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Modeling Hierarchical Systems with Operads

Published

Author(s)

Spencer Breiner, Olivier Marie Rose, Blake S. Pollard, Eswaran Subrahmanian

Abstract

This paper applies operads and functorial semantics to address the problem of failure diagnosis in complex systems. We start with a concrete example, developing a hierarchical interaction model for the Length Scale Interferometer, a high-precision measurement system operated by the US National Institute of Standards and Technology. The model is expressed in terms of combinatorial/diagrammatic structures called port-graphs, and we explain how to extract an operad LSI from a collection of these diagrams. Next we show how functors to the operad of probabilities organize and constrain the rel- ative probabilities of component failure in the system. Finally, we show how to extend the analysis from general component failure to specific failure modes.
Proceedings Title
Proceedings Applied Category Theory 2019
Volume
323
Conference Dates
July 15-19, 2019
Conference Location
Oxford, GB

Keywords

Applied Category Theory, Operad, Length Measurement System, Functorial Semantics, Hierarchical Systems

Citation

Breiner, S. , Marie Rose, O. , Pollard, B. and Subrahmanian, E. (2020), Modeling Hierarchical Systems with Operads, Proceedings Applied Category Theory 2019, Oxford, GB, [online], https://doi.org/10.4204/EPTCS.323.5 (Accessed April 15, 2024)
Created November 4, 2020, Updated February 16, 2024