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Stream: event: ACT20

Topic: July 6: Joe Moeller et al.'s talk

Paolo Perrone (Jul 02 2020 at 02:32):

Hello all! This is the thread of discussion for the talk of Joe Moeller, John Baez and John Foley, "Petri nets with catalysts".
Date and time: Monday July 6, 20:40 UTC.
Zoom meeting: https://mit.zoom.us/j/7055345747
YouTube live stream: https://www.youtube.com/watch?v=nEmPJVjLrOI&list=PLCOXjXDLt3pZDHGYOIqtg1m1lLOURjl1Q

Joe Moeller (Jul 06 2020 at 19:37):

Here's the paper my talk is about:
https://compositionality-journal.org/papers/compositionality-1-4/

Here are some other relevant things:
Monoidal Grothendieck construction https://arxiv.org/abs/1809.00727
Network models http://www.tac.mta.ca/tac/volumes/35/20/35-20abs.html
premonoidal categories https://ncatlab.org/nlab/show/premonoidal+category

Joe Moeller (Jul 06 2020 at 20:10):

Here are my slides: https://joemathjoe.files.wordpress.com/2020/07/act2020_moeller.pdf

Joe Moeller (Jul 06 2020 at 21:18):

Apologies for moving slower than I expected. I just want to make sure the content of the last slide is available, which is future directions:
image.png

Joe Moeller (Jul 06 2020 at 21:19):

You could treat a server (as in queueing theory) as a catalyst in a petri net where the resources are servers and customers. I started talking to a queueing theorist at some point about this, but I decided to focus on other things. So this is untouched afaik.

Joe Moeller (Jul 06 2020 at 21:21):

Another thing in my slides that I didn't get to was the individual token philosophy and the collective token philosophy. We have a partial representation of individual token philosophy from our work, which sorta point towards more complete representations. Several people are already working on this.

Joe Moeller (Jul 06 2020 at 21:23):

I said in the talk that you get a fibration of FP in a sorta trivial way. I'm curious if it's possible to get non-trivial fibrations of FP, and what sorts of structures it would represent within the net.

Joe Moeller (Jul 06 2020 at 21:26):

So anybody feel free to take these ideas if they spark any interest. I'd be happy to talk about them also.

John Baez (Jul 06 2020 at 21:27):

During Joe's talk some people were asking about Petri nets and catalysts in chemistry. For that I recommend folks read about the Michaelis-Menten reaction, which is this thing:

Michaelis-Menten reaction

John Baez (Jul 06 2020 at 21:28):

Here the catalyst (or "enzyme") E meets S and turns into a molecule ES which then breaks apart releasing E and a new thing P.

John Baez (Jul 06 2020 at 21:28):

Note this is not a catalyst in the very limited sense of Joe's & my paper, since E gets used up in the first reaction and produced in the second!

Joe Moeller (Jul 06 2020 at 21:30):

This is the sorta thing I think might lead to less trivial fibrations of FP. If (fixed amounts of resource) leads to a fibration, then maybe (overall fixed at the end of the day amounts of resource) leads to a fibration as well.

John Baez (Jul 06 2020 at 21:30):

For Petri nets and chemistry in general I will yet again recommend this free book of mine:

• John Baez and Jacob Biamonte, *Quantum techniques for stochastic mechanics.

This has a bunch of simple examples from chemistry, and links to the serious chemistry literature.

John Baez (Jul 06 2020 at 21:30):

Joe Moeller said:

This is the sorta thing I think might lead to less trivial fibrations of FP. If (fixed amounts of resource) leads to a fibration, then maybe (overall fixed at the end of the day amounts of resource) leads to a fibration as well.

That'd be cool.

Sophie Libkind (Jul 06 2020 at 22:06):

Thanks for the great talk, Joe! Do you think you can use the idea of catalysts to synchronize petri-nets along transitions? I'm thinking of this conversation with @Fabrizio Genovese from awhile ago

Joe Moeller (Jul 06 2020 at 22:07):

This sounds interesting. Could you say more about what you're thinking?

Sophie Libkind (Jul 06 2020 at 22:09):

I guess I was interested in when two reactions need the same catalyst

Sophie Libkind (Jul 06 2020 at 22:09):

I guess that does not mean, however, that one fires if and only if the other one does

John Baez (Jul 06 2020 at 22:09):

I don't think anyone in my group has thought hard about synchronizing Petri nets along transitions, and this would be a good direction to explore.

John Baez (Jul 06 2020 at 22:10):

Jade and I thought about it a bit when studying open Petri nets; you might use synchronizing along transitions to create a different category of open Petri where the objects are finite sets of transitions rather than species. Some people have already done this, but not in the way I'd consider perfectly beautiful.

Sophie Libkind (Jul 06 2020 at 22:10):

@James Fairbanks's question also made me wonder about having "input and output" for Petri-nets. If System 1 produces a catalyst that System 2 uses, then we can think of that as System 1 sending input to System 2 in a message passing way.

Sophie Libkind (Jul 06 2020 at 22:12):

John Baez said:

Jade and I thought about it a bit when studying open Petri nets; you might use synchronizing along transitions to create a different category of open Petri where the objects are finite sets of transitions rather than species. Some people have already done this, but not in the way I'd consider perfectly beautiful.

We're you also able to do composition via species sharing in this category?

John Baez (Jul 06 2020 at 22:15):

Sophie wrote:

Were you also able to do composition via species sharing in this category?

I don't know what's "this category" - some category I'm vaguely dreaming about? Jade and I created a category where you glue Petri nets along species. There's a category I'm vaguely dreaming about where you can only glue Petri nets along transitions, but in a funny way that amounts to "synchronizing along transitions". And then there's a category I'm vaguely dreaming about where you can do both.

Sophie Libkind (Jul 06 2020 at 22:16):

Sophie Libkind said:

I guess I was interested in when two reactions need the same catalyst

Thinking out loud... If I have an Petri-net where $\tau_1$ uses a catalyst $A_1$ and a Petri-net where $\tau_2$ uses catalyst $A_2$. If I compose by identifying $A_1$ and $A_2$, then does that synchronize the transitions $\tau_1$ and $\tau_2$?

John Baez (Jul 06 2020 at 22:16):

You need two dollar signs to do math here - the price went up.

Sophie Libkind (Jul 06 2020 at 22:17):

yikes! math-flation

John Baez (Jul 06 2020 at 22:17):

Next year you'll need three.

John Baez (Jul 06 2020 at 22:18):

The answer to your question is "no" - in the category Jade and I cooked up, identifying $A_1$ and $A_2$ creates a Petri net where now you have a catalyst that can enable $\tau_1$ or $\tau_2$.

John Baez (Jul 06 2020 at 22:19):

So we can't "synchronize" transitions.

John Baez (Jul 06 2020 at 22:19):

But that's just this particular setup.

Sophie Libkind (Jul 06 2020 at 22:21):

Is "$\tau_1$ or $\tau_2$" because you one have 1 token for the species $A_1 \sim A_2$ and hence you can only use it on one transition?

John Baez (Jul 06 2020 at 22:23):

Right. If I had a whiteboard I'd just draw what happens when you glue together Petri nets by identifying the species $A_1$ and $A_2$ and you'd see this is what happens.

Paolo Perrone (Jul 07 2020 at 10:36):

Here's the video:
https://www.youtube.com/watch?v=ffv_5I8lAlc&list=PLCOXjXDLt3pYot9VNdLlZqGajHyZUywdI

Jorge Soto-Andrade (Jul 08 2020 at 03:42):

Hi Joe, Have you thought of taking advantage of zooming in when you have a catalyst which enters and exits a box in a Petri net? Zooming in would show a sort of cyclic tiny Petri net where the catalyst really enters and exits. You find a toy example of this in our poster available at https://categoricalouroboros.wordpress.com

Joe Moeller (Jul 08 2020 at 03:44):

I have not thought of this. It sounds interesting. Could you say more about what you mean?

David Jaz (Jul 08 2020 at 11:06):

John Baez said:

Right. If I had a whiteboard I'd just draw what happens when you glue together Petri nets by identifying the species $A_1$ and $A_2$ and you'd see this is what happens.

Its not ideal, but we could try a site like wbo.

Jorge Soto-Andrade (Jul 08 2020 at 15:06):

Joe Moeller said:

I have not thought of this. It sounds interesting. Could you say more about what you mean?

Hello,
Here I am trying to attach a zooming out and zooming in of a sort of metabolic graph (a toy example of a metabolism we concocted with some fellow biochemists and biologists ) Here S, T, U constitute the food set. SU, ST, STU are products. SU and STU are catalysts. You see that each catalysis is a kind of merry go round ...
In graph theory you do this sometimes, zooming in or blowing up if you prefer: You have a graph, whose nodes - at a closer look - turn out to be tiny graphs themselves. This is helpful in (non commutative) harmonic analysis on graphs. Translation to Petri nets seems to be straightforward.
Tell me please whether you can view the attached graphs (I am not a native zuliper...)
Grafo2b_zoomed_in.pdf Grafo1b_zoomed_out.pdf

John Baez (Jul 08 2020 at 17:03):

Yes, I can see those!

One thing we need to work on more is Petri nets with "boxes" that you can zoom into and reveal smaller Petri nets. These are routinely studied by Petri net experts - they have a standard name I'm forgetting now - but I don't think the category theorists have studied them enough.