Mathematical Neuroscience

Edinburgh, March 23-25, 2009

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

This three-day conference was the second annual conference of the UK Mathematical Neuroscience Network. The meeting was focused on the current state of research in mathematical approaches to neuroscience and was attended by 80 participants consisting of both theoretical and life scientists.

Monday 23 March

Geoff Goodhill (University of Queensland) opened the meeting with a talk on a Bayesian approach to the problem of axon guidance using molecular gradients. Predictions of the model were tested experimentally and demonstrated highly sensitive chemotactic responses unreported until now. Next, Krasimira Tsaneva-Atanasova (University of Bristol) analysed the bifurcation structure of plateau bursting in endocrine cells. She showed how both supercritical and fold-sub-Hopf bifurcation can be obtained from the dynamics of calcium gated and calcium sensitive channels. Horacio Rotstein (New Jersey Institute of Technology) used dynamical system techniques (and live matlab simulations) to show that canard generated sub-threshold oscillations were at the heart of abrupt transitions in the firing behaviour of medial entorhinal cortex stellate cells. Then, Andrey Shilnikov (Georgia State University) examined the different rhythmic motifs that arise in the dynamics of small network of excitatory inhibitory neurons used to model of central pattern generators. Vincent Hakim (CNRS and Ecole Normale Supérieure) talked about previous theoretical findings concerning sparsely synchronised oscillations and showed how it relates to recent experimental results collected in cerebellar cell networks at the Laboratoire de Neurobiologie of Ecole Normale Supérieure. The first day finished productively with a well-attended poster session and reception at the International Centre for Mathematical Science (14 India St, Edinburgh).

Tuesday 24 March

The second day began with a talk by Andre Longtin (University of Ottawa) who considered the role of short term plasticity on information transfer and the role feed-back loops in generating “On” and “Off” activity. Peter Latham (University College London) discussed a framework to study spatial correlational structure in strongly coupled networks. Daniel Tranchina (New York University) spoke about the shaping of the statistics and dynamics of an output spike train produced by a population of neurons receiving temporally correlated input using a population density framework. Stefano Panzeri (Italian Institute of Technology) spoke on recent evidence for the encoding of information about natural stimuli in terms of spike timing relative to the phase of ongoing network fluctuations. David Pinto (University of Rochester) examined experimentally the onset of epileptic seizure and how it relates to the notion of a population threshold. Carson Chow (National Institutes of Health) presented a new framework for studying correlations in neural field models using a truncated expansion of a stochastic differential equation describing all order firing statistics of the network. Thomas Wennekers (University of Plymouth) discussed how cell assemblies could implement compositional concept hierarchies in a natural way.

Dinner was served at Howies restauarnt and fun had by all.

Wednesday 25 March

The final day started with a talk by Carl van Vreeswijk (CNRS) who demonstrated how to extend a result by Smith, on the growth of cumulants of stochastic point processes, to treat serial correlations relevant for the study of neural spiking activity in the presence of adaptation. Carlo Laing (Massey University) highlighted a data-mining technique to reduce the dimensionality of network models and applied this to a model for binocular rivalry. Then, Micheal Breakspear (University of New South Wales) presented experimental results on switching between high and low amplitude alpha rhythms and proposed an explanation in terms of the extremal event statistics of complex nonlinear systems. Finally Viktor Jirsa (CNRS) introduced a model using anatomical connectivity data (linking brain modules) with cortico-cortical communication delays and noise and explained how the intermittent synchronisation of subnetworks could give rise to the ultra-slow resting brain state oscillations observed in BOLD signals.

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”, with lecture slides available here.

This conference was sponsored by the EPSRC via the UK Mathematical Neuroscience Network.

Report prepared by Stephen Coombes, Jonathan Laudanski and Yulia Timofeeva, May 8th, 2009.