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Search Publications by: Spencer Breiner ()

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Displaying 1 - 16 of 16

Category Theory

January 25, 2023
Author(s)
Spencer Breiner, Eswaran Subrahmanian, Ram Sriram
Category theory (CT) is a branch of mathematics concerned with the representation and composition of structured relationships. Recent interest in systems engineering (SE) stems from the possibility that CT might provide a principled mathematical foundation

Operads for complex system design specification, analysis and synthesis

June 23, 2021
Author(s)
Spencer Breiner, Eswaran Subrahmanian, John Dusel, John Foley
As the complexity and heterogeneity of a system grows, the challenge of specifying, documenting and synthesizing correct, machine readable designs increases dramatically. Separation of the system into manageable parts is needed to support analysis at

Deconstructing UML, Part 1: Modeling Classes with Categories

May 13, 2021
Author(s)
Sarala Padi, Spencer J. Breiner, Eswaran Subrahmanian, Ram D. Sriram
In this paper we analyze elements of the Unified Modeling Language (UML), specifically the class diagram, and propose an simplified alternative language based on a branch of mathematics called category theory (CT). We argue that modeling in CT provides a

Symmetric Monoidal Categories with Attributes

January 26, 2021
Author(s)
Spencer Breiner, John S. Nolan
When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning, namely those based

Modeling Hierarchical Systems with Operads

November 4, 2020
Author(s)
Spencer Breiner, Olivier Marie Rose, Blake S. Pollard, Eswaran Subrahmanian
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

Workshop on Applied Category Theory: Bridging Theory and Practice

February 7, 2020
Author(s)
Spencer J. Breiner, Blake S. Pollard, Eswaran Subrahmanian
This report presents the summary of a workshop held at NIST on March 15-16, 2018 on the topic of applied category theory (ACT). The meeting had two main goals: (i) mapping the current ACT landscape and (ii) developing a roadmap for transitioning the field

Compositional models for power systems

September 8, 2019
Author(s)
Dhananjay Anand, Blake S. Pollard, Spencer J. Breiner, John S. Nolan, Eswaran Subrahmanian
The problem of integrating multiple overlapping models and data is pervasive in engineering, though often implicit. We consider this issue of model management in the context of the electrical power grid, as it transitions from centralized generation with

Graphical Methods in Device-Independent Quantum Cryptography

May 27, 2019
Author(s)
Spencer J. Breiner, Carl A. Miller, Neil J. Ross
We introduce a framework for providing graphical security proofs for quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more

Parallel Self-Testing of the GHZ State with a Proof by Diagrams

January 31, 2019
Author(s)
Spencer J. Breiner, Amir Kalev, Carl Miller
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

Compositional Models for Complex Systems

January 19, 2019
Author(s)
Spencer J. Breiner, Ram D. Sriram, Eswaran Subrahmanian
In this chapter we argue for the use of representations from category theory to support better models for complex systems, and provide an example of such an application might look like. Our approach rests on the well known observation that complex system

Categorical Models for Process Planning

November 19, 2018
Author(s)
Spencer J. Breiner, Eswaran Subrahmanian, Albert W. Jones
Process plans provide a structure for 1) identifying the tasks involved in a given process, 2) the resources needed to accomplish them, and 3) a variety of relationships and constraints between these. This information guides important operational decisions

Modeling the Internet of Things (& People): A Foundational Approach

November 16, 2017
Author(s)
Spencer J. Breiner, Eswaran Subrahmanian, Ram D. Sriram
This talk provides an overview of recent NIST work in the Internet of Things (IoT) domain in the Information Technology Laboratory. We begin with some examples and illustrations of the range of IoT systems. In addition to the obvious cyber physical aspects

A Category Theoretic Approach to Modeling and Analysis Using Music as a Case Study

January 31, 2017
Author(s)
Sarala Padi, Spencer J. Breiner, Eswaran Subrahmanian, Ram D. Sriram
The goal of this paper is to provide a category theoretic ontology for the creation of a collaborative platform where it allows group of people to share or use the knowledge in a domain. We use Indian music as a case study to demonstrate the power of

Modeling the Internet of Things and People: A Foundational Approach

November 1, 2016
Author(s)
Spencer J. Breiner, Eswaran Subrahmanian, Ram D. Sriram
As we extend the reach of the Internet through sensing and automation, networked systems interact more and more of our daily lives, requiring much greater sensitivity to social networks and greater robustness in the face of human behavior. A tremendous

Using Category Theory to facilitate multiple manufacturing service database integration

July 20, 2016
Author(s)
Spencer J. Breiner, Albert T. Jones, David I. Spivak, Eswaran Subrahmanian, Ryan Wisnesky
The goal of this paper is to illustrate the use of category theory as a basis for the integration of manufacturing service databases. In this paper we use as our reference prior work by Kolvatunyu, et. al (2013) on the use of Ontology Web Language(OWL)