The first plenary talk by Stephen Williams (Cambridge) discussed "Distributed processing in single neurons". In particular recording at multiple sites from layer V cortical neurons (somatic & dendritic) allow ones to observe membrane potential changes at any points in the dendritic tree. Topics covered included: the simulation of synaptic potentials, apical dendritic polarization of HCN channels, dendritic spike forward propagation, compartmentalized synaptic integration, apical dendritic integration and axo-somatic integration, with interpretation in terms of theoretical predictions from Rall's cable theory of dendrites. Next Rafal Bogacz (Bristol) gave a short talk on "Optimal decision making in the cortico-basal ganglia circuit", using integration as a way to compute an average population firing rate, and subsequently information about a stimulus. Wyeth Bair (Oxford) followed on with "A modelling framework for studying visual circuit" relating to the development of a general computational framework for probing issues such as contextual modulation and the phenomenon of iso-orientation surround suppression using models. Jianfeng Feng (Warwick) then moved the discussion to how best to deal with data "... from single ion channel to neuronal networks", with examples from local field potentials collected from sheep performing a visual recognition task. As well as describing oscillatory activity and patterns of synchronisation the practical technique of detecting functional interactions via Granger Causality was described. Pete Ashwin (Exeter) spoke on "Emergent Dynamics in coupled cell network", addressing how to achieve spatio-temporal encoding using globally coupled oscillator neuron models (via heteroclinic cycling), the sensitivity of networks to parameter detuning, dynamics in asymmetric networks and pattern formation in networks of bursters. "Brain connectivity: Relating network topology with behaviour and dynamics" by Marcus Kaiser (Newcastle) showed that one can roughly distinguish three different types of brain connectivities: structural, (as seen by neuroanatomy, or diffusion tensor imaging), functional (as seen in functional correlation studies) or effective (using methods for estimating causal relation between different regions). Rasmus Petersen (Manchester) spoke on "Estimation of stimulus-response relationships in sensory systems", describing some of his recent work on how rats use whisking to discriminate textures and the role of information theory in understanding how somatosensory cortical neurons code. Magnus Richardson (Warwick) spoke on "Experimentally verified and mathematically tractable cortical-neurone models", emphasising the great success of nonlinear integrate-and-fire neuron models in fitting real cortical spike train data. Before dinner on the first day Stuart Hughes (Cardiff) gave the second plenary talk on "Interfacing neurones and computers: blurring the boundaries between modelling and experiments". Stuart described the highly influential dynamic clamp technique and its use in unravelling the contribution of currents such as IT, ICAN, ADP in generating slow (2-7 Hz) oscillations, as well as their contribution to cortical up and down states.

The morning of day two began with the final plenary talk of Neil Burgess (UCL) on "Knowing where you are: place cells, grid cells and oscillatory interference". This wide ranging talk covered parametric distortion of place fields, boundary vector cells, memory, path integration, theta-phase and place cells, grid cells, and the representation of environment most useful for object location. Hugh Robinson (Cambridge) spoke next on "Studying gamma oscillations with conductance injection", describing how this ubiquitous cortical rhythm (30-80 Hz) is generated via an interconnected system of repetitive spiking & fast spiking cells, with both chemical and gap junction coupling. Zhaoping Li (UCL) used the language of dynamical systems to explain the "Computational advantage of E-I networks over that of the symmetric (Hopfield) networks", emphasising the differing stability properties of the shared fixed point structure. The final presentation by Mark van Rossum (Edinburgh) tackled "Shannon information capacity of discrete synapses", treating the vanilla model, covariance rules, and optimal binary synapses. David Willshaw (Edinburgh) led a final discussion on the evolution of the Mathematical Neuroscience Network.

The meeting was attended by 50 UK researchers.

Results from the discussions held throughout the two days may be summarised as follows:

The Network should

- Organise local (seminar-like) events, to be attended by both neuroscientists and mathematicians.
- Develop a web-site and establish permissions for listing member contact details.
- Promote student involvement (by participating in the MNN workshops they can strengthen the link between different research groups).
- Promote small discussion group sessions and spontaneous presentations of new ideas.
- Promote lab visits and exchanges.
- Pursue initial workshops with the following themes: i) Adaptive neurosystems (Wyeth Bair), ii) Models and Data (Arnd Roth, David Simpson), iii) Neural development (David Willshaw).