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How much can we influence the rate of innovation?

TFT. FinkMRM. Reeves 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.

Reconstructing grain-shape statistics from electron back-scatter diffraction microscopy

RFR. FarrZVMHEG 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.

Exactly solvable random graph ensemble with extensively many short cycles

PBP. BaruccaFLMFAC Journal of Physics A: Mathematical and Theoretical

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 rapid innovation

TFT. FinkMRM. ReevesRFR. FarrRP Nature Communications

Serendipity and strategy

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

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4 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.

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3 Journal of Statistical Mechanics: Theory and Experiment

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.

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2 Journal of Physics A

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.

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5 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.

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5 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.

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4 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.

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2 Physical Review E

Unbiased randomization

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

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2 Philosophical Magazine

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.

3 Journal of Physics A

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.

2 Physica A

Tie knots, random walks and topology

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