## Section: New Results

### CRN reductions

Participants : Orianne Bargain, Eléonore Bellot, François Fages, Eva Philippe, Sylvain Soliman.

We have shown in the past that model reduction relationships between CRNs can be detected on a large scale by the graph matching notion of subgraph epimorphism (Steven Gay, François Fages, Thierry Martinez, Sylvain Soliman, Christine Solnon. On the subgraph Epimorphism Problem. Discrete Applied Mathematics, 162:214–228, 2014.), furthermore quite efficiently using constraint programming or SAT solving techniques. Nevertheless, establishing whether two models are linked through a SEPI is an NP-complete problem which can be computationally expensive in some practical cases. Furthermore, the number of SEPIs can be huge, and some of them may not have a biological interpretation. In [11], we have improved the SEPI framework in this respect in three ways: by introducing optimization criteria to restrict the set of solutions, by restricting merge operations to some notion of neighborhood, and by preprocessing the CRN graphs in normal form in order to eliminate some common model reduction patterns.

Furthermore, in the framework of the ANR-DFG SYMBIONT project we investigate mathematical justification of SEPI reductions based on Tikhonov's theorem and their computation using tropical algebra methods and constraint programming techniques (Sylvain Soliman, François Fages, Ovidiu Radulescu. A constraint solving approach to model reduction by tropical equilibration. Algorithms for Molecular Biology, 9(24), 2014.).