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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### 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.

### Exact linear regression

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

### 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.

### 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.

### 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.

### One-shot statistic

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

### Financial network reconstruction

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

### Bipartite trade network

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

### Spectral partitioning

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

### Dynamics of memristors

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

### 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.

### Optimal growth rates

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

### Communities in networks

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

### Democracy in networks

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

### Structural imperfections

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

### Hierarchical structures

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

### Weighted network evolution

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

### Unbiased randomization

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

### 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.