One of the differences between memory function of hypocampus and neural networks situated at neocortex is that in the latter memory operation still reflect the topography informing synaptic connections. This means that the activity of a unit relates also to its position in the tissue.

We introduce two approaches for incorporating the information of the geometry of the underlying neural network into its dynamics. This phenomenon is carried out based on two probability rules for selecting storing patterns. First a Gibbs type distribution inspired by the architecture of the network is applied. We are then led to a second method to introduce topological effects on the dynamics of the network. In both approaches a significant enhancement on the capacity of the network is observed after considerable rigorous computations.

Some References:

1- Bahraini,A, . Abbassian,A. Topological Pattern Selection in Recurrent Networks, Journal of Neural Networks, 31, 2012, 22-32.

2- Roudi, Y, Treves, A,. An associative Network with Spatially Organized Connectivity,2004, Journal of Statistical Mechanics.

3- Gallan, R., F., On how network architecture determines the dominant patterns of spontaneous neural activity, PLoS One , 2008.

Bio: I obtained my DEA in 2001 and my PhD in 2004 at University Paris 7 under the supervision of Professor Daniel Bennequin. The title of my thesis was Super-symmetry and Complex Geometry. I joined the department of mathematical sciences of Sharif university of technology as an assistant

professor in 2004 and in 2012 I became an associate professor at the same department.