Figure 9(a) shows how to enumerate structured motifs via positional joins. The pos-list of each component is simply the set of positions (1st element of the quadruples) under it. For example, P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqqGqbauaaa@3786@(M1) = {1, 5, 10, 21, 25, 32}. As before the joins proceed from M3 to M1, i.e., first we obtain the pos-list for M2 [0,9] M3, and then for M1 [0, 5] as head and M2 [0, 9] M3 as the tail. At any stage, the head motif's pos-list corresponds to the full list of positions shown, whereas the tail's pos-list consists only of the shaded positions. For illustration, we add a link between any two positions, x and y, in adjacent columns if their difference (d = y - x - 1) falls within the corresponding gap range. If the current partial motif starting at position x also satisfies the corresponding (partial) score threshold, the link is solid; otherwise, the link is dashed. When joining M2 as the head and M3 as the tail with a gap of [0, 9], the positions x ∈ P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqqGqbauaaa@3786@(M2) that satisfy the gap constraint are 10, 19 and 25 (marked in bold), which thus form the pos-list of M2 [0, 9] M3. We then check whether each occurrence satisfies the corresponding structured score threshold. Figure 9(d) shows the minimum partial scores required for each component suffix. For example the threshold λn (M2 [0, 9] M3) = 5.87. Checking the score for CATACG[0,9]TTACG, we get 2.44 + 3.48 = 5.92 > 5.87, so we keep it. The other occurrences also satisfy the partial score threshold. Next we join P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqqGqbauaaa@3786@(M1) with P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqqGqbauaaa@3786@(M2 [0, 9] M3) to get the valid positions 1, 5, 10 and 21. When checking with the score threshold, we find that the score of CATG[0,5]CATACG[0,9]TTACG is 1.05 + 5.87 = 6.97 < 8.60 = λn, so we discard this motif (as a result the corresponding link between the positions is dashed.) Finally, we get P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqqGqbauaaa@3786@(M1 [0, 5] M2 [0, 9] M3) = {1, 5, 21} as the pos-list for the full structured motif.