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See [19, 20] for more details on MI analysis.

The following algorithm describes the MI analysis of a given parity-check matrix.

cIn addition to the MI analysis, we performed an empirical test regarding use of 0.25 CPO filter.

In the following, we use the average a posteriori variable node MI denoted by (calculated for each variable node in step (5) of the MI analysis in the appendix) to compare the convergence rates of different LDPC codes.

MI analysis was performed according to the methods described in [35].

Statistical coupling analysis (SCA), mutual information (MI) analysis and residue correlation analysis (RCA) are the most typical covariance analysis algorithms.

The sites in clusters m and n substantially overlap with those in the corresponding clusters identified by both SCA and MI analysis, respectively.

Above all, the MI analysis provides detailed indications about amino acids located in the transmembrane region of these receptors that determine G-protein signalling pathway preferences.

In MI analysis, we normalized each MI score by the corresponding pair entropy (Hcd) to reduce the impact of phylogenetic correlations [35].

In order to further verify the above results, we performed RCA as described in [36] with the same MSA used in MI analysis.

Although this MI analysis uses novel information that differs from the results of known site-directed mutagenesis studies or published GPCR crystal structures, the method is capable of identifying the well-known common ligand binding region of GPCRs between the upper part of the seven transmembrane helices and the second extracellular loop.

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