FDR-based inference on Izhikevich simulation using cross-correlation as metric

Simulation of Izhikevich neurons (10 and 100 neurons):

In the above simulation, all neurons are independent (no synaptic connections). Here is a distribution of $C_{ij}^\mathrm{max}$ for uncorrelated neurons (i.e. the "distribution of the test statistic under the null hypothesis"):

Now here is a set of neurons with some synaptic connections between them. (Not easy at all to discern the underlying graphical structure.)

We consider the distribution of $p$-values for synaptic pairs in the Izhikevich model as a function of the "synaptic strength" constant $\alpha$:

The above shows that a synaptic strength of $\alpha \approx 10$ is necessary to discern the connectivity structure in the Izhikevich model. Note that $\alpha \approx 10$ does not yield a totally trivial (i.e. deterministic firing) relationship between two synaptically connected neurons. Here is a trace of two neurons with connectivity of $\alpha = 10$ that shows that the relationship is not necessarily deterministic:

For that matter, $\alpha = 20$ doesn't yield deterministic relations either, but there are more (almost) coincident spikes between the two:

(Note: An independent characterization for the "interpretation" of $\alpha$ could be an empirically derived probability that the post-synaptic neuron fires within some interval of receiving the pre-synaptic spike.)

Next, let's try some inference on a model of $N=10$ neurons with $M=10$ synapses. (My eventual target is to run simulations on $N=100$ or even $N=10^3$ neurons.) I visualize the inference result as an adjacency matrix, where a filled green rectangle represents a correctly inferred edge, unfilled green rectangle represents an uninferred edge (false negative) and a filled red rectangle represents a falsely inferred edge (false positive). All inference instances are for $\alpha=10$.

Also, examples of inference on $N=100$:

Next, I want to obtain the ROC curve.