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Fabrizio Genovese (Jan 18 2021 at 11:11):Me, @fosco and @Daniele Palombi just put a new thing on the arxiv: https://arxiv.org/abs/2101.06234
It is a paper about extensions of Petri nets for biological processes. The applications of the paper per sé are not that interesting. What is interesting is that this paper is the continuation of a paper I had with @David Spivak about a year ago that provided a categorical semantics for Guarded Nets (arxiv: https://arxiv.org/abs/2002.02762) It turns out that that paper was only the tip of the iceberg, and that we can caracterize a lot of interesting extensions of Petri nets by studying lax functors , with free (commutative,symmetric) monoidal.
In this paper, we are able to endow tokens with properties describing the global behavior of the net they live in. Using laxity, we can then merge the local knowledge that each token has into a global thing.
If you are lazy and don't wanna read I also made a video presentation: https://www.youtube.com/watch?v=9sxVBJs1okE
And a tweet, where we can chat about it (we can here too, obviously): https://twitter.com/fabgenovese/status/1351124519231086592
Here it comes the second installment of our work about Extended Petri Nets! Petri Nets with Mana: A Framework for Chemical Reaction Modelling Video presentation: https://www.youtube.com/watch?v=9sxVBJs1okE arXiv: http://arxiv.org/abs/2101.06234 Enjoy!
- Fabrizio Romano Genovese (@fabgenovese)
Fabrizio Genovese (Jan 18 2021 at 11:16):Two more papers on this topic will follow in the next couple of weeks, so stay tuned! :smile:
Matteo Capucci (he/him) (Jan 18 2021 at 11:58):It's a beautiful paper, guys
Matteo Capucci (he/him) (Jan 18 2021 at 12:00):Two things I really liked:
Fabrizio Genovese (Jan 18 2021 at 12:12)::grinning:
Fabrizio Genovese (Jan 18 2021 at 12:13):Thanks @Matteo Capucci (he/him) !
fosco (Jan 18 2021 at 12:21):Matteo Capucci (he/him) said:
Two things I really liked:
- Manas and a reference to Turing-completeness of Magic
- Laxity as a tool to probe global observables. This one a lot!
(the like emoji is a magic wand, fyi)
Fabrizio Genovese (Jan 18 2021 at 12:25):I'm actually really glad that this idea of "laxity gives you local info about global behavior" is understood. I was fearing we didn't stress it enough in the paper. It is the main conceptual contribution of this work imho.
Matteo Capucci (he/him) (Jan 18 2021 at 13:06):That + a really funky Grothendieck construction which I'm glad I didn't have to come up with :laughing:
Fabrizio Genovese (Jan 18 2021 at 13:10):Lol :grinning: