Figure 2

Illustration of the null models. An event sequence S of length n = 100 with event types r₁, r₂, r₃, r₄ and illustration of null models UL, FL, and FL(r) w.r.t. S with distance parameter w = 20. The sequence regions from which the W, C, and D scores are computed w.r.t. sequence S and event type r₁ are shown in the top half of the figure (n/w = 5 regions for the W score, and c(r₁) = 4 regions for the C and D scores). Models FL and FL(r) keep the locations of the events fixed, while UL randomly assigns new locations. In addition, here FL(r₁) keeps the labels of events of type r₁ fixed. All methods maintain the total number of events of each type. The co-occurrence counts for the pair (r₁, r₂) in the original sequence are W (r₁, r₂, S) = 3, C(r₁, r₂, S) = 4, and D(r₁, r₂, S) = 3. For the randomized sequences the counts are W (r₁, r₂, R_UL(S)) = 1, C(r₁, r₂, R_UL(S)) = 3, D(r₁, r₂, R_UL(S)) = 3, W (r₁, r₂, R_FL(S)) = 2, C(r₁, r₂, R_FL(S)) = 4, D(r₁, r₂, R_FL(S)) = 2, W(r₁, r₂, $R_{\text{FL}(r_1)}$ (S)) = 3, C(r₁, r₂, $R_{\text{FL}(r_1)}$ (S)) = 4, and D(r₁, r₂, $R_{\text{FL}(r_1)}$ (S)) = 3.