We thus conclude that the emergent hue curves in V1 are both inherited from the LGN and built on the recurrent interactions. The competition between J1andcpoints to a continuum of regimes in which either hlgnorhctxdominates. However, in all regimes, J0works cooperatively with cto narrow the curves, and all the parame ters work together to raise the network response. Likewise, the competition between J0and T(both cortical parameters) is modulated by the value of c, and the location of the peak is always completely determined by the LGN signal, regardless of the relative magnitudes of the cortical and stimulus strength parameters (see Methods :Evolution of Peak Angle ). Comparisons with the orientation tuning ring model. Finally, we seek to compare the emergent properties of the hue tuning model with those of the orientation tuning ring model ( Ben-Yishai et al., 1995 ;Hansel & Sompolinksy, 1998 ). This leads us to separate the analysis into two regions: one corresponding to the analytical regime with J0<1 2πβand J1<1 πβ, and the other to the extended regime with J1≥1 πβand J0constrained as described in the section Stability Analysis. As detailed in Methods :Linear Solution, the former regime defines the ( J0,J1) param-eter space wherein the model permits a closed-from stable solution for cases in which the input into all cells is above threshold. By contrast, the dynamics in the latter, extended regimealways implement thresholding and thus do not permit the linear closed-form solution. For comparison purposes, note that these parameter regimes are analogous to the orientation model 's homogeneous and marginal regimes, respectively, labels which refer to the system 's responses to unoriented stimuli. An important difference between our two models is our choice to assume modularity for the color vision pathway. As described above, there is no consensus as to when and how the var-ious visual features are separated along the visual pathway. That is, we do not yet understand how the brain recognizes the extent to which an activated color-and orientation-preferring neuron is signaling for a stimulus 's color or orientation. And moreover, we do not know at which point of the visual pathway the differentiation becomes important. We have therefore chosen to emphasize the unoriented color selective cells localized in the CO blob regions of V1, though the model is intended to describe the color-processing pathway broadly, for anycolor-preferring neurons regardless of other feature tuning capabilities. Thus, the choice ofmodularity is not to reject the possibility of joint feature processing, but rather to parse out the color mechanism for a separate analysis. Furthermore, it is in keeping with perceptual studies which indicate that the red-green and blue-yellow color-opponent systems are onlyresponsive to color stimuli and not to broadband, white light ( Stockman & Brainard, 2010 ). The difference between our two models thus comes to our choice to consider the purely chro-matic component of the input afferent from the LGN, whereas the orientation model incorpo-rates external inputs with varying degrees of anisotropy, that is, h extθð Þ ¼ c1-/C15þ/C15cos 2 θð Þ 1/2/C138 ;0≤/C15≤1=2 (28) where /C15represents the degree of anisotropy. The differing assumptions underlying the formulation of h(θ,t) have important implications for the subsequent parameter analyses adopted by our two models. In the orientation tuning model, the authors detail the pronounced shift in the relative roles of the cortical and stimulusparameters in narrowing the tuning curve. In this setup, for /C150. 5, an increase in cwidens the tuning curve, whereas for /C150, the tuning curve selectivity is completely determined by the cortical parameters. The latter scenario constrains the value of the analogous anisotropiccortical parameter, J 2, to the marginal regime. Network Neuroscience 695Pattern 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 