Fig. 3: Simplicial threshold model cascades on a C. elegans neuronal complex.
From: Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes
a 2D visualization of experimentally measured locations and synapse connections between neurons in nematode C. elegans78,79. We model higher-order nonlinear dynamical dependencies among sets of (k + 1) neurons using k-simplices in the associated clique complex for which we ignore edge directions. b Histograms depict the distribution of lengths for 1- and 2-simplices, where we define the length of a 2-simplex as the maximum length over its faces. We distinguish geometric and non-geometric 1-simplices by selecting a cutoff distance of 0.169 mm, and we characterize a 2-simplex as geometric if and only if all of its faces are geometric. c Vertex colors depict their first-activation times τi for a 2D STM cascade that is initialized with the indicated seed cluster. Observe that T and Δ affect the spatio-temporal pattern of activations (i.e., wavefront propagation and appearance of new clusters) similarly to what was shown in Fig. 1b).
