13th International Conference on Membrane Computing - MTA Sztaki

R. Pagliarini, O. Agrigoroaiei, G. Ciobanu, V. Manca
τ
causal relationship between them exists, that is, x 2→ τ 1−τ 2
i xz → xj . Therefore, if
ρ C1 (x i , x j ) is smaller than a given threshold, then we consider that there isn’t a
significant direct cause-effect relationship between x i and x j . From the definition,
we have that if x i [t] = x z [t + τ 2 ] or x j [t] = x z [t + τ 2 ], for t = 0, 1, m − τ 1 , then
(8) is not defined. In this case, we set ψ(x i , x j , τ 1 | x z , τ 2 ) = 0.
As in the case of partial correlation, we can start from (7) and (8) to obtain
the partial cross-correlation between x i and x j conditioned on all the other n−2
species in the set Z = X − {x i , x j }:
φ Call (x i , x j ) =
min |ψ(x i , x j , τ 1 | Z, τ 2 )| . (9)
0≤τ 2