review E

    Unbiased randomization

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

  • EPL

    Clustering inverted

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

  • 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.

  • Interface Focus

    What you see is not what you get: how sampling affects macroscopic features of biological networks

    It is vital that we understand in detail how the topological characteristics of a real network relate to those of a finite random network.

  • 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.

  • Philosophical Magazine

    Dynamics of disordered Ising chains

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

  • Mathematics and Computers in Simulation

    Diffusional Monte Carlo model of liquid-phase sintering

    Our Monte Carlo model sheds light on the Ostwald ripening, namely the growth of big particles at the expense of the small ones.

  • 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.

  • 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.

  • 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.

  • 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

    Single elimination competition

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