About the Authors

Robert R. Wilkinson

Affiliation Department of Mathematical Sciences, The University of Liverpool, Liverpool, United Kingdom

Kieran J. Sharkey

kjs@liv.ac.uk

Affiliation Department of Mathematical Sciences, The University of Liverpool, Liverpool, United Kingdom

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Wrote the paper: KJS RRW. Performed the research: KJS RRW.