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Geometric Aspects of Observability of Hypergraphs
Joshua Pickard1, Cooper Stansbury1, Amit Surana2
1Department of Computational Medicine & Bioinformatics, Medical School, University of Michigan, Ann Arbor, MI 48109 USA.
Ifac-Papersonline
|June 6, 2025
Summary
This study extends geometric observability to nonuniform hypergraphs, crucial for understanding complex biological networks. New methods assess local and weak observability in these generalized graph structures.
Area of Science:
- Network science
- Systems biology
- Control theory
Background:
- Hypergraphs generalize graphs, representing complex multi-way relationships in real-world networks.
- Observability is key to understanding dynamical systems, particularly in biological networks.
Purpose of the Study:
- To extend geometric observability concepts from uniform to nonuniform hypergraphs.
- To develop methods for evaluating local and weak observability in polynomial dynamical systems defined on hypergraphs.
Main Methods:
- Consideration of polynomial dynamical systems with linear outputs structured by hypergraphs.
- Development of novel methodologies for assessing geometric observability in nonuniform hypergraph settings.
Main Results:
- Successful extension of geometric observability to the nonuniform hypergraph case.
- Proposed methods provide a framework for evaluating local and weak observability.
Conclusions:
- The findings advance the understanding of observability in complex network structures.
- This work provides tools for analyzing dynamical systems on generalized graph representations, with implications for systems biology.
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