All-to-all connection and gating variable - NEST Users

24 Apr 2023

Dear friends,

   Thanks to all your help, I've successfully reproduced the behavior of the modified
Izhikevich neuron described in the paper:

Chen, L., Campbell, S.A. Exact mean-field models for spiking neural networks with
adaptation. J Comput Neurosci 50, 445–469 (2022).
https://doi.org/10.1007/s10827-022-00825-9

  But when I try to connect a population of neurons among themselves, I have problems. In
particular, imagine I create 10 neurons with the following Python code:
neurons = nest.Create("izhikevich_ODE", 10)

  Then, I found in some of the examples that the neurons do not come connected, and to
connect them all-to-all, I had to do the following:
nest.Connect(neurons, neurons, 'all_to_all')
  Is that right?

  Then, in the NESTML model, how do I receive the spikes into the gating variable? If I am
not wrong, I have to set the input as
input:
  spikes real <- spike
and then add them to the synaptic gating variable as a simple convolution:
  kernel G = delta(t)
  SS' = ((-SS/tau) + S_jump/N * convolve(G, spikes)) /s
 Note: the /s is because the equations in the paper are without units.
 Is this right? As kernel, I also tried exp(-t/tau), with the same tau as the one used for
SS, but then it seemed to take forever to compute, so I left the delta... However, if the
spikes themselves are Dirac deltas, I do not completely understand the meaning of this
convolution... What is the correct way to get the spikes from the other neurons?

  thanks!

gus.-