Research
Software
Decapodes.jl
Decapodes are a graphical tool for the composition of physical systems.
Ultimately, this library will include tooling which takes advantage of the formalization of physical theories described by DEC provided by CombinatorialSpaces.jl.
Links:
AlgebraicControl.jl
Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon. We present a novel Julia library that leverages our theoretical results to automate the implementation of correct-by-construction MPC problems in software.
Preprints
Year | Title |
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2024 | The diagrammatic presentation of equations in categories Kevin Arlin, James Fairbanks, Tim Hosgood, and Evan Patterson |
2024 | Towards a Compositional Framework for Convex Analysis Richard Samuelson and Dario Stein |
2023 | A Compositional Framework for Convex Model Predictive Control Tyler Hanks, Baike She, Matthew Hale, Evan Patterson, Matthew Klawonn, and James Fairbanks |
2023 | Characterizing Compositionality of LQR from the Categorical Perspective Baike She, Tyler Hanks, James Fairbanks, and Matthew Hale |
2023 | Compositional Algorithms on Compositional Data: Deciding Sheaves on Presheaves Ernst Althaus, Benjamin Merlin Bumpus, James Fairbanks, and Daniel Rosiak |
2023 | A compositional account of motifs, mechanisms, and dynamics in biochemical regulatory networks Rebekah Aduddell, James Fairbanks, Amit Kumar, Pablo Ocal, Evan Patterson, and Brandon Shapiro |
Journal Papers
Year | Title |
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2023 | Computational category-theoretic rewriting Kristopher Brown, Evan Patterson, Tyler Hanks, and James Fairbanks Journal of Logical and Algebraic Methods in Programming |
2023 | The application of applied category theory to quantify mission success Robert K Garrett, James Fairbanks, Margaret Loper, and James Moreland Simulation |
2022 | An algebraic framework for structured epidemic modelling Sophie Libkind, Andrew Baas, Micah Halter, Evan Patterson, and James Fairbanks Philosophical Transactions of the Royal Society A |
2022 | A diagrammatic view of differential equations in physics Evan Patterson, Andrew Baas, Timothy Hosgood, and James Fairbanks Mathematics in Engineering |
2021 | Categorical Data Structures for Technical Computing Evan Patterson, Owen Lynch, and James Fairbanks Compositionality |
2021 | Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle Yaniv Mordecai, James Fairbanks, and Edward Crawley Applied Sciences |
Conference Papers
Year | Title |
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2023 | A Categorical Representation Language and Computational System for Knowledge-Based Robotic Task Planning Angeline Aguinaldo, Evan Patterson, James Fairbanks, William Regli, and Jaime Ruiz 2023 AAAI Fall Symposium on Unifying Representations for Robot Application Development |
2022 | Compositional Exploration of Combinatorial Scientific Models Kristopher Brown, Tyler Hanks, and James Fairbanks 5th International Conference on Applied Category Theory |
2022 | Computational Category-Theoretic Rewriting Kristopher Brown, Evan Patterson, Tyler Hanks, and James Fairbanks 15th International Conference on Graph Transformation |
2021 | Operadic Modeling of Dynamical Systems: Mathematics and Computation Sophie Libkind, Andrew Baas, Evan Patterson, and James Fairbanks 4th International Conference on Applied Category Theory |