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graveolens's profile
Owen Maresh
Owen Maresh
Owen Maresh
@graveolens

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Owen Maresh

@graveolens

Mathematics Sorceror (sensory alchemist) at the Arctangent Transpetroglyphics Algra Laboratory (ATAL), I transmute mathematics into living rainbows.

somerville, ma
owen.maresh.info
Joined April 2010

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    1. Jade Master‏ @JadeMasterMath 24 Apr 2019
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      I just finished a paper called Generalized Petri nets https://arxiv.org/abs/1904.09091  I use Lawvere theories to generalize Petri nets. A Petri net can be thought of as a pair of functions from a set of transitions to the free commutative monoid on some set. 1/npic.twitter.com/a1G5FHE5ZL

      10 replies 63 retweets 251 likes
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    2. Jade Master‏ @JadeMasterMath 24 Apr 2019
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      For a given transition, the image of these two functions represent it's source and target. Given a Lawvere theory Q, you can define a Q-Net to be a pair of functions from a set of transitions to the free model of Q on some set. 2/n

      1 reply 0 retweets 9 likes
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    3. Jade Master‏ @JadeMasterMath 24 Apr 2019
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      To justify a generalization you need to show there are examples of it, and that in these examples familiar consequences follow. If you take Q = the Lawvere theory of monoids you get pre-nets. These are Petri nets which are equipped with an ordering of the species on the input 3/n

      1 reply 0 retweets 10 likes
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    4. Jade Master‏ @JadeMasterMath 24 Apr 2019
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      and output of each transition. Pre-nets are useful for modeling processes where the identities of the token are distinct and you want to keep track of which token caused which process to occur. Details can be found in this paper https://www.sciencedirect.com/science/article/pii/S0890540101930500 … 4/n

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    5. Jade Master‏ @JadeMasterMath 24 Apr 2019
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      The second example I talk about are integer nets or lending nets. These are given by setting Q = the Lawvere theory of abelian groups. The idea is that even if there aren't enough tokens for a given transition to fire, in an integer net, a transition can borrow tokens. 5/npic.twitter.com/1l3vTPOKGP

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    6. Jade Master‏ @JadeMasterMath 24 Apr 2019
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      In the above picture taken from this paper https://arxiv.org/abs/1805.05988  by @fabgenovese and @wires_wires , borrowed tokens are represented in red. Note that integer nets are similar to Lending nets introduced in this paper https://www.sciencedirect.com/science/article/pii/S0167642315001021 … which model contract logic 6/n

      1 reply 1 retweet 10 likes
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    7. Jade Master‏ @JadeMasterMath 24 Apr 2019
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      The third example I talk about is elementary net systems. These are given by setting Q= the Lawvere theory of semilattices (i.e. commutative idempotent monoids). Elementary systems are Petri nets which can have a maximum of one token in each place. 7/npic.twitter.com/HNoVAKXdVp

      2 replies 0 retweets 9 likes
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    8. Jade Master‏ @JadeMasterMath 24 Apr 2019
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      These are useful for modeling processes like non-concurrent computer programs with only one user. Indeed, familiar consequences follow in all the above examples. Symmetric monoidal categories are the language of processes which can be done in sequence and in parallel. 8/n

      2 replies 0 retweets 11 likes
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      Owen Maresh‏ @graveolens 24 Apr 2019
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      Replying to @JadeMasterMath

      https://en.wikipedia.org/wiki/Howard_T._Odum …

      9:13 AM - 24 Apr 2019
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      • @no identd Jade Master
      1 reply 0 retweets 2 likes
        1. New conversation
        2. Jade Master‏ @JadeMasterMath 24 Apr 2019
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          Replying to @graveolens

          You're second person to mention that to me today. Actually @johncarlosbaez and the rest of his research group have been working on formalizing that stuff recently.

          1 reply 0 retweets 2 likes
        3. @no identd‏ @no_identd 27 Apr 2019
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          Replying to @JadeMasterMath @graveolens @johncarlosbaez

          @no identd Retweeted Owen Maresh

          https://twitter.com/graveolens/status/1121084772082753536 …

          @no identd added,

          Owen Maresh @graveolens
          Replying to @JadeMasterMath
          the ecological theories of Howard Odum might be interesting
          0 replies 0 retweets 0 likes
        4. End of conversation

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