Inferring Causal Networks of Dynamical Systems through Transient Dynamics and Perturbation

The paper’s PCI algorithm defines the distance layers Dk(p), uses Case 2 to downweight edges when y lies beyond k+1 (including D∞), and derives the Case 3 Bayes update P(x→y | ∃v∈Dk(p) v→y) = P(x→y) / (1 − ∏v∈Dk(p)(1 − P(v→y))) (its Eq. (5))—all of which match the candidate’s steps (a)–(b) and formulae. The algorithm initializes A(x,y)=0.5, performs multiplicative updates (divide by 10 in Case 2; divide by 1−∏(1−A) in Case 3), and thresholds at 0.5, consistent with the candidate’s step (c) product-form summary. Minor issues: the paper implicitly assumes independence across {v→y} for Eq. (5), which the candidate states explicitly, and there is a small pseudocode/text mismatch for whether y∈D∞(p) is penalized in Case 2; the prose states it is, per k+1<m≤∞, while the printed loop looks like it excludes D∞ (see Algorithm 1 vs. Case 2 prose). Overall, both are aligned and use the same Bayes/independence argument.