### The rate of innovation

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

### 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 random graph ensemble with extensively many short cycles

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

### Serendipity and strategy

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

### Optimal growth rates

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

### Emergence of strongly connected components in continuum disk-spin percolation

Single realization of random positions and orientations of 100 disks with an external field pointing in the direction of the red arrow.

### 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.

### 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.

### Reconstructing a credit network

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

### 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.

### 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.

### 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.

### Tie knots, random walks and topology

The thirteen canonical knot classes and the corresponding most aesthetic knots.