Metabolic P (MP) grammars are a particular class of multiset rewriting grammars introducedin the MP systems' theory for modelling metabolic processes. In this paper, a new algebraicformulation of inverse problems, based on MP grammars and Kronecker product, is given, forfurther motivating the correctness of the LGSS (Log-gain Stoichiometric Stepwise) algorithm,introduced in 2010s for solving inverse problems in the MP framework. At the end of thepaper, a section is included that introduces the problem of multicollinearity, which couldarise during the execution of LGSS, and that denes an algorithm, based on a hierarchicalclustering technique, that solves it in a suitable way.
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