What does Netstim.interval do?

[OJAG]

Hi All,

I am suplying random stream of spikes to the cells in a small network following the Poisson process dynamics. According to Poisson processes definition, if one spike occurs at t=t_i, the probability P of generating the next spike t_(i+1) anywhere in the interval t_i+tau<=t_(I+1)<t_i+tau+dt ,for dt small,i s the probability that no spike occurs at t=tau times the probability r*dt of generating the spike within the following interval dt, where r=firing rate, is

P(t_(i+1)-t_i)=r*dt*exp(r*tau) [1]

NetStim handles with interval by mean of the expression

invl(mean) =mean + mean*erand() [2]


where mean=interval and erand = exprand(1)

Are the interval variables in [1] and [2] the same?
if so, what the exponential single random number generator exprand(1) does?. If not, what does [2] and the statement " interval:mean time between spikes (ms)" exacty means? Could it be that the random stream of delivered is a periodic signal?


I have seen from my simulations, that by modifying the NetStim.interval, while maintaining constant the NetStim.number I can alter the behaviour of the cells spiking pattern.

One possible interpretation for this result relates this cells response with variations in the intrinsic frequency of the random spikes stream, represented by my NetStim but this interpretation would also correspond to a deterministic property of a completely random process. So what exactly does NetStim.interval do?


Thanks a lot,

OJAG

[ted]

The following code

Code: Select all

objref s
s = new NetStim()
s.noise = 1
s.interval = ISI
s.number = NUM

creates a NetStim that will generate a stream of events that occur at times t0, t1, . . . ti, . . . such that the inter-event intervals are governed by the negative exponential distribution with mean interval equal to ISI. If you execute a large number of simulations, each of which runs for "long enough", the mean number of events in the output stream will be NUM.

[OJAG]

Hi Ted,

Thanks for your answer. I understand now what interval is, but in that case if number is the result of averaging the events number for many "long enough" simulations.

Why is it necessary to also define number as the input parameter s.number = NUM, or in the default case (netstim.mod) where number= 10 <0,1e9>: number of spikes (independent of noise) ?

Doesn't it result conflicting ? or Are interval and number not related to each other?

How does NEURON handle with this part of the netstim.mod file assuming a poisson process (noise=1)?

Code: Select all

PROCEDURE next_invl() {
	if (number > 0) {
		event = invl(interval)
	}
	if (ispike >= number) {
		on = 0
	}
}

Thanks for your comments in advance

OJAG

[ted]

The "interval" and "number" parameters are independent of each other.

With regard to the average number of spikes produced during a simulation, let me correct myself. The maximum number of spikes that will be generated in any simulation is "number". However, the actual number that occur may be smaller--even 0. In the limit, as simulation duration approaches infinity, the expected number of spikes approaches "number".

[pjthomas]

Ted, when you refer to a "negative exponential distribution", are you actually referring to an exponential distribution?
The Binomial and Negative Binomial distributions are two closely related discrete distributions. (see e.g.
http://mathworld.wolfram.com/BinomialDistribution.html and
http://mathworld.wolfram.com/NegativeBi ... ution.html)
Are you drawing some distinction between "exponential" and "negative exponential?" The interarrival intervals for a Poisson process are
supposed to correspond to an exponential distribution -- I sure hope this is what NEURON is actually doing. Could you clarify?
Thanks,

-Peter Thomas

[ted]

Ted, when you refer to a "negative exponential distribution", are you actually referring to an exponential distribution?

Yep.
http://eom.springer.de/N/n066210.htm