Luca Cardelli, “Strand algebras for DNA Computing”

http://lucacardelli.name/Papers/Strand%20Algebras%20for%20DNA%20Computing%20(Natural%20Computing).pdf

I don’t know that term, but I have a guess as to what you mean. If we have a transition

wolf + rabbit wolf + wolf

in our Petri net, we can also use this transition to turn

wolf + rabbit + rabbit

into

wolf + wolf + rabbit

(One rabbit stands by and watches the other get eaten.) Manoj actually gave an example of this sort when explaining the concept of :

By a complex I will mean a population vector: a snapshot of the number of tokens in each species. In the example above, (#rabbit, #wolf) is a complex. If are two complexes, then we write

if we can get from to by a single transition in our Petri net. For example, we just saw that

via the predation transition.

So, his use of does not correspond precisely to a transition, but rather a transition ‘with bystanders’. Is this what you’re calling ‘dilution’?

]]>Does your explanation extend to the question of why this is not true for all critical siphons?

My “translation” for conservation law should be made more precise by adding:

“conservation law”: *a group which forms an “island of stability” by having a net constant wealth via one but arbitrary way of exchange.*

That is in the X,Y example one would – if one would apply all two transitions and not just one, keep the numbers of tokens constant. Or in other words X+Y satisfies a kind of “total conservation law.” So the X,Y example is critical but would not be totally critical. I could imagine that eventually by demanding “total conservation” on a support one might get around the minimal condition, but this is just a rough guess.

]]>David Angeli, Patrick De Leenheer, Eduardo Sontag,

“A Petri Net Approach to Persistence Analysis in Chemical Reaction Networks.”

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.152.627&rep=rep1&type=pdf

The same authors also say,

“Traps for Petri-Nets enjoy the following invariance property: if a trap is non-empty at time zero (meaning that at least one of its places has tokens), then the trap is non-empty at all future times. In contrast, in a continuous set-up (when tokens are not integer quantities but may take any real value), satisfaction of the siphon-trap property does not prevent (in general) concentrations of species from decaying to zero asymptotically.”

in this paper:

A Petri net approach to the study of persistence in chemical reaction networks.

http://web.mit.edu/~esontag/www/FTP_DIR/angeli_leenheer_sontag_math_biosciences_MBS-D-06-00188R1.pdf