FabGenovese

6 ms·

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by FabGenovese 6y ago
:D I know especially John is very interested in finding an application of this stuff to solve modelling problems for climate change etc, but yes, this is not the content of this work ^_^
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by FabGenovese 6y ago
There are countless different flavors of Petri nets. The edges can be weighted, meaning that a transition can get more than one token from a given input place to fire, and can put more than one token in a output place when it fires. About t
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by FabGenovese 6y ago
Please don't, a 2yr old kid should basically play and have fun imho, there's so much time to experience the absolute misery of mathematical frustration.
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by FabGenovese 6y ago
Natual isomorphisms with FDHilb are very difficult to get here: Different flavors of Petri nets present different flavors of FREE monoidal categories. "Free" here means that we have categories that satisfy exactly the equations th
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by FabGenovese 6y ago
Nice, if everyone thought like you do, number theory wouldn't have existed, elliptic curves along with it, and hence much of public key cryptography as well. Indeed, number theory has been exquisitely useless for a couple of millennia,
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by FabGenovese 6y ago
I've got a paper about colored nets as well :) https://arxiv.org/abs/2002.02762 Timed nets is in the works ^_^
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by FabGenovese 6y ago
No. I don't know why everyone is getting so much fixated with the epidemiological aspect, that in our paper is barely mentioned. Ours is a technical contribution that uses results from groupoid theory and homotopy theory to provide a f
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by FabGenovese 6y ago
The main difference is that a Petri net is basically an hypegraph, where you have directed edges connecting multiple vertexes both in the source and in the target. Graphs give you finite state machines in the obvious way: You mark the verte
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by FabGenovese 6y ago
You can turn Petri nets into stochastic nets using some formal procedures. Stochastic nets have a "master equation" which spits out a system of PDEs representing reactions where many many things happen at the same time, and so it
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by FabGenovese 6y ago
I'm one of the authors of the paper. Ask me anything!
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by FabGenovese 6y ago
Petri nets can be used for populations dynamics, and indeed the structured cospans approach to Petri net is being used to simulate epidemic diffusion right now: https://www.algebraicjulia.org/blog/post/2020/10
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by FabGenovese 6y ago
It's funny, this is exactly what people have been saying of Categorical Quantum Mechanics and ZX calculus for 14 years, until they didn't, and now ZX calculus is used to draft quantum protocols and businesses like Cambridge Quantu