Input: gene expression time-series (either based on pseudotime-series, “RNA-velocity” or live imaging data, among others) ${\underset{\_}{X^{(i)}}}^t$ for each gene i

Output: A matrix of pairwise causality scores

Parameters: d: vector of delays, L: number of conditioning genes

Pseudocode:

1. For each pair of genes (i, j):

- For all delays δ ∈ d: Calculate RDIδ (X(i) → X(j))

- Set ${\delta }_{i,j}^{\max }:=\underset{\delta \in d}{\arg \max }RD{I}_{\delta }\left(X^{(i)}\to X^{(j)}\right)$

2. For each gene j:

- For all i: sort $RD{I}_{{\delta }_{i,j}^{\max }}\left(X^{(i)}\to X^{(j)}\right)$ values in descending order

- According to the sorting above, take the L + 1 nodes i with the highest incoming RDI values to j and store them in a set as $in{c}_j^{\max }$. Store their corresponding delays ${\delta }_{i,j}^{\max }$ in a set $d_j^{\max }$.

3. For each pair of genes (i, j):

- If $i\in in{c}_j^{\max }$, remove i from $in{c}_j^{\max }$. Otherwise, remove the node l with the lowest $RD{I}_{{\delta }_{i,j}^{\max }}\left(X^{(l)}\to X^{(j)}\right)$ from $in{c}_j^{\max }$.

4. For each pair of genes (i, j): Output $RD{I}_{{\delta }_{i,j}^{\max }}\left(X^{(i)}\to X^{(j)}|{\left\{X_{t-{\delta }_{l,j}^{\max }}^{(l)}\right\}}_{l\in in{c}_j^{\max }}\right)$