Information Measure for Long-Range Correlated Sequences:

A new approach to estimate the Shannon entropy of a long-range correlated sequence is proposed. The entropy is written as the sum of two terms corresponding respectively to power-law (ordered) and exponentially (disordered) distributed blocks (clusters). The approach is illustrated on the 24 human chromosome sequences by taking the nucleotide composition as the relevant information to be encoded/decoded. Interestingly, the nucleotide composition of the ordered clusters is found, on the average, comparable to the one of the whole analyzed sequence, while that of the disordered clusters fluctuates. From the information theory standpoint, this means that the power-law correlated clusters carry the same information of the whole analysed sequence. Furthermore, the fluctuations of the nucleotide composition of the disordered clusters are linked to relevant biological properties, such as segmental duplications and gene density. Complex systems are probed by observing a relevant quantity over a cer-tain temporal or spatial range, yielding long-range correlated sequences or arrays, with the remarkable feature of displaying ‘ordered ’ patterns, which emerge from the seemingly random structure. The degree of ‘order ’ is in-1 a