Network connectivity. In order to place the network in the appropriate dynamic regime, PN-PN connectivity must be sparse, while connection probabilities involving LNs can vary broadly. (**a**) Sample spike rasters of background PN activity from networks with progressively denser connectivity. The cell type specific connection probabilities associated with each raster are given by PN-PN*=*0.1+d, PN-LN*=*0.1+d, LN-PN*=*0.15+d, and LN-LN*=*0.25+d. (**b**) Sample spike rasters of background PN activity from a network in which only PN-PN connectivity is dense (0.5) while connections involving LNs remain sparse (PN-LN*=*0.1, LN-PN*=*0.15, LN-LN*=*0.25). The strength of PN-PN synapses has been weakened as much as possible while maintaining appropriate dynamical behavior under stimulation. The rasters shown are from networks with or without GABAergic transmission, and in the presence of normal- or triple-strength slow inhibitory synapses. (**c**) Plots from a network in which connection probabilities involving LNs are dense (0.5) while the PN-PN connection probability remains sparse (0.1). The strength of LN inhibition and PN excitation to LNs has been weakened to compensate for the increased synaptic density (top row—intact network, bottom row—no GABAergic transmission). From left to right: spike rasters of spontaneous PN activity, power spectrum of the network LFP under stimulation, trial-averaged spike rasters from three sample PNs (20 trials, black bar represents stimulus)

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