COMMENT
Multiple presynaptic spike generator with correlated outputs
------------------------------------------------------------
ALGORITHM
This mechanism has been written to be able to use synapses in a single
neuron receiving various types of presynaptic trains. Several randomly
spiking outputs are generated here, but correlated with each other
according to a given correlation coefficient (correl).
"Distributed generator"
The algorithm generates N output variables with correlation according
to the following algorithm. N2 independent Poisson-distributed variables
are generated and distributed among the N output variables. If N2<N, there
will be some redundancy in the N outputs and the correlation is a complex
function of N and N2:
If N2 = 1, correl=1 (all outputs are identical to the same rnd variable)
If N2 = N, correl=0 (all outputs are independent rnd variables)
If N2>1 and N2<N, the correlation is intermediate
The program calculates N2 from the linear interpolation:
N2 = N + (1-N) * sqrt(correl)
The algorithm starts by generating N2 independent variables (R[i]), then
distribute these N2 variables among the N outputs using a coin-tossing
procedure.
INPUT PARAMETERS
N : number of random channels generated
freq : mean frequency of firing of each channel (Hz, nb spikes per second)
correl : value of the desired correlation
refract: minimal period between spikes (ms)
min_val: min value of presynaptic variable (mV)
max_val: max value of presynaptic variable (mV)
on : on=1 the generator is on, on=0 it is interrupted (default=1)
on=2, a spike is forced for all outputs, then on is reset to 1
on=3, a spike is forced for outputs selected by the vector "sync"
sync : array of flags; when sinc[i] is set to 1, then channel i will
fire when on=3
latency: latency at which spikes begin (ms; initialized to 0)
shutoff: time at which the generator is shutoff (ms; initialized to -10000)
OUTPUT PARAMETERS
x : array of N elements, contain the values of the outputs
ns : array of N elements, spike count for each channel (reset by init)
ls : array of N elements, time of last spike (reset by init)
spont : spontaneous probability of firing, calculated at each dt
ext : external trigger, calculated at each dt
prob : probability of firing, calculated at each dt
PROCEDURES
new_seed : sets the seed to the value passed as argument
printvec : prints the vectors
EXAMPLE OF HOW TO USE
access PRE // presynaptic compartment is fake here
objectvar pg
pg = new corrGen(0.5) // create random spike generator
pg.N = 10 // number of output channels
pg.freq = 40 // mean frequency of firing of each channel (Hz)
pg.correl = 0 // correlation between outputs
pg.refract = 1 // refractory period for spikes (ms)
pg.min_val = -70 // min value of presynaptic variable (mV)
pg.max_val = 40 // max value of presynaptic variable (mV)
pg.latency = 50 // time at which generator begins (ms)
Alain Destexhe, Laval University, 1995
Modif: June 98: added special case for correl=0 to accelerate
-------------------------------------------------------------------
ENDCOMMENT
DEFINE MAXCHANNELS 25000 : maximum number of outputs
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
POINT_PROCESS corrGen8
RANGE N, freq, correl, refract, min_val, max_val
RANGE on, latency, shutoff
RANGE x, ns, ls, sync
RANGE spont, prob, N2
RANGE new_seed, printvec
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
PARAMETER {
dt (ms)
N = 100 : number of outputs
N2 = 1 : number of independent variables
freq = 40 (/s) : mean frequency of firing of each channel
correl = 0 : correlation between outputs
refract = 1 (ms) : refractory period for spikes
min_val = -70 (mV) : min value of presynaptic variable
max_val = 40 (mV) : max value of presynaptic variable
on = 1 : logical on/off variable
latency = 0 (ms) : time at which spikes begin
shutoff = 1e6 (ms) : shutoff time
}
ASSIGNED {
x[MAXCHANNELS] (mV) : outputs
R[MAXCHANNELS] : independent variables
ns[MAXCHANNELS] : spike counters for each channel
ls[MAXCHANNELS] : time of last spike for each channel
sync[MAXCHANNELS] : flag for sync firing
spont : probability of spontaneous firing
prob : probability of firing
}
INITIAL { LOCAL i
spont = (0.001) * freq * dt : initiate spontaneous probability
if(spont > 0.5) {
VERBATIM
printf("\n\nERROR in correlated random generator\n");
printf("firing probability is too high: spont=%g\n",(float)spont);
printf("decrease integration step or mean firing frequency\n");
exit(-1);
ENDVERBATIM
}
FROM i=0 TO N-1 {
ns[i] = 0
ls[i] = -10000
}
N2 = N + sqrt(correl) * (1-N)
go()
}
BREAKPOINT {
SOLVE go
}
UNITSOFF
PROCEDURE go() { LOCAL i, j, sum
: reset all channels
FROM i=0 TO N-1 {
x[i] = min_val
}
if( (on==1) && (t>=latency) && (t<=shutoff) ) {
: Determine how to distribute random variables among the N outputs:
if(correl==0) { : If correl=0, create N random variables
FROM i=0 TO N-1 {
if(get_random(1) <= spont) { : toss coin...
x[i] = max_val : spike!
} else {
x[i] = min_val
}
}
} else { : if correl>0, distribute N2 rnd in N outputs
FROM i=0 TO N2-1 { : first generate N2 random variables
if(get_random(1) <= spont) { : toss coin...
R[i] = max_val : spike!
} else {
R[i] = min_val
}
}
FROM i=0 TO N-1 { : scan each output variable
j = get_random(N2) : chose one of the rnd variable
x[i] = R[j] : assign the rnd variable
}
}
: update the counters and check for refractory period
FROM i=0 TO N-1 {
if((t-ls[i]) <= refract) { : force to zero if refractory
x[i] = min_val
}
if(x[i] == max_val) { : if variable has fired
ns[i] = ns[i] + 1 : increase spike count
ls[i] = t : memorize last spike
}
}
} else if(on==2) {
FROM i=0 TO N-1 { : fire all channels
x[i] = max_val : spike !
ns[i] = ns[i] + 1 : increase spike count
ls[i] = t : memorize last spike
}
on = 1 : reset to normal
} else if(on==3) {
FROM i=0 TO N-1 { : fire channels selected by sync
if(sync[i]) {
x[i] = max_val : spike !
ns[i] = ns[i] + 1 : increase spike count
ls[i] = t : memorize last spike
}
}
on = 1 : reset to normal
}
}
UNITSON
FUNCTION get_random(maxval) { : simple random
get_random = maxval * rand()/(2^15) : windows, linux is random()/(2^31)
}
PROCEDURE new_seed(seed) { : procedure to set the seed
srand(seed) : windows, linux is srandom(seed)
VERBATIM
printf("Setting random generator with seed = %g\n", _lseed);
ENDVERBATIM
}
PROCEDURE printvec() { LOCAL i : procedure to print the vectors
VERBATIM
{
int i;
printf("i\tx\tns\tls\n");
for(i=0; i<N; i++) {
printf("%d\t%g\t%g\t%g\n",i,(float)x[i],(float)ns[i],(float)ls[i]);
}
}
ENDVERBATIM
}