Persistence diagram extracted from one tile Tⁱ of the SLICS, in the KV450-like setup. The scattered points represent the features in Dgm(H₀(𝕏)) (red) and Dgm(H₁(𝕏)) (blue). For each feature, the x-value corresponds to the S/N-level at which that feature is born, whereas the y-value corresponds to the S/N-level at which it disappears again. The orange and green dots mark our evaluation points of the respective persistent Betti functions . The two dashed rectangles visualise regions in the diagram inside of which all features are counted, when computing the Betti functions at the evaluation points ( − 2, −0.6) and (0.2, 0.2).