No 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 relative probabilities of component failure in the system. Finally, we show how to extend the analysis from general component failure to specific failure modes.

The goal of this paper is to illustrate the use of category theory (CT) as a basis for the integration of manufacturing service databases. In this paper, we use as our reference prior work by Kulvatunyou et al. (2013, “An Analysis of OWL-Based Semantic Mediation Approaches to Enhance Manufacturing Service Capability Models,” Int. J. Comput. Integr. Manuf., 27(9), pp. 803–823) on the use of web ontology language (OWL)-based semantic web tools to study the integration of different manufacturing service capability (MSC) databases using a generic-model approach that they propose in their paper. We approach the same task using a different set of tools, specifically CT and FQL, a functorial query language based on categorical mathematics. This work demonstrates the potential utility of category-theoretic information management tools and illustrates some advantages of categorical techniques for the integration and evolution of databases. We conclude by making the case that a category-theoretic approach can provide a more flexible and robust approach to integration of existing and evolving information.

Quantum self-testing addresses the following question: is it possible to verify the existence of a multipartite state even when one's measurement devices are completely untrusted? This problem has seen abundant activity in the last few years, particularly with the advent of parallel self-testing (i.e., testing several copies of a state at once), which has applications not only to quantum cryptography but also quantum computing. In this work we give the first error-tolerant parallel self-test in a threeparty (rather than two-party) scenario, by showing that an arbitrary number of copies of the GHZ state can be self-tested. In order to handle the additional complexity of a three-party setting, we use a diagrammatic proof based on categorical quantum mechanics, rather than a typical symbolic proof. The diagrammatic approach allows for manipulations of the complicated tensor networks that arise in the proof, and gives a demonstration of the importance of picture-languages in quantum information.