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.

### 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.

### 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.

### Exact linear regression

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

### Deep layered machines

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

### Ample & pristine numbers

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

### Replica analysis of overfitting

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

### 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.

### 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.

### Recursively divisible numbers

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

### Replica clustering

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

### The mathematical structure of innovation

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

### 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.

### 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.

### Energy harvesting with AI

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

### 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.

### Renewable resource management

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

### The rate of innovation

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

### Memristive networks

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

### Physics of networks

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

### A Hamiltonian recipe

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

### 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.

### Exactly solvable model of memristive circuits: Lyapunov functional and mean field theory

In this paper we sketch a general methodology for studying the phase diagram of memristive circuits.

### 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.

### One-shot statistic

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

### Hypercube eigenvalues

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

### Volunteer clouds

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

### From ecology to finance

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

### How well do experience curves predict technological progress? A method for making distributional forecasts

We presented a method to test the accuracy and validity of experience curve forecasts.

### Resolution of ranking hierarchies in directed networks

Identifying ranking hierarchies in complex networks is of paramount importance in many disciplines and applications

### 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.

### Exactly solvable random graph

Controlling analytically second or higher-order properties of networks is a great mathematical challenge.

### 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.

### Serendipity and strategy

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

### Modelling financial systemic risk

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

### Bayesian analysis of medical data

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

### 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.

### Quantum neural networks

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

### 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.

### Bipartite trade network

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

### Quantum thermodynamics

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

### 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

### 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.

### Spectral partitioning

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

### Memristive networks

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

### Entropic equality for worst-case work at any protocol speed

A battery from which work is taken or given to a single heat bath.

### Harnessing the secret structure of innovation

Firms can harness the shifting importance of component building blocks to build better products and services.

### Dynamics of memristors

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

### Pathways towards instability

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

### Disentangling links in networks

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

### 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.

### Non-linear distress propagation

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

### Immunisation of systemic risk

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

### Optimal growth rates

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

### The price of complexity

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

### Tunnelling interpreted

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

### Form and function in gene regulatory networks

The structure of network motifs determines fundamental properties of their dynamical state space.

### Cascades in flow networks

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

### Self-organising adaptive networks

An adaptive network of oscillators in fragmented and incoherent states can re-organise itself into connected and synchronized states.

### Instability in complex ecosystems

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

### Clusters of neurons

Percolation theory shows that the formation of giant clusters of neurons relies on a few parameters that could be measured experimentally.

### How predictable is technological progress?

Predicting the evolution of technology allow us to make better investments and policies.

### Cyclic isotropic cosmologies

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

### Eigenvalues of neutral networks: Interpolating between hypercubes

The first 16 ‘‘bricklayer’s graphs’’ and the principal eigenvalue of their adjacency matrices.

### Photonic Maxwell’s demon

By analogy with Maxwell’s original thought experiment, the setup uses energy extracted from a thermal system.

### Coupling news sentiment with web browsing data improves prediction of intra-day price dynamics

Complementary of the cumulative distribution function of the number of clicks a news receives for the ten assets.

### Subcritical U-Bootstrap percolation models have non-trivial phase transitions

Our results re-open the study of critical probabilities in bootstrap percolation on infinite lattices.

### Communities in networks

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

### The effects of Twitter sentiment on stock price returns

Distribution of sentiment polarity for the 260 detected Twitter peaks

### Democracy in networks

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

### Quantifying noise in mass spectrometry and yeast two-hybrid protein interaction detection experiments

Protein detection experiments seek to measure for each pair of protein species whether they interact in any complex.

### 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.

### Twitter-based analysis of the dynamics of collective attention to political parties

Daily tweet volume for each party around elections

### A measure of majorization

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

### Spin systems on hypercubic Bethe lattices: a Bethe–Peierls approach

Hypercubic Bethe lattices retain many of the loops of the topology of realistic spin systems.

### DebtRank: a microscopic foundation for shock propagation

The DebtRank algorithm was introduced to account for the build-up of distress in the markets, before the occurrence of defaults.

### Organized knowledge economies

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

### Structures and stability of calcium and magnesium carbonates at mantle pressures

Predicting stable structures of calcium and magnesium carbonate is crucial for understanding the Earth's deep carbon cycle.

### How the interbank market becomes systemically dangerous: an agent-based network model of financial distress propagation

We assess the fragility of the interbank lending market from 2004 to 2013

### 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.

### The heterogeneous dynamics of economic complexity

The growth dynamics of countries in the fitness-income plane exhibits a high degree of heterogeneity.

### Maximum percolation time in two-dimensional bootstrap percolation

What is the maximum percolation time in a two-dimensional grid?

### How the taxonomy of products drives the economic development of countries

A less developed country has to learn simple capabilities in order to start a stable industrialization and development process.

### Random graph ensembles with many short loops

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

### 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.

### Credit default swaps networks and systemic risk

CDS spreads over time for the selected institutions

### 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.

### Easily repairable networks

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

### Entanglement typicality

We provide a measure of purity of an entanglement state.

### 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.

### Bootstrap percolation on Galton–Watson trees

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

### Memory effects in stock price dynamics: evidences of technical trading

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

### Self-healing networks: redundancy and structure

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

### Structural imperfections

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

### 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.

### 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.

### 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.

### 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.

### 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.

### Low-temperature behaviour of social and economic networks

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

### Scales in weighted networks

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

### Immune networks: multi-tasking capabilities at medium load

An intriguing analogy exists between neural networks and immune networks.

### Towers of strength

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

### Hierarchical structures

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

### Interbank controllability

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

### Reconstructing a credit network

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

### Complex derivatives

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

### 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.

### Weighted network evolution

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

### Ultralight fractal structures from hollow tubes

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

### A network analysis of countries’ export flows: firm grounds for the building blocks of the economy

The network of countries and products and the two possible projections.

### 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

### 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.

### Web search queries can predict stock market volumes

Graphical illustration of the analysis presented in this paper.

### Unbiased randomization

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

### Clustering inverted

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

### Random cellular automata

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

### 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.

### Shear elastic deformation and particle packing in plant cell dispersions

Schematic of the disruption of close-packed polyhedral cells in tomato tissue into individual cells.

### Transfer operator analysis of the parallel dynamics of disordered Ising chains

The dynamics of one-dimensional Ising chains is of interest in the context of ageing phenomena.

### 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.

### Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs

Our approach gives a rigorous quantitative method for prioritising network properties.

### Assessing self-assembly

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

### Ever-shrinking spheres

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

### 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.

### Strategy for conkers

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