Quantifying the global symmetry of firing patterns.

a) Generated spike maps in a 1m × 1m arena. Each spike k is color-coded with its grid score ; global Ψ score shown above. Top: Perfect grid. Middle: Weakly perturbed grid field locations. Bottom: Strong perturbations. See text for description of perturbations. b) Autocorrelograms of the spike maps shown in a; ρ score shown above. c) Decay of Ψ score (top) and ρ score (bottom) with increasing noise on grid field locations. Box plot for 100 random realizations at each noise level. For details on the box plot see S1 Appendix. Noise values for the examples shown in a are indicated with markers. d) Correlation of Ψ score with ρ score and Pearson’s coefficient r for the generated data used in a, b, c. e) Same as d but with experimentally recorded data from [6, 16].