Preprints available

[Anthony BURKITT]

The following two papers on the analysis of integrate and fire 
neurons are available at the site:

http://www.medoto.unimelb.edu.au/people/burkitta/Pubs.html

1. Analysis of integrate and fire neurons: synchronization 
of synaptic input and spike output

2. New technique for analyzing integrate and fire neurons

I'd welcome comments.
Cheers,
Tony Burkitt

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Analysis of integrate and fire neurons: synchronization 
of synaptic input and spike output

A. N. Burkitt and G. M. Clark

A new technique for analyzing the probability distribution of output 
spikes for the integrate and fire model is presented. This technique 
enables us to investigate models with arbitrary synaptic response 
functions that incorporate both leakage across the membrane and 
a rise time of the postsynaptic potential. The results, which are 
compared with numerical simulations, are exact in the limit of a 
large number of small amplitude inputs. This method is applied 
to the synchronization problem, in which we examine the 
relationship between the spread in arrival times of the inputs (the 
temporal jitter of the synaptic input) and the resultant spread in 
the times at which the output spikes are generated (output jitter). 
The results of previous studies, which indicated that the ratio of 
the output jitter to the input jitter is consistently less than one 
and that it decreases for increasing numbers of inputs, are 
confirmed for three classes of the integrate and fire model. 
In addition to the previously identified factors of axonal 
propagation times and synaptic jitter, we identify the
variation in the spike generating thresholds of the neurons 
and the variation in the number of active inputs as being important 
factors that determine the timing jitter in layered networks. 
Previously observed phase differences between optimally and 
suboptimally stimulated neurons may be understood in terms 
of the relative time taken to reach threshold.

http://www.medoto.unimelb.edu.au/people/burkitta/synch.ps.zip

Accepted for publication in Neural Computation (to appear)

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New technique for analyzing integrate and fire neurons

A. N. Burkitt and G. M. Clark

By integrating over the distribution of arrival times of the afferent
postsynaptic potentials (PSPs), the probability density of the 
summed potential is calculated.  An output spike is generated 
when the potential reaches threshold, and the probability density 
of output spikes (the first-passage density) is calculated.
This "integrated-input" technique enables the investigation of 
models that incorporate the decay of the membrane potential 
and rise time of the synaptic current.  PSPs with a distribution 
of amplitudes, including inhibitory PSPs, are also analyzed.
The results are exact in the limit of large numbers of small 
amplitude inputs.

http://www.medoto.unimelb.edu.au/people/burkitta/cns98.ps.zip

Presented at CNS*98, to appear in Neurocomputing (in 1999).

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Anthony N. Burkitt
The Bionic Ear Institute                 
384-388 Albert Street
East Melbourne, VIC 3002
Australia
   
Email:  a.burkitt at medoto.unimelb.edu.au 
http://www.medoto.unimelb.edu.au/people/burkitta      
Phone: +61 - 3 - 9283 7510
Fax:     +61 - 3 - 9283 7518                                             
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