Three preprints on integrate-and-fire neuron models

[Anthony BURKITT]

Dear Connectionists,

I would like to announce the availability of three papers 
that have been accepted for publication and are of potential 
interest to people working on integrate-and-fire neurons. 
Electronic copies are available at the site:
http://www.medoto.unimelb.edu.au/people/burkitta/Pubs.html
or contact me at a.burkitt at medoto.unimelb.edu.au 
Feedback and comments are naturally very welcome.
Cheers,
Tony Burkitt

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Synchronization of the neural response to noisy periodic synaptic input

A. N. Burkitt and G. M. Clark

The timing information contained in the response of a neuron to noisy
periodic synaptic input is analyzed for the leaky integrate-and-fire 
neural model.  We address the question of the relationship between the 
timing of the synaptic inputs and the output spikes.  This requires an 
analysis of the interspike interval distribution of the output spikes, 
which is obtained in the Gaussian approximation.  The conditional output 
spike density in response to noisy periodic input is evaluated as a 
function of the initial phase of the inputs.  This enables the phase 
transition matrix to be calculated, which  relates the phase at which 
the output spike is generated to the initial phase of the inputs.
The interspike interval histogram and the period histogram for the 
neural response to ongoing periodic input are then evaluated by using 
the leading eigenvector of this phase transition matrix.  The 
synchronization index of the output spikes is found to increase sharply 
as the inputs become synchronized.  This enhancement of synchronization 
is most pronounced for large numbers of inputs and lower frequencies of 
modulation, and also for rates of input near the critical input rate.
However, the mutual information between the input phase of the stimulus 
and the timing of output spikes is found to decrease at low input rates 
as the number of inputs increases.  The results show close agreement 
with those obtained from numerical simulations for large numbers of inputs.

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

Accepted for publication in Neural Computation (to appear).

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Shot noise in the leaky integrate-and-fire neuron

N. Hohn and A. N. Burkitt

We study the influence of noise on the transmission of temporal
information by a leaky integrate-and-fire neuron using the theory
of shot noise. The model includes a finite number of synapses and
has a membrane potential variance de facto modulated by the
input signal. The phenomenon of stochastic resonance in spiking
neurons is analytically exhibited using an inhomogeneous Poisson
process model of the spike trains, and links with the traditional
Ornstein-Uhlenbeck process obtained by a diffusion approximation
are given. It is shown that the modulated membrane potential
variance inherent to the model gives better signal processing
capabilities than the diffusion approximation.

http://www.medoto.unimelb.edu.au/people/burkitta/article_PRE_ES7178.ps.zip

Published in Phys. Rev. E 63, 031902.
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Balanced neurons: Analysis of leaky integrate-and-fire neurons 
with reversal potentials

A. N. Burkitt

A new technique is presented for analyzing leaky integrate-and-fire 
neurons that incorporates reversal potentials, which impose a 
biologically realistic lower bound to the membrane potential.
The time distribution of the synaptic inputs is modeled as a 
Poisson process. The analysis is carried out in the Gaussian 
approximation, which comparison with numerical simulations 
confirms is most accurate in the limit of a large number of
inputs.
The hypothesis that the observed variability in the spike times 
of cortical neurons is caused by a balance of excitatory and 
inhibitory synaptic inputs is supported by the results for the 
coefficient of variation of the interspike intervals.  It's 
value decreases with both increasing numbers and amplitude 
of inputs, and is consistently lower than 1.0 over a wide 
range of realistic parameter values.  The dependence of the 
output spike rate upon the rate, number and amplitude of the 
synaptic inputs, as well as upon the value of the inhibitory 
reversal potential, are given.

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

Accepted for publication in Biological Cybernetics (to appear).

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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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