Time to converge

[Erik Fransen]

We have recently done some simulations of recurrent networks with
realistic, spiking pyramidal cells (Hodgkin-Huxley type eq.,
multi-compartment model (1)) as units. Our results show that relaxation
times are rather short (2).  

In case of a complete and undistorted pattern as stimuli, response
time was around 25 ms. With incomplete or distorted or mixed patterns
as stimuli, response time was around 50 ms. This has been done
with a small network of 50 cells. Axonal plus synaptic delay times
were 1 ms. Currently we are working on a much larger network. 

Thus, relaxation in recurrent cortical circuits seems compatible with
a stimulus-response time of 90 ms. In a sequence of processing stages
(retina, LGN, V1 ...) the first "leading wave" would take about 15 ms
per stage. Priming could lower this time considerably. Actual
computation in each stage will take place in parallel, but in cases
of "familiar" inputs later responses will not differ much from the
first.  So, with "familiar" inputs the response will look like a pure
feed-forward operation. Only with more complex inputs relaxation will
modify the initial response. Our feeling is that in 200 ms a lot of 
multi-stage relaxations can take place...


                    Erik Fransen    Anders Lansner
		    SANS
                    Dept. of Numerical Analysis and Computing Sci. 
                    Royal Inst. of Technology, Stockholm
        
(1) Ekeberg, Wallen, Lansner, Traven, Brodin, Grillner (1991), 
    A Computer Based Model for Realistic Simulations of Neural Networks,
    (to appear in Biol. Cybernetics)
(2) Lansner & Fransen (1991), Modeling Hebbian Cell Assemblies 
    Comprised of Cortical Neurons, (Submitted)