/*
* ArtificialSynchrony.sli
*
* This file is part of NEST.
*
* Copyright (C) 2004 The NEST Initiative
*
* NEST is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 2 of the License, or
* (at your option) any later version.
*
* NEST is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with NEST. If not, see <http://www.gnu.org/licenses/>.
*
*/
%%%%%%%%%%%%%%%% Write welcome message %%%%%%%%%%%%%%%%%%%%%%
(\n\n) =
1 1 80 { (#) =only } for ( ) =
(Artificial synchrony can be introduced by discrete-time simulation
of neuronal networks, because they typically constrain spike times to a
grid determined by the computational step size. Hansel et al. (1998) used
a small all to all connected network of spiking neurons to demonstrated
that this artificial synchrony can be reduced by a finer resolution or by
interpolating for the correct spike times. In a further step Morrison et
al. (2007) showed that by interpolating the exact spike times and
distributing them, not only the artificial synchrony is avoided
but even machine precision can be obtained for small time steps.
Here, we simulate the 'Hansel' network of 128 all to all connected
excitatory I&F neurons with alpha shaped PSC in the
1. precise implementation by Morrison et al. (2007).
2. grid constrained implementation
The synchrony of the network can be calculated from the membrane
potentials of each neuron following Hansel et al. (1998). Thus, by
varying the coupling weights and estimating the corresponding
synchrony of the network the results of Hansel et al. (1998), Morrison
et al. (2007) and Diesmann et al. (2008) can be reproduced.
An additional Perl script performs the task to calculate the synchrony
and generate the final plot.
References:
D. Hansel, G. Mato, C. Meunier, and L. Neltner. On numerical
simulations of integrate-and-fire neural networks. Neural Computation,
10(2):467-483, Feb., 15 1998.
A. Morrison, S. Straube, H. E. Plesser, and M. Diesmann. Exact
subthreshold integration with continuous spike times in discrete time
neural network simulations. Neural Computation, 19(1):47-79, 2007.
Diesmann M, Hanuschkin A, Helias M, Kunkel S and Morrison A
(2008). The performance of solvers for integrate-and-fire models with
exact spike timing. Frontiers in Neuroinformatics. Conference
Abstract: Neuroinformatics 2008.
AH 09) =
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%%%%%%%%%%%%%%%%% Simulation parameter %%%%%%%%%%%%%%%%%%%%%%%%%
(Set Simulation Parameters ) =only
/nr 128 def % number of neurons in the network
/h 0.03125 def % simulation resolution h=2^-5
/C_m 250.0 def % membrane capacitance
/E_L 0.0 def % leaky potential
/I_e 575.0 def % suprathreshold current
/tau_m 10.0 def % membrane time constant
/V_reset 0.0 def % reset potential
/V_th 20.0 def % threshold potential
/t_refra 0.25 def % refractory time
/tau_syn_ex 1.648 def % syn. time constant 3/2ln3
%/tau_syn_in 1.648 def
/INTERPOL 3 def % cubic interpolation (canonical model)
/gamma 0.5 def % parameter determining the degree of synchrony at the beginning
/tofile true def % write potentials of the neurons to file
/delay 0.25 def % synaptic delay
%% initialize random number generator
rngdict /gsl_mt19937 get 2000 CreateRNG /myrng Set % usage 'myrng drand' for double in in [0, 1)
(-DONE-) =
%%%%%%%%%%%%%%%%% Setup report %%%%%%%%%%%%%%%%%%%%%%%%%
(gamma []: \t) =only gamma = % The initial synchronization is determined by gamma.
(delay [ms]:\t) =only delay =
(tau_r [ms]:\t) =only t_refra =
%% Calculate spike period T (needed for setup of initial membrane potential)
tau_m C_m div /R Set
R I_e mul E_L add V_reset sub R I_e mul E_L add V_th sub div ln tau_m mul dup /T Set
(ISI [ms]:\t) =only T =only
1.0 exch div % now we have the fire rate
(, i.e. firingrate [Hz]: ) =only 1000.0 mul =
%%%%%%%%%%%%%%%%% Start Simulation Section %%%%%%%%%%%%%%%%%%%%%%%%%
1 1 2 {
/sim Set % sim = 1 Canon / sim = 2 Grid
sim 1 eq {
/params <<
/C_m C_m
/E_L E_L
/I_e I_e
/tau_m tau_m
/tau_syn tau_syn_ex
/V_m E_L
/V_reset V_reset
/V_th V_th
/t_ref t_refra
/Interpol_Order INTERPOL
>> def
}
{
/params <<
/C_m C_m
/E_L E_L
/I_e I_e
/tau_m tau_m
/tau_syn_ex tau_syn_ex
/V_m E_L
/V_reset V_reset
/V_th V_th
/t_ref t_refra
>> def
} ifelse
() =
1 1 40 { (#) =only } for
sim 1 eq {(\nRun the canonical simulations first: )= }
{(\nRun the grid constrained simulations now: )= } ifelse
modeldict begin
userdict begin
0.0 0.2 5.0 {
cvd /strength Set
(weigth [pA]:\t) =only strength =
%set resolution and limits on delays
% limits must be set BEFORE connecting any elements
[0]
<<
/resolution h % time steps in ms
/off_grid_spiking true % precise neuron model
/rngs [myrng] % set rnd seed
/overwrite_files true % overwrite previous output
>> SetStatus
sim 1 eq { /iaf_psc_alpha_canon nr Create pop }
{ /iaf_psc_alpha nr Create pop } ifelse
/neurons [0] GetNodes def
% connect neurons all to all
neurons {
/ii Set
neurons {
dup
/ii2 Set
ii
% neq { % uncomment to avoid self connections
ii ii2 strength delay Connect
% } if
} forall
} forall
/* % uncomment to verify connections
%% Readout if everything works
neurons {
/ii Set
(\n\nneuron ) = ii = (connects to) =
<< /source ii /synapse_model /static_synapse >> FindConnections
{ GetStatus /target get } Map ==
} forall
*/
%% Set the neuron parameters according to definition
(Set neuron parameters ) =only
neurons {
params SetStatus
} forall
(-DONE-) =
%% Set initial potentials
(Set initial potentials [mV] (Morrison et al. 2007) ) =only
neurons {
/ii Set
R I_e mul % like Morrison et al. 2007
1 -1.0 gamma mul ii 1 sub nr cvd div T tau_m div mul mul exp sub mul
%dup = % uncomment to print out value of initial potentials
%%% Alternatively take just random initial states
% myrng drand
% V_th V_reset sub mul
% V_reset add dup
% =
/V_0 Set
ii << /V_m V_0 >> SetStatus % set initial potential to each neuron
} forall
(-DONE-) =
(Create voltmeter ) =only
%% generate spike detectors and voltmeter for each neuron
% /spike_detector Create /detec Set % spike detectors will generate enormous amount of data!
% detec << /to_file tofile /withgid true /interval 0.1 >> SetStatus
/voltmeter Create /volt Set
volt << /to_file tofile % write to file
/to_memory false % not to memory
/withgid true % important to know which neuron
/withtime true
% /interval 1.0 % record only every msec.
>> SetStatus
sim 1 eq {volt << /label (voltmeter-Canon-) strength cvs join >> SetStatus}
{volt << /label (voltmeter-Grid-) strength cvs join >> SetStatus} ifelse
(-DONE-) =
neurons {
dup
% detec 1.0 h Connect % connect spike_detector
volt exch 1.0 h Connect % connect voltmeter
} forall
10000 Simulate % simulate for 10s
ResetKernel
} for % for each coupling strength
end
end
} for % for each neuron model