Department of Applied Mathematics University of Leeds, Leeds ls2 9jt, UK

UK Nonlinear News Review

Mathematical Neuroscience
Edinburgh, 17-19 March 2008

Organisers: Stephen Coombes (Nottingham) and Yulia Timofeeva (Warwick)

Prof William Kath (Northwestern University) opened the meeting and introduced his research in collaboration with the Spruston laboratory on synaptic integration in CA1 pyramidal neurons. The properties of distal dendritic inputs and their effects on the probability of axonal action potential initiation were addressed using a combination of compartmental models and experimental data. Next, Brent Doiron (Pittsburgh) focussed on the role of microcircuit architectures and synaptic dynamics on macroscopic network behaviour. He showed how computational modelling and mean field analysis could be used to interpret in vitro recordings within layer 2/3 of the mouse auditory cortex. Simon Schultz (Imperial) spoke on recent advances in two-photon calcium imaging with a particular application to the study of cell correlations in population coding. Gaute Einevoll (Norwegian University of Life Sciences) covered the latest progress in measuring population-level activity in vivo using multielectrode recording methods and the use of such results in parametrising cortical-network models. The last talk of the day was given by Wyeth Bair (Oxford) who argued for a more flexible approach to modelling visual responses in the primary visual cortex. The first day finished productively with a well-attended poster session and reception at the International Centre for Mathematical Science (14 India St, Edinburgh).

The second day began with a talk by Prof Henry Tuckwell (Max Planck Institute) who considered stochastic neurobiological systems at the level of both linear and nonlinear single neuron models and also coupled pairs of neurons. Mark van Rossum (Edinburgh) then looked at models of the visual cortex and the consequences of synaptic depression on visual processing. Prof Nigel Stocks (Warwick) presented his results on the effect of noise on neural population dynamics, concentrating on suprathreshold stochastic resonance. Prof Peter Ashwin (Exeter) discussed winnerless competition models of neural function and focussed on their relevance for spatio-temporal encoding. Then Prof Paul Bressloff (Utah) described two alternative approaches for modelling the primary visual cortex by treating it either as a two-dimensional cortical sheet or as a system of coupled modules. Rodica Curtu (Iowa) focussed on a class of competition firing rate models and on the dependence of period of oscillations on stimulus strength.

Informal discussions were continued later that day during the workshop dinner.

The final day started with a talk by Prof Olivier Faugeras (INRIA) who addressed questions on the solutions of the mean field equation of a neural network model using techniques from functional analysis. David Liley (Swinburne University of Technology) looked at the interpretation of EEG results in the context of a general theory of electrorhythmogenesis. Afterwards, Piotr Suffczynski (Warsaw) discussed a thalamocortical network computational model that exhibits bistability and compared its predictions with experimental data. Finally, Prof David Terman (Ohio) proposed a biologically based model of the human sleep/wake cycle based on Saper's flip/flop switch model.

This was a very vibrant international meeting with many productive exchanges. It was preceded by a one-day training workshop for PhD students and post-docs entitled An introduction to Mathematical Neuroscience.