Calibrating spatiotemporal models of microbial communities to microscopy data: A review
Fig 5
Panels (a-c) illustrate the topology of a dataset changing as the length scale, L, is varied. (a) For small values of L, the balls (disks) are mostly disconnected; only 2 of the 9 intersect. (b) At an intermediate scale, all 9 balls intersect, forming a single connected component, giving rise to a loop. (c) At larger scales, there is a single connected component and no loop. (d) The progression illustrated in (a-c) is documented in the persistence barcode; the blue bars correspond to separate connected components, the ends of which corresponds to intersection (merge) events, e.g., at L = L1. The red bar corresponds to the loop, which forms at L = L2 and which becomes filled in at L = L3. (e) The same information can be represented in persistence diagram in which the (x,y) coordinates of points correspond to the right and left ends, respectively, of each bar in the barcode.