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Integrating Fragmented Risk Knowledge: Sheaf Theory for Risk Analysts.

Louis Anthony Cox1,2,3

  • 1Cox Associates, Denver, Colorado, USA.

Risk Analysis : an Official Publication of the Society for Risk Analysis
|February 26, 2026
PubMed
Summary
This summary is machine-generated.

Sheaf theory offers a mathematical framework to integrate local risk information into global strategies for complex systems. This approach aids in managing interconnected systems by ensuring consistent, context-aware risk assessment and decision-making.

Keywords:
distributed systemsemergency planninginformation fusionpolicy consistencyrisk communicationrisk modelingsensor networkssheaf theory

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Area of Science:

  • Complex Systems Analysis
  • Mathematical Modeling
  • Risk Management Science

Background:

  • Increasingly interconnected sociotechnical systems require advanced risk assessment tools.
  • Existing "systems-of-systems" approaches lack methods for integrating local knowledge into global risk strategies.
  • Partial and context-dependent information poses challenges for coherent risk management.

Purpose of the Study:

  • To introduce sheaf theory as a principled mathematical framework for local-to-global reasoning in complex systems.
  • To demonstrate the practical applications of sheaf theory for risk analysis and management.
  • To explore how sheaf theory can address challenges in integrating distributed risk information.

Main Methods:

  • Application of sheaf theory for reasoning about structural consistency and context-dependent information.
  • Exploration of mathematical techniques for integrating local risk assessments into global strategies.
  • Illustrative examples from diverse fields including risk psychology, sensor fusion, and causal modeling.

Main Results:

  • Sheaf-theoretic methods can detect policy conflicts and information gaps in complex systems.
  • The framework supports modular, multi-level modeling and simulation of belief propagation under constraints.
  • Demonstrated utility across risk communication, environmental monitoring, emergency planning, and regulatory governance.

Conclusions:

  • Sheaf theory provides a robust mathematical foundation for addressing local-to-global challenges in risk analysis.
  • The methods offer practical solutions for managing complex, interconnected systems with distributed information.
  • Integration of sheaf theory into mainstream risk science is proposed for enhanced risk management capabilities.