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Figure 2 | Algorithms for Molecular Biology

Figure 2

From: Periodic pattern detection in sparse boolean sequences

Figure 2

Building elements for the scoring function (Eq. 3). Left upper panel: The sites modulo the period are numerated clockwise. Their relative positions depend on the value P of the period. The normalized (with respect to the period P) distance between the jth nearest neighbors on each side of i is called x i , j P . Right upper panel: The jth nearest neighbors on each side of any site i are separated by 2j - 1 sites. Hence, in order to compute the p-value p j N ( x i , j P ) associated to any distance x i , j P , one needs the density distribution, respectively the repartition function, for the distances between sites that are separated by 2j - 1 sites, that is ρ 2 j 1 N and F 2 j 1 N respectively. For any x 0[1], p j N ( x ) corresponds to the area of the tails of ρ 2 j 1 N (indicated in brown for N = 11, j = 2 and x = x 2 , 2 P ). For questions of computational readiness, p j N ( x ) is approximated by min ( F 2 j 1 N ( x ) , 1 F 2 j 1 N ( x ) ) - see Eq. (4) - which is represented by the cuspate red curve. Left lower panel: The contribution of both x 10 , 1 P and x 6 , 1 P is evaluated from the same density function ρ 1 11 ( x ) since both distances correspond to sites that are separated by one single site. Right lower panel: x 10 , 1 P corresponds to a dense region whereas x 6 , 1 P reflects a poor region (see left upper panel).

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