Redundancy Attributes of a Complex System: Application to Bioinformatics

In general, a complex system consists of a large number of interacting units, which when viewed in an information-theoretic perspective, could be seen to possess gross redundant features. Further, a complex system is inherently stochastical in its extensive spatiotemporal universe and hence, some of its statistical features could manifest as patterns occurring more frequently than others; and, likewise some other patterns could form rare elements of the same set. In information-theoretic perspectives (in Shannon's sense) such more (or less) probabilistic occurrences of features specify the redundant (or nonredundant) aspects of the complex system. This attribute of information redundancy in a complex system could be adopted to devise a useful complexity metric as described in this paper. The use of such a complexity metric is demonstrated in differentiating codon-noncodon domains in human and bacterial genomes (which constitute a complex system when seen at the scale of observing a DNA sequence made of vast domains of protein molecules).