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Geometric Aspects of Observability of Hypergraphs.

Joshua Pickard1, Cooper Stansbury1, Amit Surana2

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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.

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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.