Table 1.

Granger causality analysis to estimate connectivity

Steps	Formulation
1. Modeling the CIF using GLM framework	$log{\lambda }_i\left(t\mathrm{\mid }{\theta }_i,H\left(t\right)\right)={\theta }_{i,0}+{\sum }_{n=1}^N{\sum }_{m=1}^{M_i}{\theta }_{i,n,m}{R}_{n,m}\left(t\right),$where, ${\theta }_{i,0}$ represents the baseline activity, and ${\theta }_{i,n,m}$ represents the effect of ensemble spiking history $R_{n,m}\left(t\right)$ of neuron n on the firing probability of neuron i at time t for n = 1, …, N neurons. Here $R_{n,m}\left(t\right)$ is modeled as the spiking history using a binwidth W (set as 3 ms) spanning the interval [t – mW, t-(m-1)W]
2. Selecting model order	Akaike’s Information Criterion
3. Likelihood of causality	${\mathrm{\Gamma }}_{ij}=log\frac{L_i\left({\theta }_i\right)}{L_i\left({\theta }_i^j\right)}$
	$=log\frac{Pr\left(t+1ofi\mid \mathrm{p}ast\mathrm{o}f\mathrm{e}veryone\mathrm{u}ptot\right)}{Pr\left(t+1\mathrm{o}fi\mid \mathrm{p}ast\mathrm{o}f\mathrm{e}veryone\mathrm{e}xceptj\mathrm{u}ptot\right)}$
4. Connection polarity	$\mathrm{sgn}∣{\sum }_{m=1}^{M_i}{\theta }_{i.j.m}∣$