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Figure 7 | BMC Bioinformatics

Figure 7

From: The complexity of gene expression dynamics revealed by permutation entropy

Figure 7

Illustration of the concept of Permutation Entropy ( PE ). The two artificial, exemplary gene expression time-series profiles in arbitrary units (a.u.) have the same length, but the resulting PE is different. For Example 1, only one order pattern is observed, namely (1,2,3); i.e., all values are strictly in ascending order. According to Eq. 1, its associated PE computes as PE1 = -5/5*log2(5/5) = 0. In Example 2, five different order patterns are observed (sliding window of three consecutive expression values): (2,3,1), (3,1,2), (1,3,2), (3,2,1), and (2,1,3). The position in each triplet corresponds to the temporal order, the associated value to the rank of corresponding expression value within the triplet, and correspondingly PE2 = -5*(1/5)*log2(1/5) = 2.32. Thus, Example profile 2 has a greater PE complexity compared to profile 1. The selected cases illustrate the extreme values of 0 and maximal PE of 2.32. There exists a certain degeneracy, which means that the PE for two genes may be the same even though their ordinal pattern sequences are different. For example, a gene may exhibit a temporal motif sequence of 1+3+6+7+9, while another gene followed a 2+5+10+12+9 pattern sequence, their entropy values are the same (PE = 2.32; i.e., the maximally possible value corresponding to 5 different patterns). Consequently, only seven discrete PE values are possible.

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