Pixel Matrices and Other Compositional Analyses of Interconnected Systems
Abstract
The new world of interconnected-everything brings new challenges to those who wishto understand it and keep society safe from unintended and unimagined consequences.With constant communication and feedback loops being the norm, the space of behaviorsis too large to analyze by simulation alone. Today’s nearly unlimited computational powermust be used more wisely, so that our knowledge of a system can evolve along with thesystem itself. New mathematical techniques are needed to provide the algebraic formulasfor combining our insights, just as we combine components, allowing us to anticipate thebehavior of an assembled system. Category theory is the mathematics of combination andcompositionality, so it is well-suited as a foundation for such work.We propose to investigate compositional techniques for analyzing systems of all sorts.At the mathematical center of many disciplines, one needs to solve a system of simultaneousequations. As mundane, abstract, and worked-over as this may seem, a new elementarytechnique was recently discovered with the potential to change how we approach suchproblems. This technique is highly compositional—the solutions to subsystems can becombined to form a solution of the whole—and it emerged out of a similarly compositionalapproach to understanding the behavior of networked machines. Just as circuits can becombined to form computers, machines of all scales can be interconnected to form morecomplex machines. The common theme is compositionality: whether combining theconstraints and requirements necessary to design a robot, or combining the equations thatdescribe its function, our goal is to find analyses that are scalable and reusable, so that theknowledge we gain today is efficiently utilized in the networks of tomorrow.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2017
- Source ID
- FA95501710058
Entities
People
- David Spivak
Organizations
- Air Force Office of Scientific Research
- Harvard University
- United States Air Force