Dr Stephen Coombes

Moved to the Nonlinear and Complex Systems Group, Loughborough as of 1st Nov '96

Personal details:

Address:
Neural Computing Group,
Department of Engineering Mathematics,
University Of Bristol,
Queen's Building, University Walk,
Bristol BS8 1TR, United Kingdom

Tel: +44 (0)117 331 5604
Fax: +44 (0)117 331 5636
E-mail: S.Coombes@bristol.ac.uk
WWW: http://www.fen.bris.ac.uk/engmaths/research/neural/staff/sc.html

Contents

Research Interests:

Current Research:

Neuronal Population Dynamics

Apart from the action potential, one very important nonlinear phenomenon in a variety of nerve cells is post-inhibitory rebound (PIR). This is an active process in which the excitability of the neuron is enhanced temporarily following a period of hyper-polarisation. A simple model of PIR has been proposed that is formally equivalent to a piece-wise linear circle map with two discontinuities. Moreover, a mean field theory has been constructed to allow the analytic study of a large interacting population of such neurons. The properties of this system are under investigation in collaboration with Dr Stuart Doole.

Central Pattern Generation

PIR is an important mechanism underlying central pattern generation in the embryo of the Xenopus tadpole. In collaboration with Professor Alan Roberts I am examining simple models of coupled neural networks with PIR dynamics. More recently I have begun work with Dr Gabriel Lord to uncover the role that various cellular, synaptic and network properties have in determining rhythmic output in model CPGs. We are currently modelling the effects of axonal propagation delays, electrical synapses and nonlinear cell membrane properties in half-center oscillators built from integrate-and-fire neurons.

Single Neuron Computation

There is a growing body of material (particularly simulation results) on the computational properties of single neurons. Analytical techniques have recently been developed to calculate the response functions for passive dendritic trees of arbitrary topology. In collaboration with Dr Paul Bressloff I hope to extend this work to incorporate electro-diffusion and the effects of active spines.

Recent Publications:

Click the year of the paper to obtain a copy from the preprint server. Hypertext titles are available in LaTex2Html format.

  1. S Coombes, Computing with Higher Order Neurons and Recurrent Networks, PhD thesis 1995
  2. S Coombes and J G Taylor, 1995, The Storage and Stabilisation of Patterns in a Hopfield Net, Neural Network World, Vol 5, 2, 133-150
  3. S Coombes and J G Taylor, 1995, Using Features for the Storage of Patterns in a Fully Connected Net, Neural Networks, Vol 9, No 5, 837-844
  4. C Campbell and S Coombes, 1995, Determining the Optimal Number of Hidden Nodes in a Feed Forward Network, Annals of Mathematics in Artificial Intelligence, Baltzer
  5. S Coombes and C Campbell, 1995, Efficient Learning Beyond Saturation by Single-Layered Neural Networks, Submitted to IWANN '97
  6. S Coombes, S H Doole and C Campbell, 1996, Central Pattern Generation in a Model Neuronal Network with Post Inhibitory Rebound and Reciprocal Inhibition, Neural Network World, Vol 6, No 2, 155-162
  7. S Coombes and S H Doole, 1996 Neuronal Population Dynamics with Post Inhibitory Rebound: A Reduction to Piecewise Linear Discontinuous Circle Maps, Dynamics and Stability of Systems, vol 11, No 3, 193-217
  8. S Coombes and S H Doole 1996 Neuronal populations with reciprocal inhibition and rebound currents: effects of synaptic and threshold noise, Physical Review E, Vol 54, No 4, 4054-4065

Online Talks

Some Links

Other Interests

Cross Country Running

Back to Neural Computing

Back to Engineering Mathematics

This page maintained by Stephen Coombes
email: S.Coombes@bristol.ac.uk