$1.($Spike trains$)$ Generate N $=50$ Poisson spike trains with rate $\backslash$lambda $=10$ spikes$/$s$,$ each lasting T $=5$ seconds. These will represent a fictitious dataset comprising recordings from the same neuron in N $=50$ trials of a fictitious experiment $($one spike train for each trial$).$ To generate the spike trains, generate first the inter$-$spike intervals $($ISIs$),$ and then obtain the spike times by cumulating the ISIs.

Here is the outline of the procedure:

$$ Use the fact that the ISIs of a Poisson spike train are exponentially distributed with parameter $\backslash$lambda $,$ i$.$e$.,$ ISI$=-$log$($u$)/\backslash$lambda $,$ where log$()$ denotes the natural logarithm in Matlab, and the random variable $$u$$ follows a uniform distribution between zero and one. The instruction u$=$rand$($n$,1)$ will generate n such random deviates. For the actual number of spikes to be generated, see Box $1.$

$$ The ISIs are the differences between successive spike times, $\{($t$2$t$1),($t$3$t$2),...,($tn $$tn$1)\},$ where t$1,$ t$2,...,$ tn are the spike times. Obtain the vector of spike times, t $\{$t$1,$ t$2,...,$ tn$\},$ by cumulating the ISIs: t$=$cumsum$($ISI$).$

$$ Repeat the above procedure N $=50$ times, once for each spike train.