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Setting Limits on Supersymmetry Using Simplified Models
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A group theoretic approach to model comparison with simplicial representations.

Sean T Vittadello1, Michael P H Stumpf2

  • 1School of Mathematics and Statistics and School of BioSciences, The University of Melbourne, Parkville, VIC, 3010, Australia. sean.vittadello@unimelb.edu.au.

Journal of Mathematical Biology
|October 9, 2022
PubMed
Summary

This study introduces a new mathematical framework to compare complex biological models. It uses group theory and simplicial complexes for automated model equivalence determination, simplifying understanding of biological systems.

Keywords:
Group actionModel comparisonModel equivalenceModel similarityOrbit spaceSimplicial complex

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Area of Science:

  • Computational Biology
  • Mathematical Modeling
  • Systems Biology

Background:

  • Biological systems are complex, generating large datasets that require mathematical models for understanding.
  • Existing models often use diverse mathematical formalisms, hindering direct comparison and unified descriptions.
  • Comparing models based on conceptual structure is crucial for advancing biological systems research.

Purpose of the Study:

  • To develop a rigorous and automatable methodology for comparing mathematical models of biological systems.
  • To enhance the existing framework for model comparison using simplicial complexes.
  • To introduce a group-theoretic approach for model comparison.

Main Methods:

  • Representing models as labeled simplicial complexes to capture conceptual structure.
  • Developing group actions on simplicial complexes to identify related model components (vertices).
  • Providing an alternative framework representing models as groups for direct group-theoretic analysis.

Main Results:

  • A rigorous and automatable method for determining model equivalence based on vertex symmetry in simplicial representations.
  • Simplified and expedited comparison of mathematical models.
  • A new group-theoretic framework enabling direct application of group theory to model comparison.

Conclusions:

  • The developed methodology significantly advances the comparison of mathematical models in systems biology.
  • Automated model equivalence determination using group actions on simplicial complexes enhances research efficiency.
  • The group-theoretic framework offers a powerful alternative for unifying mathematical descriptions of biological systems.