Fig. 4.
The SCM. (A) Neurons can only synapse if they are in physical contact. We schematically indicate physical contacts via touching neuron contours in the figure, and contacting neuron pairs are marked by a one in the matrix . Note that neurons can be in physical contact with themselves and even form synapses. (B) Given the lack of physical contact, only a fraction of the genetically allowed synapses are observed. The dashed links in the network, shown as ones in gray cells in the adjacency matrix below, indicate neural connections that are genetically permitted but are not observed because the neurons are not in contact. (C) When inferring genetic rules, distant neuron pairs must be ignored in the model (gray cells), as we do not know whether the lack of connection has a genetic origin or is simply due to spatial constraints. We therefore arrive at a truncated matrix representation, which does not obey standard matrix operations, and hence is challenging to work with. (D) If we treat all unobserved cells (gray and blank) as zeros, the matrix representation leads to incorrect rules, as it always assumes the lack of genetic compatibility where there may be some. (E) The edge list representation offers a linear description that is formally equivalent with the matrix representation. (F) Distant pairs of neurons can be removed from the edge list representation, and, as a truncated list is still a list, it allows us to uncover the correct rules based on Eq. 5.