An Iterative Information-Theoretic Approach to the Detection of Structures in Complex Systems

Figure 2

(a) The chemical system under analysis in the CRN case study. Elliptic nodes represent chemical species: the ones filled in blue stand for those injected into the CSTR (food species), while the empty white ones are the more complex species built by specific condensation of the food species. Rectangular shapes represent reactions, where incoming arrows are oriented from substrates to reactions and outgoing arrows from reactions to products. Dashed lines indicate the catalytic role of a particular molecular species within the specific reaction context. The kinetic constants of all reactions which take place have the same value (; ; and ); the incoming concentration of each food species is 0.01 mol, whereas, every second, 5% of the CSTR volume is renewed. (b) The five RSs found after the first five iterations of the iterated sieving algorithm. (c) The situation at the end of the iterated sieving algorithm. Note, however, that, if the method is further iterated (d), despite finding groups with significance below the chosen threshold (corresponding to a critical value of close to 3.0), the iterative sieve detects the correct configuration anyway. For the sake of completeness, the results of all sieving steps are reported in the attached Supplementary Materials (available here).

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