Figure 1

SS in experimental and model feedforward networks. (a) Schematic of the “unfolding” of a feedforward architecture from a seemingly undirected network of neurons. We neglect feedback and interpopulation coupling (dashed lines). (b) Spike-time rasters (dots) and population activity histograms (solid; bin width $1\mathrm{ms}$) from iteratively constructed in vitro networks of cortical neurons (200 neurons per population); see [13] for details. No external noise was delivered to the neurons. As shown previously [13], adding noise to the in vitro network did not prevent synchrony. (c) Simulations of a feedforward network with linear IF neurons. We show network behavior $10\mathrm{s}$ after stimulus onset, long after onset-induced synchrony has dissipated. Unlike in experiments, external noise was added (see text). Dot rasters are shown for a portion of the histogram. Model parameters are $N=500,\beta =0.5,J_{ex}=2,J_{in}=-0.96,V_T=1,V_L=V_R=0,{\sigma }_e=0.31$, ${ϵ}_{ex}=0.1$, and ${ϵ}_{in}=0.048$. Simulations were performed with a stochastic Euler scheme with a time step of ${10}^{-5}$ [15]. In both panels (b) and (c) we show only populations 1, 6, and 10 [left-hand side of (b)].Reuse & Permissions

Figure 2

(Color online) DMFT predicts only transient synchrony. Expected firing rate ${\nu }_m\left(t\right)$ for $m=0,\dots ,4$ with $F_m\left(t\right)=0$. Open circles are simulations of the IF network, lines are simulations of the mean field with either $R_{m,eq}$ defined appropriately [18] (solid blue lines), or $R_{m,eq}=1$ (dashed red lines). The right panels show the solutions long after the initial transient. Model parameters are the same as in Fig. 1c except ${\nu }_0=40\mathrm{Hz}$, ${\sigma }_e=0.63$, and $N=1000$.Reuse & Permissions

Figure 3

(Color online) SS obtained in the finite size mean field equations. (a) Realizations of the SMFT for $N=500$ (thin red) and $10000$ (thick black) for $m=1,5,$ and 10 (left). Estimated distributions $p_m\left(\nu \right)$ (right). (b) Skewness $S_m$ for varying $N$ and $m$ computed from simulations of the IF network. Model parameters are the same as in Fig. 1c but with ${\sigma }_e=0.54$ and ${\nu }_0=15\mathrm{Hz}$.Reuse & Permissions

Figure 4

Oscillations accompany SS. (a) Normalized autocorrelations $A_1\left(\tau \right)$ and $A_{10}\left(\tau \right)$ calculated for simulations of the IF network (gray) and the SMFT (black) when $N=500$. Inset: $A_{10}\left(\tau \right)$ computed with $R_{m,eq}=1$ (black) superimposed with the result from IF simulations (gray). (b) $A_{10}\left(\tau \right)$ computed with $N=500$ and $10000$. Parameters are identical to those of Fig. 3.Reuse & Permissions