Network aging simulation notes, week Dec 16-20, 2013

Product $n$ and $p$ will decide the average links for the essential node. So, if $np$<1, most of the networks are dead. When $np$ is small, simulation take forever to generate enough viable individuals. Even in this case, it is looking for the extreme cases, so it is not a 'true' representation of the original distribution. From the biological perspective, it probably does not matter, because only viable new cells will be observed.

It can be seen that small $p$ values favor Gompertz model and large $p$ values favor Weibull model. (Because p=1.00 mean perfect network and Weibull aging).

Because the lattice network actually predict binomial mortality model,  and only early stage is exponential. So, fitting the entire curve with Gompertz and Weibull is not a good way to test the prediction. It can be seen that $t_0 = (1/p -1) / lambda$, so small $p$ lead to large $t_0$, and large $p$ leads to small $t_0$.  It can also be shown that small lambda lead to large $t0$. So, small $p$ and small $lambda$ should should give to better Gompertz model.