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Paolo Perrone (Jul 02 2020 at 02:40):Hello all! This is the thread of discussion for the talk of Joachim Kock, "Whole-grain Petri nets and processes".
Date and time: Monday July 6, 11:40 UTC.
Zoom meeting: https://mit.zoom.us/j/7055345747
YouTube live stream: https://www.youtube.com/watch?v=1A76CO3K28U&list=PLCOXjXDLt3pZDHGYOIqtg1m1lLOURjl1Q
Paolo Perrone (Jul 06 2020 at 11:22):The talk will start in 3 minutes!
Paolo Perrone (Jul 06 2020 at 11:22):Main reference: Elements of Petri nets and processes
http://arxiv.org/abs/2005.05108
Paolo Perrone (Jul 06 2020 at 11:23):His paper: Graphs, hypergraphs, and properads
http://arxiv.org/abs/1407.3744
James Fairbanks (Jul 06 2020 at 12:07):Great talk @Joachim Kock! Have you given any thought to the continuous time dynamical systems semantics / reaction networks semantics of Petri nets? How does that fit into this picture?
Paolo Perrone (Jul 06 2020 at 12:08):Question from the chat:
Question: The talk went out of my depth pretty rapidly, but is there a general way to state the lesson of "you can do something other than quotienting/adding structure to get a correspondence"? What do I need to look at to understand this?
Joachim Kock (Jul 06 2020 at 15:53):James Fairbanks said:
Have you given any thought to the continuous time dynamical systems semantics / reaction networks semantics of Petri nets? How does that fit into this picture?
Hi James, I am really interested in figuring out any connections with the continuous case. My first problem is that I don't understand the role of tokens in the continuous case. Is there a token game at all? Is there any semantics in symmetric monoidal categories?
James Fairbanks (Jul 06 2020 at 16:26):you can get dynamical systems by assuming that each reaction describes a vector field according to https://arxiv.org/abs/1704.02051
John Baez (Jul 06 2020 at 18:32):Petri nets with nonnegative numbers attached to transitions have two main forms of continuous-time semantics: the rate equation which involves nonnegative real numbers of tokens evolving deterministically, and the master equation which involves natural numbers of tokens evolving stochastically. Both are discussed ad nauseum in this free book:
and these blog articles:
John Baez (Jul 06 2020 at 18:34):The paper James Fairbanks pointed to describes the rate equation semantics as a functor out of a symmetric monoidal category of open Petri nets with nonnegative numbers attached to transitions.
John Baez (Jul 06 2020 at 18:34):The master equation semantics has not yet been treated functorially.
Paolo Perrone (Jul 06 2020 at 20:30):Here's the video!
https://www.youtube.com/watch?v=cJfasciuCIs&list=PLCOXjXDLt3pYot9VNdLlZqGajHyZUywdI
