Table 2. Summary of results on statistical signatures of three network scenarios.

Average noise and signal correlation coefficients are denoted by c_N and c_S, respectively, while c_in determines the strength of signal correlations in the input; see Methods. See S1 Appendix for detailed derivations.

Network model	〈Cii〉i	〈Cij〉i ≠ j	cN	cS
Recurrent network model	N〈B2〉(〈r〉(s) + a + 〈Vext〉)	N〈B2〉(〈r〉(s) + a + 〈Vext〉)	$\frac{1}{1+\rho }$	$\frac{1+(N-1)c_{\text{in}}}{1+\rho +(N-1)c_{\text{in}}}$
Feed-forward network model	〈r〉 + a + N〈Vext〉〈F2〉	N〈F〉2〈Vext〉(s)	$\frac{N{\langle F\rangle }^2\langle V_{\text{ext}}\rangle }{\langle r\rangle +a+N\langle V_{\text{ext}}\rangle \langle F^2\rangle }$	$\frac{1+(N-1)c_{\text{in}}}{1+\rho +(N-1)c_{\text{in}}}$
Gain-fluctuation model	$\frac{1}{N}{V}_{\text{ext}}{\sum }_i{r}_i^2+\langle r\rangle$	Vext〈r〉2	$\frac{V_{\text{ext}}{\langle r\rangle }^2}{\frac{1}{N}{V}_{\text{ext}}{\sum }_i{r}_i^2+\langle r\rangle }$	-