Autoassociative Memory Retrieval and Spontaneous Activity Bumps in   Small-World Networks of Integrate-and-Fire Neurons
  Qualitatively, some real networks in the brain could be characterized as 'small worlds', in the sense that the structure of their connections is intermediate between the extremes of an orderly geometric arrangement and of a geometry-independent random mesh. Small worlds can be defined more precisely in terms of their mean path length and clustering coefficient; but is such a precise description useful to better understand how the type of connectivity affects memory retrieval?   We have simulated an autoassociative memory network of integrate-and-fire units, positioned on a ring, with the network connectivity varied parametrically between ordered and random. We find that the network retrieves when the connectivity is close to random, and displays the characteristic behavior of ordered nets (localized 'bumps' of activity) when the connectivity is close to ordered. Recent analytical work shows that these two behaviours can coexist in a network of simple threshold-linear units, leading to localized retrieval states. We find that they tend to be mutually exclusive behaviours, however, with our integrate-and-fire units. Moreover, the transition between the two occurs for values of the connectivity parameter which are not simply related to the notion of small worlds. 
A. Anishchenko (1), E. Bienenstock (1), A. Treves (2) ((1) Brown   University, (2) SISSA)