A Group Theoretic Approach to Model Comparison With Simplicial Representations
The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. Because biological systems are generally not well understood, most mathematical models of these systems are based on experimental data, resulting in a seemingly heterogeneous collection of models that ostensibly represent the same system. To understand the system we therefore need to understand how the different models are related to each other, with a view to obtaining a unified mathematical description. This goal is complicated by the fact that a number of distinct mathematical formalisms may be employed to represent the same system, making direct comparison of the models very difficult. A methodology for comparing mathematical models based on their underlying structure is therefore required. In a previous work we developed an appropriate framework for model comparison where we represent models as labelled simplicial complexes and compare them with two general methodologies, namely comparison by distance and comparison by equivalence. In this article we continue the development of our model comparison methodology in two directions. First, we develop an automatable methodology for determining model equivalence using group actions on the simplicial complexes, which greatly simplify and expedite the process of determining model equivalence. Second, we develop an alternative framework for model comparison by representing models as groups, which allows for the application of group-theoretic techniques within our model comparison methodology.