| Description: |
pp_psc_delta is an implementation of a leaky integrator,
where the potential jumps on each spike arrival.
Spikes are generated randomly according to the current value of the
transfer function which operates on the membrane potential. Spike
generation is followed by an optional dead time. Setting with_reset to
true will reset the membrane potential after each spike.
The transfer function can be chosen to be linear, exponential or a sum of
both by adjusting three parameters:
rate = Rect[ c1 * V' + c2 * exp(c3 * V') ],
where the effective potential V' = V_m - E_sfa and E_sfa is called
the adaptive threshold.
By setting c3 = 0, c2 can be used as an offset spike rate for an otherwise
linear rate model.
The dead time enables to include refractoriness. If dead time is 0, the
number of spikes in one time step might exceed one and is drawn from the
Poisson distribution accordingly. Otherwise, the probability for a spike
is given by 1 - exp(-rate*h), where h is the simulation time step. If dead_time
is smaller than the simulation resolution (time step), it is internally
set to the time step.
Note that, even if non-refractory neurons are to be modeled, a small value
of dead_time, like dead_time=1e-8, might be the value of choice since it
uses faster uniform random numbers than dead_time=0, which draws Poisson
numbers. Only for very large spike rates (> 1 spike/h) this will cause errors.
The model can optionally include something which would be called adaptive
threshold in an integrate-and-fire neuron. If the neuron spikes, the
threshold increases and the membrane potential will take longer to reach it.
Here this is implemented by subtracting the value of the adaptive threshold
E_sfa from the membrane potential V_m before passing the potential to the
transfer function, see also above. E_sfa jumps by q_sfa when the neuron
fires a spike, and decays exponentially with the time constant tau_sfa
after (see [2] or [3]). Thus, the E_sfa corresponds to the convolution of the
neuron's spike train with an exponential kernel.
This adaptation kernel may also be chosen as the sum of n exponential
kernels. To use this feature, q_sfa and tau_sfa have to be given as a list
of n values each.
This model has been adapted from iaf_psc_delta. The default parameters are
set to the mean values in [2], which have been matched to spike-train
recordings.
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| References: |
[1] Multiplicatively interacting point processes and applications to neural
modeling (2010) Stefano Cardanobile and Stefan Rotter, Journal of
Computational Neuroscience
[2] Predicting spike timing of neocortical pyramidal neurons by simple
threshold models (2006) Jolivet R, Rauch A, Luescher H-R, Gerstner W.
J Comput Neurosci 21:35-49
[3] Pozzorini C, Naud R, Mensi S, Gerstner W (2013) Temporal whitening by
power-law adaptation in neocortical neurons. Nat Neurosci 16: 942-948.
(uses a similar model of multi-timescale adaptation)
[4] Grytskyy D, Tetzlaff T, Diesmann M and Helias M (2013) A unified view
on weakly correlated recurrent networks. Front. Comput. Neurosci. 7:131.
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