New attractor states for synchronous activity in synfire chains with
excitatory and inhibitory coupling

Arash Yazdanbakhsh
Department of Cognitive and Neural Systems
Boston University


If all of the neurons fire in each layer of a cortical neural network or
all fade, there will not be an efficient information transfer across the
layers. This is the case that was thought to happen in a cortical neural
network by Diesmann, Gewaltig, Aertsen (1999). 

We show that interestingly there are other states in the firing states
of the layers. The cells in each successive layer instead of either all
firing or all fading can have at least three other states:

1- A constant ratio of the total cells fire in each layer
2- A regular fluctuating ratio of the total cells fire in each layer 
3- The number of firing cells in each layer does not follow any
regularity 

All of these new found states are important from an information transfer
viewpoint.

A feed forward network composed of leaky integrate and fire neurons can
be one of the simplest models for a local population of neurons in the
cortex. The leaky integrate and fire membrane potential uses the idea
that recipient cells integrate the inputs from the previous layer of
cells till reaching the threshold. Then the cells fire and send a pulse 
as an output and the cell potential will be reset to the resting potential. 
If these cells are arranged layer by layer and are connected together an
interesting phenomenon may happen: Their firing synchronizes even when
the input pulse packet is not fully synchronized. The simple intuitive
idea behind that is just the closest firings in time are summed up
temporally to make the next layer cell fire and as a result, the 
closest firings in time survive and contribute to the next layer more
synchronous firing (due to the same reason). However, sometimes the
firing timing are not close enough to create a strong next layer
synchronous firing and the number of firing, layer by layer would
decrease till the full fade. These two states were demonstrated by
Diesmann, Gewaltig, Aertsen (1999). The outcome of this situation will
be the loss of the information, as any pattern of firing in the first
layers will result in either full fade or full firing. Our finding in
Biol.Cybern.86, 367–378 (2002) shows that there are other states that
favor information transfer.