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I honestly doubt it will have any practical applications in biology. Computation chemistry and synthetic biology run on differential equations, anything discret

I honestly doubt it will have any practical applications in biology. Computation chemistry and synthetic biology run on differential equations, anything discrete is generally useless. Perhaps it will have some use in a couple of decades when synthetic biology progresses beyond brute force simulations but at the current level it is the wrong abstraction.

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 makes more sense to think in terms of concentrations etc. We are working to capture this categorically as well. We are perfectly conscious of how a discrete system won't help you if you have an Avogadro number of things going around. Just give us time. :)
- ampdepolymerase 6y ago
  We may disagree on this point but thanks for taking the time to reply nonetheless :) I will take a look at your paper.
wires 6y ago
you have to understand that the real power behind this work is not the Petri nets but that fact that they are described so abstractly that they can take on different shapes, such as stochastic nets, or coloured nets, or... It puts the different models on the same footing (and hence allowing you to unify tools and do more work) Also, I'd even argue that biology/chemistry needs to embrace categorical methods and we would see some deep discoveries.
akimball 6y ago
The differential equations are themselves in many cases an abstraction over statistical numbers of discrete events. Arguably, in those cases, they are the wrong abstraction - a thesis which can only be proven by demonstrating the superiority of a different abstraction. Has one been demonstrated? Not yet, for most purposes. Is this a promising avenue of study? IMO, yes.

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 makes more sense to think in terms of concentrations etc. We are working to capture this categorically as well. We are perfectly conscious of how a discrete system won't help you if you have an Avogadro number of things going around. Just give us time. :)

ampdepolymerase 6y ago
We may disagree on this point but thanks for taking the time to reply nonetheless :) I will take a look at your paper.

wires 6y ago

you have to understand that the real power behind this work is not the Petri nets but that fact that they are described so abstractly that they can take on different shapes, such as stochastic nets, or coloured nets, or... It puts the different models on the same footing (and hence allowing you to unify tools and do more work) Also, I'd even argue that biology/chemistry needs to embrace categorical methods and we would see some deep discoveries.

akimball 6y ago

The differential equations are themselves in many cases an abstraction over statistical numbers of discrete events. Arguably, in those cases, they are the wrong abstraction - a thesis which can only be proven by demonstrating the superiority of a different abstraction. Has one been demonstrated? Not yet, for most purposes. Is this a promising avenue of study? IMO, yes.