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Jonathan Crofts

Lecturer/Senior Lecturer

School of Science & Technology

Staff Group(s)
Physics and Mathematics

Role

Dr Jonathan Crofts is a Senior Lecturer of Applied Mathematics. His teaching currently includes the modules Advanced Calculus (Year 2), Linear Systems (Year 3) and Topics in Mathematical Biology (Year 4). His research is primarily concerned with the modelling of complex biological systems using the techniques of network science, and applied mathematics more generally.

Career overview

Dr  Crofts completed his PhD at the University of Leicester in 2007. His research centred around the development of novel numerical schemes to detect unstable periodic orbits (UPOs) in both continuous and discrete dynamical systems. This work provided a first rigorous mathematical analysis of the so-called stabilising transformation technique for determining UPOs, and, as a result, the application of this method to very high (possibly infinite) dimensional systems.

Dr Crofts then moved to the University of Strathclyde to work on the MRC funded project Complex Brain Networks in Health Development and Disease. As part of the project he spent an initial 6 months at the University of Oxford being trained in computational neuroscience/imaging. This included attendance at MSc level neuroscience lectures, as well as training in fundamental neuroimaging techniques and software packages such as FSL, Freesurfer and Caret. Working closely with neuroscientists at Oxford, he developed a number of mathematical computational tools for analysing brain anatomical networks arising in neuroinformatics.

In 2010, Dr Crofts joined Nottingham Trent University as a lecturer in Applied Mathematics.

Research areas

Dr Crofts is a member of the Biomathematics and Bioinformatics research group.

His research interests are in computational and applied mathematics with strong interests in computational biology including:

  • Mathematics of networks, hypernetworks and multiplex networks
  • Dynamical systems on networks
  • Applications of networks to biology
  • Understanding structure-function relations in biological networks
  • Network classification problems

If you are considering applying for an MRes or PhD in any of the areas above, please email Dr Crofts for further information. Some available PhD titles include:

  • Multiplex network models of the brain
  • Dynamics on spatially constrained brain networks
  • A multiplex network approach to cancer patient stratification and identification of subtype-specific prognostic multi-omics signatures

Opportunities arise to carry out postgraduate research towards an MPhil / PhD in the areas identified above. Further information may be obtained on the NTU Research Degrees website https://www.ntu.ac.uk/research/research-degrees-at-ntu

Current and recent postgraduate supervisory experience:

Research fellows:

  • Casimiro Pio Carrino Investigating the role of non-reciprocal prefrontal connectivity in attentional processing: a computational approach (2016)
  • Dr Yi-Ping Lo Simulation and analysis of epileptic seizure progression (2012-2013)

PhD Students

  • Amelia Padmore (in progress) Multiplex network models of the brain
  • Jacob Rowbottom (in progress) A hybrid convolution quadrature method for modelling time-dependent waves with broadband frequency content
  • Anahita Bayani (in progress) Modelling anti-inflammatory systems through cellular automata
  • Bethany Hall (in progress) In silico modelling of longevity of Drosophila melanogaster: a network approach
  • Rebecca Martin (completed 2018) Collocation techniques for solving neural field models on complex cortical geometries
  • Daniel Buxton (completed 2017) Remotely acting mutations in genetic disease and cancer: features and properties
  • Nicole Pearcy (completed 2015) Unravelling the complexity of metabolic networks
  • Stacey Bedwell (completed 2015) Topographic connectivity of the mammalian prefrontal cortex

MRes students

  • Iain Pinder (in progress) Synchrony and bifurcations in a network of delayed Wilson-Cowan oscillators

External activity

Refereeing for scientific journals:

  • Journal of Complex Networks
  • Chaos
  • PLOS Computational Biology
  • PLOS ONE
  • Scientific Reports
  • Europhysics Letters
  • Physica A

Sponsors and collaborators

Current and recent research is being conducted in collaboration with:

  • Reuben O'Dea, University of Nottingham
  • Marcus Kaiser, University of Newcastle
  • Cheol E Han, Korea University
  • Des Higham, University of Strathclyde
  • Ernesto Estrada, University of  Zaragoza
  • Ruslan Davidchack, University of  Leicester

Sponsorship:

Publications

Selected publications

For full list click 'Go to Jonathan Crofts publications' link above.

See all of Jonathan Crofts's publications...