In agreement with these findings, we let | x-x0|=|θ-θ0|, absorbing the regression param-eters into the connectivity strength values E0,E1,I0,a n d I1in Equation 8. Substituting this change of variables and setting J0=E0-I0,J1=E1-I1(measured in m V/spikes · sec-1) gives wθ-θ0ð Þ ¼ J0þ J1cosθ-θ0ð Þ : (9) As detailed in Figure 3, for J1> 0, this functional form captures the local excitation and lateral inhibition connectivity ansatz typically assu med in neural field models as an analogy to diffusion-driven pattern formation ( Amari, 1977 ;Bressloff, 2003 ;Hoyle, 2006 ;Kim, Rouault, Druckmann, & Jayaraman, 2017 ;Turing, 1952 ). Notably, neurons in close proximity in both cortical and hue space maximally excite each other, and those separated by Δθ=πmaximally inhibit each other, evoking the hue-opponency of perception on a cellular level. We empha-size, however, that this choice of metric is guided by our physiological definition of hue and does not associate a perceived color difference to measurements in hue space. Here, it is also important to distinguish between the connectivity function and the center-surround receptive fields of single-and double-opponent color cells ( Shapley & Hawken, 2011 ). While the structures of both can be approximated by the same functional form, the resemblance is superficial: the former characterizes the interactions between different neuro-nal populations, and the latter is a property of single cells, often adapted for computer vision algorithms ( Somers, Nelson, & Sur, 1995 ;Turner, Schwartz, & Rieke, 2018 ). Finally, we weigh the influence of the presynaptic cells by convolving the connectivity function with the network activity, arriving at the cortical input to the target hue population at time t: h ctxθ;tð Þ ¼Zπ-πwθ-θ0ð Þ aθ0;tð Þ dθ0: (10) The recurrent input is thus a continuous function in θ, derived from the population-level inter-actions. As put forward by the above-mentioned imaging studies, these interactions are colo-calized with the cone-opponent feedforward input, h lgn, within the same CO blob regions of Figure 2. (A) Hue map of individual hue-selective cells obtained by 2-photon calcium imaging of neuronal responsiveness to seven test hues. Scale bar: 200 μm. (B) Regions of peak response to test hues (solid contours). The dashed white lines demarcate the color-preferring regions, colocalized with the CO blobs. Scale bar: 0. 5 mm. Modified with permission from Liu et al. (2020). Network Neuroscience 685Pattern 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 