Network theory
Network theory , not to be confused with network science, is a research program by John Baez and collaborators on the mathematical modeling of networks (processes) in science and engineering.
Literature
Electrical engineering and control theory
- Baez & Fong, 2015: A compositional framework for passive linear networks
(arxiv, nCat Cafe , Azimuth )
- Fong, 2016, PhD thesis: The algebra of open and interconnected systems (arxiv)
- Baez & Erbele, 2015: Categories in control (arxiv, pdf, nCat Cafe , Azimuth )
- Erbele, 2016, PhD thesis: Categories in control: applied PROPs (arxiv)
- Sec. 6: Closely related independent work:
- Bonchi, Sobocinski, Zanasi, 2014: A categorical semantics of signal flow graphs (doi, pdf)
- Bonchi, Sobocinski, Zanasi, 2015: Full abstraction for signal flow graphs (doi)
- Bonchi, Sobocinski, Zanasi, 2017: Interacting Hopf algebras (doi, arxiv)
- Wadsley & Woods, 2015: PROPs for linear systems (arxiv, nCat Cafe )
- Baez, Coya, Rebro, 2017: Props in network theory (arxiv, nCat Cafe , talk )
Markov processes and Petri nets
See the dedicated pages on Markov processes and Petri nets.
Network models
- Baez, Foley, Moeller, Pollard, 2020: Network models (pdf, arxiv, Azimuth )
- Moeller, 2020: Noncommutative network models (doi, arxiv)
- Baez & Foley, 2021, in AMS Notices: Operads for designing systems of systems (pdf)
- Network models have connections to Petri nets
- Moeller & Vasilakopoulou, 2020: Monoidal Grothendieck construction (pdf,
arxiv, Azimuth 1 ,2 , nLab )
- Sec. 5: Examples inspired by network theory
- Moeller, 2021, PhD thesis: The Grothendieck construction in categorical network theory (arxiv)
Decorated and structured cospans
- Fong, 2015: Decorated cospans (pdf, arxiv, nCat Cafe )
- Baez & Courser, 2019: Structured cospans(pdf, arxiv, nCat Cafe , Azimuth )
- Cicala, 2020: Rewriting structured cospans (arxiv)
Miscellaneous