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Abstract
Metabolic P (MP) grammars are a particular class of multiset rewriting grammars introduced in the MP theory for modelling metabolic processes. In this paper, a new algebraic formulation of inverse problems, based on MP grammars and Kronecker product, is given, for further 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 the paper, a section is included that introduces the problem of multicollinearity, which could arise during the execution of LGSS, and that defines an algorithm, based on a hierarchical clustering technique, that solves it in a suitable way.
Notes
See http://www.mathworks.it/index.html for details on the MATLAB software.
The correlation between regressors is intended to be calculated by means of the Pearson's correlation coefficient Citation37, which ranges from −1 to 1 and provides a measure of dependence between the behaviours of two magnitudes (−1, perfect anti-correlation; 0, no correlation; 1, perfect correlation).
Every time there is the need of choosing between several possible MP grammars (obtained by LGSS using different initial settings), according to classical statistics, the most parsimonious MP model should be preferred (for avoiding the problem of overfitting, as introduced at the end of Section 2).