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, RUL(S)) = 1, C(r1, r2, RUL(S)) = 3, D(r1, r2, RUL(S)) = 3, W (r1, r2, RFL(S)) = 2, C(r1, r2, RFL(S)) = 4, D(r1, r2, RFL(S)) = 2, W(r1, r2, (S)) = 3, C(r1, r2, (S)) = 4, and D(r1, r2, (S)) = 3.