5 April 2017:

1) Gheorghe Craciun visited UCR and gave a talk today on his proof of the [Global Attractor Conjecture](https://sinews.siam.org/Details-Page/discussing-the-proof-of-the-global-attractor-conjecture-1), which until recently was one of the biggest open questions in mathematical chemistry.

2) Blake Pollard and I put our paper [A compositional framework for reaction networks](https://arxiv.org/abs/1704.02051) on the arXiv today. The conclusions summarize a lot of the work our group has done so far, and fits it into a big commutative diagram. Craciun and I have already used these ideas to construct a large new class of reaction networks with nice stability properties.

> **Abstract.** Reaction networks, or equivalently Petri nets, are a general framework for describing processes in which entities of various kinds interact and turn into other entities. In chemistry, where the reactions are assigned "rate constants", any reaction network gives rise to a nonlinear dynamical system called its "rate equation". Here we generalize these ideas to "open" reaction networks, which allow entities to flow in and out at certain designated inputs and outputs. We treat open reaction networks are morphisms in a category. Composing two such morphisms connects the outputs of the first to the inputs of the second. We construct a functor sending any open reaction network to its corresponding "open dynamical system". This provides a compositional framework for studying the dynamics of reaction networks. We then turn to statics: that is, steady state solutions of open dynamical systems. We construct a "black-boxing" functor that sends any open dynamical system to the relation that it imposes between input and output variables in steady states. This extends our earlier work on black-boxing for Markov processes.

3) My former student Brendan Fong, who developed the "decorated cospan" and "decorated corelation" approach to network theory in this thesis, put related two papers onto the arXiv:

[Decorated corelations](https://arxiv.org/abs/1703.09888) and [A universal construction for (co)relations](https://arxiv.org/abs/1703.08247). I need to blog about these!

4) Brendan also gave an expository talk about "The mathematics of system composition" at [BAE Systems](https://en.wikipedia.org/wiki/BAE_Systems), a British defense company.

5) My former student Mike Stay wrote two papers with Greg Meredith on the use of categories in computer science: [Name-free combinators for concurrency](https://arxiv.org/abs/1703.07054) and [Representing operational semantics with enriched Lawvere theories](https://arxiv.org/abs/1704.03080).

6) My student Daniel Cicala got invited to the American Mathematical Society conference on [Homotopy Type Theory](https://homotopytypetheory.org/2016/10/04/hott-mrc/) that will take place in Snowbird, Utah on June 4-10.

1) Gheorghe Craciun visited UCR and gave a talk today on his proof of the [Global Attractor Conjecture](https://sinews.siam.org/Details-Page/discussing-the-proof-of-the-global-attractor-conjecture-1), which until recently was one of the biggest open questions in mathematical chemistry.

2) Blake Pollard and I put our paper [A compositional framework for reaction networks](https://arxiv.org/abs/1704.02051) on the arXiv today. The conclusions summarize a lot of the work our group has done so far, and fits it into a big commutative diagram. Craciun and I have already used these ideas to construct a large new class of reaction networks with nice stability properties.

> **Abstract.** Reaction networks, or equivalently Petri nets, are a general framework for describing processes in which entities of various kinds interact and turn into other entities. In chemistry, where the reactions are assigned "rate constants", any reaction network gives rise to a nonlinear dynamical system called its "rate equation". Here we generalize these ideas to "open" reaction networks, which allow entities to flow in and out at certain designated inputs and outputs. We treat open reaction networks are morphisms in a category. Composing two such morphisms connects the outputs of the first to the inputs of the second. We construct a functor sending any open reaction network to its corresponding "open dynamical system". This provides a compositional framework for studying the dynamics of reaction networks. We then turn to statics: that is, steady state solutions of open dynamical systems. We construct a "black-boxing" functor that sends any open dynamical system to the relation that it imposes between input and output variables in steady states. This extends our earlier work on black-boxing for Markov processes.

3) My former student Brendan Fong, who developed the "decorated cospan" and "decorated corelation" approach to network theory in this thesis, put related two papers onto the arXiv:

[Decorated corelations](https://arxiv.org/abs/1703.09888) and [A universal construction for (co)relations](https://arxiv.org/abs/1703.08247). I need to blog about these!

4) Brendan also gave an expository talk about "The mathematics of system composition" at [BAE Systems](https://en.wikipedia.org/wiki/BAE_Systems), a British defense company.

5) My former student Mike Stay wrote two papers with Greg Meredith on the use of categories in computer science: [Name-free combinators for concurrency](https://arxiv.org/abs/1703.07054) and [Representing operational semantics with enriched Lawvere theories](https://arxiv.org/abs/1704.03080).

6) My student Daniel Cicala got invited to the American Mathematical Society conference on [Homotopy Type Theory](https://homotopytypetheory.org/2016/10/04/hott-mrc/) that will take place in Snowbird, Utah on June 4-10.