16 citations · 72 across the 14 of their papers we have counts for
15 papers
Characterizing Compositionality of LQR from the Categorical Perspective
Baike She, Tyler Hanks, James Fairbanks +1
Composing systems is a fundamental concept in modern control systems, yet it remains challenging to formally analyze how controllers designed for individual subsystems can differ f…
Modeling Model Predictive Control: A Category Theoretic Framework for Multistage Control Problems
Tyler Hanks, Baike She, Matthew Hale +3
Model predictive control (MPC) is an optimal control technique which involves solving a sequence of constrained optimization problems across a given time horizon. In this paper, we…
Compositional Algorithms on Compositional Data: Deciding Sheaves on Presheaves
Ernst Althaus, Benjamin Merlin Bumpus, James Fairbanks +1
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initia…
A compositional account of motifs, mechanisms, and dynamics in biochemical regulatory networks
Rebekah Aduddell, James Fairbanks, Amit Kumar +3
Regulatory networks depict promoting or inhibiting interactions between molecules in a biochemical system. We introduce a category-theoretic formalism for regulatory networks, usin…
Compositional Exploration of Combinatorial Scientific Models
Kristopher Brown, Tyler Hanks, James Fairbanks
We implement a novel representation of model search spaces as diagrams over a category of models, where we have restricted attention to a broad class of models whose structure is p…
A diagrammatic view of differential equations in physics
Evan Patterson, Andrew Baas, Timothy Hosgood +1
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this w…
An Algebraic Framework for Structured Epidemic Modeling
Sophie Libkind, Andrew Baas, Micah Halter +2
Pandemic management requires that scientists rapidly formulate and analyze epidemiological models in order to forecast the spread of disease and the effects of mitigation strategie…
Computational category-theoretic rewriting
Kristopher Brown, Evan Patterson, Tyler Hanks +1
We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples…
Categorical Data Structures for Technical Computing
Evan Patterson, Owen Lynch, James Fairbanks
Many mathematical objects can be represented as functors from finitely-presented categories to . For instance, graphs are functors to from…
Operadic Modeling of Dynamical Systems: Mathematics and Computation
Sophie Libkind, Andrew Baas, Evan Patterson +1
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structur…
Compositional Scientific Computing with Catlab and SemanticModels
Micah Halter, Evan Patterson, Andrew Baas +1
Scientific computing is currently performed by writing domain specific modeling frameworks for solving special classes of mathematical problems. Since applied category theory provi…
Unsupervised Construction of Knowledge Graphs From Text and Code
Kun Cao, James Fairbanks
The scientific literature is a rich source of information for data mining with conceptual knowledge graphs; the open science movement has enriched this literature with complementar…
A Compositional Framework for Scientific Model Augmentation
Micah Halter, Christine Herlihy, James Fairbanks
Scientists construct and analyze computational models to understand the world. That understanding comes from efforts to augment, combine, and compare models of related phenomena. W…
Spectral Partitioning with Blends of Eigenvectors
James P. Fairbanks, Geoffrey D. Sanders, David A. Bader
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopp…
A Ramsey Theorem for Indecomposable Matchings
James Fairbanks
A matching is indecomposable if it does not contain a nontrivial contiguous segment of vertices whose neighbors are entirely contained in the segment. We prove a Ramsey-like result…