Towards a theory of modelling with Boolean automata networks - I. Theorisation and observations.

Authors: Sylvain Sené, Mathilde Noual
Subjects: Discrete Mathematics

link: http://arxiv.org/abs/1111.2077
Abstract

Although models are built on the basis of some observations of reality, the
concepts that derive theoretically from their definitions as well as from their
characteristics and properties are not necessarily direct consequences of these
initial observations. Indeed, many of them rather follow from chains of
theoretical inferences that are only based on the precise model definitions and
rely strongly, in addition, on some consequential working hypotheses. Thus, it
is important to address the question of which features of a model effectively
carry some modelling meaning and which only result from the task of formalising
observations of reality into a mathematical language. In this article, we
address this question with a theoretical point view that sets our discussion
strictly between the two stages of the modelling process that require knowledge
of real systems, that is, between the initial stage that chooses a global
theoretical framework to build the model and the final stage that exploits its
formal predictions by comparing them to the reality that the model was designed
to simulate. Taking Boolean automata networks as instances of models of systems
observed in reality, we analyse in this setting the remaining stages of the
modelling process and we show how the meaning of theoretical concepts can
subtly rely on formal choices such as definitions and hypotheses.

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