where Mi, 1 ≤ i ≤ k, is a simple motif component, and li and ui (for 1 ≤ i <k and where 0 ≤ li ≤ ui), are the minimum and maximum number of gaps allowed between Mi and Mi+1, respectively. Note that a gap is defined to be the number of intervening positions after Mi but before Mi+1. In other words, if si and ei represent the start and end positions of component Mi, then for i ∈ [1, k - 1], the number of gaps is given as gi = ei+1 - si - 1, and we require that gi ∈ [li, ui]. The number of simple motif components, k, is also called the length of ℳ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaaimaacqWFZestaaa@3790@. Let Wi, 1 ≤ i <k, denote the span of the gap range, [li, ui], which is calculated as: Wi = ui - li + 1.