Modular models. The aim is to understand how the organization of memory representations is determined by the underlying plasticity and network connectivity. Early work had considered the simplest modular network model of semantic memory, rejecting it because of inadequate storage capacity [1,2]. A more sophisticated version incorporates the key ingredients, sparsity in module activation and correlations between activation and connectivity, that allow to relieve the capacity limitations .
Metric content. To further probe representational structures
an off-shot of information analyses, the metric and ultrametric
structure of discrete perceptual and memory sets has been quantified
measures, first applied to responses of face cells in the primate
cortex  and of spatial view cells of hippocampal
cortices . In an effort to reach towards studies of human performance, we have
shown how to extract such measures
neuropsychological test administered to patients with different types
disorders [4, 18,19]; while we are studying the effect of the underlying
structures on the neuronal and behavioural
measures using the above formal network models.
Feedforward self-organization. Analytical techniques and simulations have also been applied to formal but realistic models of self-organizing competitive networks, aiming at a quantitative understanding of the functional properties of this simple type of neuronal organization . The effects of learning of the spike count distribution of single cells to large sets of stimuli have been predicted using one such model .
What and where: lamination. Within the general research goal of attempting to understand the main evolutionary traits  leading from the reptilian to the mammalian cerebral cortex, a crucial question has been what drove the emergence of a laminated neocortex. Consider the conflict between relaying positional and identity information by a model cortical patch . Positional ("where?") information is the one expressed by the location of activated neurons on the 2D cortical sheet; identity ("what?") information is expressed instead in the detailed activation pattern, at a fixed focus on the sheet. Simulating a simplified model patch, including three layers with initially uniform properties, it was found that the differentiation of a granular layer with distinct connectivity and firing properties leads to a small but reliable quantitative advantage in relaying an optimal mixture of both kinds of information. Further, a differentiation between supra- and infragranular layers is shown to optimally match their extrinsic connectivity, thus accounting for another advantage which isocortical lamination may have brought to mammals [11,12]. If you would like to run the simulations yourself, please ask for the code. Having evolved lamination in their topographic sensory cortical systems, mammals went about multiplying cortical areas within each system; a model of the advantages this brought to the analysis of complex stimuli has been studied using face processing as an example .
What and where: capacity and stability. A
approach has been
recently developed (YR) to study attractor-mediated retrieval of memory
patterns localized on a cortical patch. Such activity states are still
distributed non-uniformly over many units, but the denser short-range
connectivity allows, beyond a critical line, for the activity to be
concentrated on a restricted patch rather than spread out across the
network . It has been shown analytically and with computer
the storage capacity for such localized retrieval states is only
reduced with respect to that for non-localized retrieval, with the
states still proportional to the number of independently modifiable
per pyramidal cell . While analytical neural network studies of
dynamics provide crucial quantitative insight into its power and
simulations allow approaching closer to real cortical networks.
Integrate & Fire units in a model network similar to the one
above with non-dynamical units led to divergent results ,
analysis of the effects of saturation (YR, AA). Moreover, localized
attractor states are found to be unstable to positional drift, and
their theoretical continuity is broken by spatial collapse anto a few
randomly distributed favoured positions - unless a stabilizing signal
is provided, e.g. acting on local neuronal gain .
Ambiguity and attractors. Visual processing of facial expressions offers a suitable physiological model with which to test predictions arising from mathematical models, also because of the evidence of parallel processing along a distinct sub-cortical pathway. This was the aim of a Human Frontier Science Programme collaboration with the labs of Ray Dolan at UCL and of Bharathi Jagadeesh at U Washington in