Figure 4
From: A universal null-distribution for topological data analysis
Computing p-values for the 8-shape (a wedge of circles). (top-left) Persistence diagrams for two instances of the 8-shape with different neck gaps, with the significance lines shown for \(\alpha =0.05\) (the dotted and dashed lines correspond to \(W=0.1\) and \(W=0.4\), respectively). (top-right) The average number of signal cycles detected in 100 repetitions, as a function of the neck gap. (bottom) In green we show significant cycles. On the left (\(W=0.1\)) we see two significant cycles (p-values = 0.0005, 0.012), and on the right (\(W=0.4\)) only the outer cycle is significant (p-value=0.0015).
