Measuring information integration: An illustrative example. To measure information integration, we performed an exhaustive search of all subsets and bipartitions for a system of n = 8 elements. Noise levels were ci = 0.00001, cp = 1. (A) Connection matrix CON(X). Connections linking elements 1 to 8 are plotted as a matrix of connection strengths (column elements = targets, row elements = sources). Connection strength is proportional to grey level (dark = strong connection, light = weak or absent connection). (B) Covariance matrix COV(X). Covariance is indicated for elements 1 to 8 (corresponding to A). (C) Ranking of the top 25 values for Φ. (D) Element composition of subsets for the top 25 values of Φ (corresponding to panel C). Elements forming the subset S are indicated in grey, with two shades of grey indicating the bipartition into A and B across which the minimal value for EI was obtained. (E) Ranking of the Φ values for all complexes, i.e. subsets not included within subsets of higher Φ. (F) Element composition for the complexes ranked in panel E. (G) Digraph representation of the connections of system X (compare to panel A). Elements are numbered 1 to 8, arrows indicate directed edges, arrow weight indicates connection strength. Grey overlays indicate complexes with grey level proportional to their value of Φ. Figs. 2 to 7 use the same layout to represent computational results.