Vincenzo Manca and Luca Marchetti
The paper is focused on a new perspective in solving dynamics inverse problems, by considering recurrent equations based on Metabolic P (MP) grammars. MP grammars are a particular type of multiset rewriting grammars, introduced in 2004 for modeling metabolic systems, which express dynamics in terms of finite difference equations. Regression algorithms, based on MP grammars, were introduced since 2008 for algorithmically solving dynamics inverse problems in the context of biological phenomena. This paper shows that, when MP regression is applied to time series of circular functions (where time is replaced by rotation angle), the dynamics that is found turns out to coincide with recurrent equations derivable from classical analytical definitions of these functions. This validates the MP regression as a general methodology to discover deep logics underlying observed dynamics. At the end of the paper some applications are also discussed, which exploit the regression capabilities of the MP framework for the analysis of periodical signals and for the implementation of sequential circuits providing periodical oscillators.
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