state value. Within each time step (typically chosen to be 1 msec), we coarse-grain the net-work into n= 501 populations with hue preferences separated evenly across the DKL angle domain [-π,π]. The choice of an odd nallows us to numerically integrate Equation 10 using the Composite Simpson 's Rule, whereupon we rectify { h(θ,t)-T} and evaluate the right-hand side of Equation 1. Below, we use the term tuning curve only in reference to the emergent steady-state activity profiles. Figure 5 shows an example of a hue tuning curve obtained with this method. Note that the peak of the tuning curve is located at the LGN hue input angle /C18/C22, which is equivalent to the steady-state value of-γin Equation 26 (see Methods :Evolution of Peak Angle ). Furthermore, the steady-state solution requiresda∞θð Þ dt= 0 so that Equation 1 becomes a∞θð Þ ¼ gh∞θð Þ1/2/C138 : (27) Thus, the shape of the activity profile at the steady state is equivalent to the net cortical input, cut off by gatδ1≡θ⋆ c1andδ2≡θ⋆ c2. Here, θ⋆ c1andθ⋆ c2are the critical cutoff angles for the steady-state activity profile, beyond which a∞(θ) would take on negative values. We emphasize that the values of the cortical parameters J0,J1,c,T, and βare bounded by the physiological properties of V1. Varying these parameters in the subsequent analysis is therefore an investigation of their relative effects on hue processing, and we are not fine-tuning their weights to obtain specific hue tuning curves. Here, we explore a range of values for the cortical and stimulus parameters under the con-straint that the network activity remains between 0 and 60 spikes/sec, as motivated above. We further restrict J1> 0 and J0< 0 to elicit the local excitation and global inhibition connectivity ansatz of previous neural field models. Our main aim is to graphically characterize the relative effects of the parameters on the width, Δc=θ⋆ c2-θ⋆ c1, and peak height, a∞(θ/C22), of the network tuning curves. Together, these two properties reflect the network selectivity and emergent sig-nal strength, respectively. Note that these effects are robust to small additive white noise and may also be gleaned from the net input, expressed as in Equation 20 and evaluated at the steady-state values of the coefficients. Figure 5. Steady-state activity profile for a neuronal network encoding stimulus θ/C22=π/8. Parameters are as in Figure 4. Network Neuroscience 690Pattern forming mechanisms of color vision Downloaded from http://direct. mit. edu/netn/article-pdf/7/2/679/2118501/netn_a_00294. pdf by guest on 09 August 2024 