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# This week's progress

I've been writing weekly progress reports to my grad students. It may make sense to copy them here. Let me give it a try.

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1.

17 November 2016:

Hi -

Daniel Cicala points out the math conference December 3rd and 4th at Union College in upstate NY. There will be talks on category theory organized by Susan Niefeld - she does this every year, and I've spoken there once. If you can go, do it!

(If you read the category theory mailing list you can stay up to date on such conferences.)

Here is this week's progress:

1) Blake and I went to San Diego and learned about Metron's "ExAMS" software for designing complex systems. Then John Foley came up and, with help from Joseph Moeller, we figured out a bunch of stuff.

This software raises lots of interesting questions. I believe it's based on "timed hierarchical colored Petri nets with guards". I would like to make sure this is true, and understand this kind of network category-theoretically. In case anyone wants to help me, here's an intro:

When we met, Tom Mifflin at Metron seemed pretty eager for our work to go in this direction.

2) I went to the Mathematical Association of America conference and gave a talk on The answer to the ultimate question of life, the universe and everything. Brandon and Daniel also went there.

3) I finally blogged about Brendan's thesis:

As you can see, it's a lazy blog article - yet it still manages to give a detailed introduction to his work! If you haven't yet learned everything that Brendan is doing, this is a good place to start.

Comment Source:17 November 2016: Hi - Daniel Cicala points out the [math conference December 3rd and 4th at Union College](http://www.math.union.edu/%7Etoddg/ucc/) in upstate NY. There will be talks on category theory organized by Susan Niefeld - she does this every year, and I've spoken there once. If you can go, do it! (If you read the category theory mailing list you can stay up to date on such conferences.) Here is this week's progress: 1) Blake and I went to San Diego and learned about Metron's "ExAMS" software for designing complex systems. Then John Foley came up and, with help from Joseph Moeller, we figured out a bunch of stuff. I blogged about ExAMS here: * [Complex Adaptive System Design (Part 2)](https://johncarlosbaez.wordpress.com/2016/10/18/complex-adaptive-system-design-part-2/) This software raises lots of interesting questions. I believe it's based on "timed hierarchical colored Petri nets with guards". I would like to make sure this is true, and understand this kind of network category-theoretically. In case anyone wants to help me, here's an intro: * Wil M. P. van der Aalst, Christian Stahl, and Michael Westergaard, [Strategies for modeling complex processes using colored Petri nets](http://wwwis.win.tue.nl/%7Ewvdaalst/publications/p710.pdf). When we met, Tom Mifflin at Metron seemed pretty eager for our work to go in this direction. 2) I went to the Mathematical Association of America conference and gave a talk on [The answer to the ultimate question of life, the universe and everything](http://math.ucr.edu/home/baez/42/). Brandon and Daniel also went there. 3) I finally blogged about Brendan's thesis: * [Open and interconnected systems](https://johncarlosbaez.wordpress.com/2016/10/23/open-and-interconnected-systems/). As you can see, it's a lazy blog article - yet it still manages to give a detailed introduction to his work! If you haven't yet learned everything that Brendan is doing, this is a good place to start.
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2.

23 November 2016:

Lots of progress this week:

1) Jason uploaded his thesis to the arXiv! That's great, because it establishes priority - now he can prove he did this stuff before anyone else, even if it takes a while for him to publish a paper.

2) Blake gave a talk about open chemical reaction networks at the Santa Fe Institute workshop on Statistical Mechanics, Information Processing and Biology:

It was a real hit. Susanne Still said it was "great" - she works on Markov processes and the information bottleneck method for predictive inference. Jim Crutchfield liked it so much he invited Blake to give a talk up at U. C. Davis! He's a real bigshot: the Wikipedia article on him says

Over the last three decades Prof. Crutchfield has worked in the areas of nonlinear dynamics, solid-state physics, astrophysics, fluid mechanics, critical phenomena and phase transitions, chaos, and pattern formation. His current research interests center on computational mechanics, the physics of complexity, statistical inference for nonlinear processes, genetic algorithms, evolutionary theory, machine learning, quantum dynamics, and distributed intelligence. He has published over 100 papers in these areas.

If Blake can strike up a relationship with Crutchfield and maybe work on a project, that'll be excellent.

3) Joshua Tan, a grad student at Oxford (and friend of Brendan), invited me to join a bunch of people in writing a grant proposal.

It's for an NSF grant called "Smart & Connected Communities", and part of the plan would be to model cities as composable, open systems using category theory. Here are the other people involved in writing the proposal:

• Dennis Frenchman is a professor at MIT and an expert in building digital tools for cities. He is the likely PI.

• Sokwoo Rhee is a director at NIST managing 100+ smart cities projects and will be collaborating directly with us, but he is a silent partner due to federal rules.

• Stephen Walter is a program director at the City of Boston, Mayor's Office of New Urban Mechanics.

• Matthew Claudel is a student of Dennis' who has been working with me to write the proposal. His research is in urban innovation.

• Possibly: Eric Gordon, a professor at the Engagement Lab at Emerson College, who works on civic participation.

• Other personnel attached to the project include Elizabeth Christoforetti (Harvard, MIT urban planner) and Nissia Sabri (startup, hardware specialist).

This would be a great step toward my ultimate goal: using network theory for studying complex systems like biological systems and designing systems to deal with climate change.

Comment Source:23 November 2016: Lots of progress this week: 1) Jason [uploaded his thesis to the arXiv](https://arxiv.org/abs/1611.07591)! That's great, because it establishes priority - now he can prove he did this stuff before anyone else, even if it takes a while for him to publish a paper. 2) Blake gave a talk about open chemical reaction networks at the Santa Fe Institute workshop on [Statistical Mechanics, Information Processing and Biology](http://www.santafe.edu/gevent/detail/science/2452/): * [Compositional frameworks for open systems](https://johncarlosbaez.wordpress.com/2016/11/27/compositional-frameworks-for-open-systems/). It was a real hit. [Susanne Still](http://www2.hawaii.edu/%7Esstill/) said it was "great" - she works on Markov processes and the information bottleneck method for predictive inference. [Jim Crutchfield](http://csc.ucdavis.edu/%7Echaos/) liked it so much he invited Blake to give a talk up at U. C. Davis! He's a real bigshot: the Wikipedia article on him says > Over the last three decades Prof. Crutchfield has worked in the areas of nonlinear dynamics, solid-state physics, astrophysics, fluid mechanics, critical phenomena and phase transitions, chaos, and pattern formation. His current research interests center on computational mechanics, the physics of complexity, statistical inference for nonlinear processes, genetic algorithms, evolutionary theory, machine learning, quantum dynamics, and distributed intelligence. He has published over 100 papers in these areas. If Blake can strike up a relationship with Crutchfield and maybe work on a project, that'll be excellent. 3) [Joshua Tan](http://www.joshuatan.com/research/), a grad student at Oxford (and friend of Brendan), invited me to join a bunch of people in writing a grant proposal. It's for an NSF grant called "[Smart & Connected Communities](https://www.nsf.gov/pubs/2016/nsf16610/nsf16610.htm#pgm_desc_txt)", and part of the plan would be to model cities as composable, open systems using category theory. Here are the other people involved in writing the proposal: * Dennis Frenchman is a professor at MIT and an expert in building digital tools for cities. He is the likely PI. * Sokwoo Rhee is a director at NIST managing 100+ smart cities projects and will be collaborating directly with us, but he is a silent partner due to federal rules. * Stephen Walter is a program director at the City of Boston, Mayor's Office of New Urban Mechanics. * Matthew Claudel is a student of Dennis' who has been working with me to write the proposal. His research is in urban innovation. * Possibly: Eric Gordon, a professor at the Engagement Lab at Emerson College, who works on civic participation. * Other personnel attached to the project include Elizabeth Christoforetti (Harvard, MIT urban planner) and Nissia Sabri (startup, hardware specialist). This would be a great step toward my ultimate goal: using network theory for studying complex systems like biological systems and designing systems to deal with climate change.
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3.
edited December 2016

28 November 2016:

1) Daniel Cicala passed his oral exam today! He spoke about this paper that he put on the arXiv last week:

Abstract. We introduce the notion of a span of cospans and define, for them, horizontal and vertical composition. These compositions satisfy the interchange law if working in a topos C and if the span legs are monic. A bicategory is then constructed from C-objects, C-cospans, and doubly monic spans of C-cospans. The primary motivation for this construction is an application to graph rewriting.

2) Tobias Fritz is visiting us! He'll be speaking in the network theory seminar tomorrow and also joining our group meeting on Wednesday at 11 am. Here's his talk:

Abstract. The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some hypothetical Bayesian network structure. In the presence of hidden nodes (unobserved variables), this is a challenging problem for which no exact methods are known. The inflation technique of http://arxiv.org/abs/1609.00672 provides a new practical tool for approaching this problem. It has the potential to be generalized to other kinds of networks, in particular those that live in semicartesian monoidal categories.

3) My former grad student Chris Rogers will be giving a special seminar on symplectic stuff on Thursday 3:40-5:00, either in the Undergraduate Study Room or in some better room like room 284 or 268 - it's not exactly clear, but I'll try to inform you when I find out.

It will be very good for Brandon and Adam to attend this, since they're doing symplectic stuff. However, Chris will blow them out of the water with his erudition.

• From Hamiltonian mechanics to homotopy Lie theory

Abstract. In Hamiltonian mechanics, physicists model the phase space of a physical system using symplectic geometry, and they use Lie algebras to describe the space's infinitesimal symmetries. Given such a Lie algebra of symmetries, the geometry naturally produces a new Lie algebra called a "central extension''. This central extension plays a crucial role, especially in quantum mechanics. The famous Heisenberg algebra, for example, arises precisely in this way.

In this talk, I will explain how the above recipe can be enhanced to geometrically produce examples of "homotopy Lie algebras''. A homotopy Lie algebra is a topologist's version of a Lie algebra: a chain complex equipped with structures which satisfy the axioms of a Lie algebra only up to chain homotopy. They provide important tools for rational homotopy theory and deformation theory. The homotopy Lie algebras produced from our construction turn out to have interesting relationships with the theory of loop groups and what are called "string structures'' in algebraic topology

Comment Source:28 November 2016: 1) Daniel Cicala passed his oral exam today! He spoke about this paper that he put on the arXiv last week: * [Spans of cospans](https://arxiv.org/abs/1611.07886). > **Abstract.** We introduce the notion of a span of cospans and define, for them, horizontal and vertical composition. These compositions satisfy the interchange law if working in a topos C and if the span legs are monic. A bicategory is then constructed from C-objects, C-cospans, and doubly monic spans of C-cospans. The primary motivation for this construction is an application to graph rewriting. 2) Tobias Fritz is visiting us! He'll be speaking in the network theory seminar tomorrow and also joining our group meeting on Wednesday at 11 am. Here's his talk: * [Inferring hidden network structure: the case of causal inference](https://simons.berkeley.edu/talks/tobias-fritz-12-06-2016). > **Abstract.** The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some hypothetical Bayesian network structure. In the presence of hidden nodes (unobserved variables), this is a challenging problem for which no exact methods are known. The inflation technique of [http://arxiv.org/abs/1609.00672](http://arxiv.org/abs/1609.00672) provides a new practical tool for approaching this problem. It has the potential to be generalized to other kinds of networks, in particular those that live in semicartesian monoidal categories. 3) My former grad student Chris Rogers will be giving a special seminar on symplectic stuff on Thursday 3:40-5:00, either in the Undergraduate Study Room or in some better room like room 284 or 268 - it's not exactly clear, but I'll try to inform you when I find out. It will be very good for Brandon and Adam to attend this, since they're doing symplectic stuff. However, Chris will blow them out of the water with his erudition. * From Hamiltonian mechanics to homotopy Lie theory > **Abstract.** In Hamiltonian mechanics, physicists model the phase space of a physical system using symplectic geometry, and they use Lie algebras to describe the space's infinitesimal symmetries. Given such a Lie algebra of symmetries, the geometry naturally produces a new Lie algebra called a "central extension''. This central extension plays a crucial role, especially in quantum mechanics. The famous Heisenberg algebra, for example, arises precisely in this way. > In this talk, I will explain how the above recipe can be enhanced to geometrically produce examples of "homotopy Lie algebras''. A homotopy Lie algebra is a topologist's version of a Lie algebra: a chain complex equipped with structures which satisfy the axioms of a Lie algebra only up to chain homotopy. They provide important tools for rational homotopy theory and deformation theory. The homotopy Lie algebras produced from our construction turn out to have interesting relationships with the theory of loop groups and what are called "string structures'' in algebraic topology
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4.

10 December 2016:

Some very good news this time:

1) Brendan Fong has accepted a postdoc at MIT working with David Spivak. Having seen them discuss math together, I think we can expect great things!

2) I'm 99% sure that Daniel Cicala has been accepted to the Kan Extension Seminar, a high-powered online course on category theory. This time it'll be about functorial semantics - you can see the papers they'll discuss by clicking the link.

3) I gave a talk on Compositionality in network theory at this week's workshop on Compositionality at the Simons Institute for the Theory of Computing. You can see a video by clicking the link. I explained Brendan's theory of decorated cospans, illustrating it with a paper that Blake and I are writing about Petri nets.

4) Brendan gave a talk on Modelling interconnected systems with decorated corelations at the same workshop. This goes further, introducing decorated corelations, which are a generalization of decorated cospans. Again you can see a video by clicking the link.

These talks seem to have gone over well, along with other closely connected talks by David Spivak, Ross Duncan, Pawel Sobocinski and others. I was invited by Michael Mislove, who edits a column on semantics at the journal Logic, Semantics and Theory of Programming, to contribute a column. The whole lot of us were invited to participate more in various conferences on logic and computer science, since what we're doing seems to fit into that heading.

5) Blake's work on Markov processes was cited in at least two talks, and Prakash Panagaden gave me a draft of his paper on a bicategory of Markov processes, which I append here - Blake, Kenny and Daniel should read it!

I think we can and should do better, but we'll have to avoid stepping on Prakash's toes. For one thing, we can build a symmetric monoidal bicategory. For another thing, they are doing discrete-time Markov processes, with 2-morphisms being maps called 'simulations'. We can do something else. Daniel's work on perfect measure spaces should come into this, as well as what Kenny has been doing on bicategories with coarse-grainings as 2-morphisms.

6) Some negative news: the grant proposal I mentioned recently, engineered by Joshua Tan, has fallen through. I'm not too upset.

Comment Source:10 December 2016: Some very good news this time: 1) Brendan Fong has accepted a postdoc at MIT working with David Spivak. Having seen them discuss math together, I think we can expect great things! 2) I'm 99% sure that Daniel Cicala has been accepted to the [Kan Extension Seminar](https://golem.ph.utexas.edu/category/2016/10/the_kan_extension_seminar_retu.html), a high-powered online course on category theory. This time it'll be about functorial semantics - you can see the papers they'll discuss by clicking the link. 3) I gave a talk on [Compositionality in network theory](https://johncarlosbaez.wordpress.com/2016/11/29/compositionality-in-network-theory/) at this week's workshop on Compositionality at the Simons Institute for the Theory of Computing. You can see a video by clicking the link. I explained Brendan's theory of decorated cospans, illustrating it with a paper that Blake and I are writing about Petri nets. 4) Brendan gave a talk on [Modelling interconnected systems with decorated corelations](https://johncarlosbaez.wordpress.com/2016/12/09/modelling-interconnected-systems-with-decorated-corelations/) at the same workshop. This goes further, introducing decorated corelations, which are a generalization of decorated cospans. Again you can see a video by clicking the link. These talks seem to have gone over well, along with other closely connected talks by David Spivak, Ross Duncan, Pawel Sobocinski and others. I was invited by Michael Mislove, who edits a column on semantics at the journal Logic, Semantics and Theory of Programming, to contribute a column. The whole lot of us were invited to participate more in various conferences on logic and computer science, since what we're doing seems to fit into that heading. 5) Blake's work on Markov processes was cited in at least two talks, and Prakash Panagaden gave me a draft of his paper on a bicategory of Markov processes, which I append here - Blake, Kenny and Daniel should read it! I think we can and should do better, but we'll have to avoid stepping on Prakash's toes. For one thing, we can build a symmetric monoidal bicategory. For another thing, they are doing discrete-time Markov processes, with 2-morphisms being maps called 'simulations'. We can do something else. Daniel's work on perfect measure spaces should come into this, as well as what Kenny has been doing on bicategories with coarse-grainings as 2-morphisms. 6) Some negative news: the grant proposal I mentioned recently, engineered by Joshua Tan, has fallen through. I'm not too upset.
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5.
edited December 2016

Finally catching up to today, 13 December 2016:

1) Kenny Courser's paper A bicategory of decorated cospans was accepted by Theory and Applications of Categories!

The referee wants him to say more about examples. That makes a lot of sense. I'd also like to deal with this issue: in our favorite examples, the 2-morphisms in Kenny's bicategory are a bit too restrictive.

For example, in the bicategory of cospans of finite sets where the apex is decorated by a graph, the 2-morphism do not allow arbitrary graph morphisms, only those that are "cocartesian lifts" of maps between finite sets.

2) On December 14th, Brendan is giving a talk called "All hypergraph categories are decorated corelation categories" at Macquarie University in Australia.

Brendan: make sure to say hi to Ross Street and my old friend James Dolan!

3) At Berkeley, it became clear that the stuff we do fits into "theoretical computer science", which is a very broad subject by now.

All of us were invited to submit papers to CALCO 2017, a conference on algebra and coalgebra in computer science. Daniel reminded me of this, saying:

Actually, a few of the gang could probably submit, since their interests include:

• String Diagrams and Network Theory

- Combinatorial approaches

- Theory of PROPs and operads

- Rewriting problems and higher-dimensional approaches

- Automated reasoning with string diagrams

- Applications of string diagrams

- Connections with Control Theory, Engineering and Concurrency


So, think of submitting papers here! Daniel has a plan to do this.

Comment Source:Finally catching up to today, 13 December 2016: 1) Kenny Courser's paper [A bicategory of decorated cospans](https://arxiv.org/abs/1605.08100) was accepted by _Theory and Applications of Categories_! The referee wants him to say more about examples. That makes a lot of sense. I'd also like to deal with this issue: in our favorite examples, the 2-morphisms in Kenny's bicategory are a bit too restrictive. For example, in the bicategory of cospans of finite sets where the apex is decorated by a graph, the 2-morphism do not allow arbitrary graph morphisms, only those that are "cocartesian lifts" of maps between finite sets. 2) On December 14th, Brendan is giving a talk called "All hypergraph categories are decorated corelation categories" at Macquarie University in Australia. Brendan: make sure to say hi to Ross Street and my old friend James Dolan! 3) At Berkeley, it became clear that the stuff we do fits into "theoretical computer science", which is a very broad subject by now. All of us were invited to submit papers to [CALCO 2017](http://coalg.org/calco17/index.html), a conference on algebra and coalgebra in computer science. Daniel reminded me of this, saying: > Actually, a few of the gang could probably submit, since their interests include: > * String Diagrams and Network Theory > - Combinatorial approaches > - Theory of PROPs and operads > - Rewriting problems and higher-dimensional approaches > - Automated reasoning with string diagrams > - Applications of string diagrams > - Connections with Control Theory, Engineering and Concurrency So, think of submitting papers here! Daniel has a plan to do this.
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6.

For some reason dates aren't showing up in Azimuth Forum entries, so it's good I included the dates in the entries here! I have some new entries...

Comment Source:For some reason dates aren't showing up in Azimuth Forum entries, so it's good I included the dates in the entries here! I have some new entries... 
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7.

22 December 2016:

Here are two things that happened this week:

1) Brandon and Brendan's paper Corelations are the prop for extraspecial commutative Frobenius monoids has been accepted for publication by Theory and Applications of Categories subject to making some small corrections.

2) It doesn't really count as mathematics, but I've started the Azimuth Backup Project to help back up climate data before Trump becomes president - because almost all his big hires are people who deny the importance of global warming.

Other teams are doing this too, and you can get the basic idea in this article of mine:

You can see our team's progress here:

We've got a great team, including a guy who used to drive a Mars rover for NASA, and so far we've backed up about a terabyte of data! In a couple of days I'll start a Kickstarter campaign to raise funds to store the data. We'll try to store it at least until larger institutions accept this responsibility.

Comment Source:22 December 2016: Here are two things that happened this week: 1) Brandon and Brendan's paper [Corelations are the prop for extraspecial commutative Frobenius monoids](https://arxiv.org/abs/1601.02307) has been accepted for publication by _Theory and Applications of Categories_ subject to making some small corrections. 2) It doesn't really count as mathematics, but I've started the Azimuth Backup Project to help back up climate data before Trump becomes president - because almost all his big hires are people who deny the importance of global warming. Other teams are doing this too, and you can get the basic idea in this article of mine: * [Saving Climate Data (Part 1)](https://johncarlosbaez.wordpress.com/2016/12/13/saving-climate-data/). You can see our team's progress here: * [Azimuth Backup Project (Part 1)](https://johncarlosbaez.wordpress.com/2016/12/16/azimuth-backup-project/). * [Azimuth Backup Project (Part 2)](https://johncarlosbaez.wordpress.com/2016/12/20/azimuth-backup-project-part-2/). We've got a great team, including a guy who used to drive a Mars rover for NASA, and so far we've backed up about a terabyte of data! In a couple of days I'll start a Kickstarter campaign to raise funds to store the data. We'll try to store it at least until larger institutions accept this responsibility.
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8.
edited January 2017

13 January 2017:

We had a hugely productive meeting on Wednesday and I'm really excited about the new ideas:

• The connection between Brandon Coya's work on bond graphs and Ross Street's work on weak bimonoids, noticed by Brendan, is really fascinating - it implies that there's a "quantum groupoid" associated to electrical circuits, and it implies that our conjectured list of axioms characterizing the category of bond graphs was missing some highly nonobvious relations.

• Daniel Cicala is revisiting Franciscus Rebro's work on the bicategory of cobordisms and will prove it's a symmetric monoidal bicategory.

• Kenny Courser had the smart idea of revisiting Jeffrey Morton and Jamie Vicary's work on Khovanov's categorified Heisenberg algebra and making it rigorous using our new ability to get ahold of symmetric monoidal bicategories, and I realized we can actually do this.

• Adam Yassine seems to have proved that there's a bicategory of symplectic manifolds and cospans whose legs are Poisson fibrations — good for the study of open systems in classical mechanics.

And that's not all! In our Metron project,

• Blake Pollard and John Foley are developing a new framework for search and rescue operations (and many other distributed optimization problems).

• Joseph Moeller created a new algebraic structure generalizing the "operad for communication networks", and I think we can prove this new structure has an elegant category-theoretic description.

It's all great stuff. But these weekly reports are supposed to be about things that have been completed, just to focus your attention on getting things finished. So here are two things like that:

• The math department at U.C. Riverside is hosting the Fall Meeting of the AMS Western Section on Saturday and Sunday, Nov. 4 and 5, 2017. My proposal for a special session on Applied Category Theory has been accepted! I hope you submit proposals for talks — if you're able to come despite the fact that, as usual for such meetings, we have no money. I'll say in a while how you can propose a talk: there will be a webpage where you can do this.

• U. C. Riverside has agreed to be a repository of climate data collected by the Azimuth Backup Project. This means we don't have to figure out how to hold this data permanently. We've raised over $10,000 by now, so we're fine in the short term. Comment Source:13 January 2017: We had a hugely productive meeting on Wednesday and I'm really excited about the new ideas: * The connection between Brandon Coya's work on bond graphs and Ross Street's work on weak bimonoids, noticed by Brendan, is really fascinating - it implies that there's a "quantum groupoid" associated to electrical circuits, and it implies that our conjectured list of axioms characterizing the category of bond graphs was missing some highly nonobvious relations. * Daniel Cicala is revisiting Franciscus Rebro's work on the bicategory of cobordisms and will prove it's a symmetric monoidal bicategory. * Kenny Courser had the smart idea of revisiting Jeffrey Morton and Jamie Vicary's work on Khovanov's categorified Heisenberg algebra and making it rigorous using our new ability to get ahold of symmetric monoidal bicategories, and I realized we can actually do this. * Adam Yassine seems to have proved that there's a bicategory of symplectic manifolds and cospans whose legs are Poisson fibrations &mdash; good for the study of open systems in classical mechanics. And that's not all! In our Metron project, * Blake Pollard and John Foley are developing a new framework for search and rescue operations (and many other distributed optimization problems). * Joseph Moeller created a new algebraic structure generalizing the "operad for communication networks", and I think we can prove this new structure has an elegant category-theoretic description. It's all great stuff. But these weekly reports are supposed to be about things that have been completed, just to focus your attention on getting things finished. So here are two things like that: * The math department at U.C. Riverside is hosting the Fall Meeting of the AMS Western Section on Saturday and Sunday, Nov. 4 and 5, 2017. My proposal for a special session on **Applied Category Theory** has been accepted! I hope you submit proposals for talks &mdash; if you're able to come despite the fact that, as usual for such meetings, we have no money. I'll say in a while how you can propose a talk: there will be a webpage where you can do this. * U. C. Riverside has agreed to be a repository of climate data collected by the Azimuth Backup Project. This means we don't have to figure out how to hold this data permanently. We've raised over$10,000 by now, so we're fine in the short term.
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9.
edited February 2017

21 January 2017:

1) Kenny Courser dealt with the referee's comments on his paper A bicategory of decorated cospans, resubmitted it to Theory and Applications of Categories, and put the new improved version on the arXiv.

2) Daniel Cicala has submitted his paper Spans of cospans to Theory and Applications of Categories. Is that true, Daniel? If not, make it so. Also, it probably makes sense to update the version on the arXiv.

(Kenny and Daniel are now teaming up to write a wonderful paper on bicategories of spans and cospans, including the "maps-of-spans" case already dealt with more generally by Mike, but more importantly the "spans-of-spans" case and "spans-of-cospans" case.)

3) Joseph Moeller has written up the statement of a theorem on generalizations of the operad of communication networks, suitable for inclusion in the paper that Blake is working on for DARPA. This paper is due the day after tomorrow!

4) I've been invited to join another project run by the US Defense Department!

I got an email from Michael A. Smith, a microbiologist who's the director of the Defense Biological Product Assurance Office. These are the people who check whether mysterious white powders showing up in people's mail are actually anthrax... and they also keep track of diseases that suddenly spring up, like Ebola or MIRS. They used to be called the Critical Reagents Program.

Smith is interested in whether modifications of the network of hospitals and laboratories in Africa could help them better keep track of new epidemics that show up on this continent. He read my book with Jacob Biamonte on Petri nets, and he thinks I might able to help. I'll start by listening in to a phone conversation he's having with Gary Kobinger, who helped develop a vaccine for Ebola, and who

developed and pioneered use of small mobile laboratories — a lab in a suitcase, essentially — that have changed the way testing is done during Ebola outbreaks.

I'm already way too busy, but this sounds interesting! Michael Smith said that his higher-ups mainly evaluate him on whether he spends money fast enough. I could certainly help with that... but it would also be cool if network ideas could help combat disease.

5) I arranged to visit the Institute for Scientific Interchange in Turin, Italy during the last week of June. This center is very interested in the mathematical foundations of complex systems, including networks.

I ran a workshop there in May 2015 and the director, Mario Rasetti, said I was welcome to visit any time. I decided to see if this offer was real: I'm visiting the category theorist Marco Grandis in nearby Genoa in mid-June, so I emailed Rasetti and asked if I could visit after that.

It turns out he's been reading our papers with interest! He'd actually like me to visit for a sabbatical or maybe even get some long-term affiliation with this center. I'll find out more in June.

Comment Source:21 January 2017: 1) Kenny Courser dealt with the referee's comments on his paper [A bicategory of decorated cospans](https://arxiv.org/abs/1605.08100), resubmitted it to _Theory and Applications of Categories_, and put the new improved version on the arXiv. 2) Daniel Cicala has submitted his paper [Spans of cospans](https://arxiv.org/abs/1611.07886) to _Theory and Applications of Categories_. Is that true, Daniel? If not, make it so. Also, it probably makes sense to update the version on the arXiv. (Kenny and Daniel are now teaming up to write a wonderful paper on bicategories of spans and cospans, including the "maps-of-spans" case already dealt with more generally by Mike, but more importantly the "spans-of-spans" case and "spans-of-cospans" case.) 3) Joseph Moeller has written up the statement of a theorem on generalizations of the operad of communication networks, suitable for inclusion in the paper that Blake is working on for DARPA. This paper is due the day after tomorrow! 4) I've been invited to join another project run by the US Defense Department! I got an email from [Michael A. Smith](https://www.linkedin.com/in/michael-smith-b6468844), a microbiologist who's the director of the [Defense Biological Product Assurance Office](https://globalbiodefense.com/2017/01/02/dod-seeks/). These are the people who check whether mysterious white powders showing up in people's mail are actually anthrax... and they also keep track of diseases that suddenly spring up, like Ebola or MIRS. They used to be called the Critical Reagents Program. Smith is interested in whether modifications of the network of hospitals and laboratories in Africa could help them better keep track of new epidemics that show up on this continent. He read [my book with Jacob Biamonte on Petri nets](http://math.ucr.edu/home/baez/stoch_stable.pdf), and he thinks I might able to help. I'll start by listening in to a phone conversation he's having with Gary Kobinger, who helped develop a vaccine for Ebola, and who > developed and pioneered use of small mobile laboratories — a lab in a suitcase, essentially — that have changed the way testing is done during Ebola outbreaks. I'm already way too busy, but this sounds interesting! Michael Smith said that his higher-ups mainly evaluate him on whether he spends money fast enough. I could certainly help with that... but it would also be cool if network ideas could help combat disease. 5) I arranged to visit the [Institute for Scientific Interchange](https://en.wikipedia.org/wiki/Institute_for_Scientific_Interchange) in Turin, Italy during the last week of June. This center is very interested in the [mathematical foundations of complex systems](http://www.isi.it/en/research/mathematics-foundation-of-complex-systems), including networks. I ran a workshop there in May 2015 and the director, Mario Rasetti, said I was welcome to visit any time. I decided to see if this offer was real: I'm visiting the category theorist Marco Grandis in nearby Genoa in mid-June, so I emailed Rasetti and asked if I could visit after that. It turns out he's been reading our papers with interest! He'd actually like me to visit for a sabbatical or maybe even get some long-term affiliation with this center. I'll find out more in June. 
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10.

14 February 2017:

1) I gave a talk called Biology as Information Dynamics at a workshop called Biological Complexity: Can it be Quantified? at the Beyond Center at Arizona State University. The last result in my talk is new: it's an improved version of Fisher's fundamental theorem of natural selection, which is more general than the usual version, and phrased in terms of information geometry.

I talked about gene regulatory networks with Sara Walker, who works there. A gene regulatory network is a very simple thing: a finite set of 'genes' with two kinds of arrows from some genes to some other genes: 'express' and 'repress'. It would be nice to study 'open' gene regulatory networks using the decorated cospan formalism. There seems to be a fairly simple semantics for these networks where time goes in integer steps and at each time each gene is either on (expressed) or off (repressed).

I also had some conversations with Jim Crutchfield, who wants Blake Pollard to visit him up at U.C. Davis.

2) Tom Mifflin of Metron said that DARPA likes our work so much that they're starting two new programs related to these ideas. One will be at the Strategic Technology Office, and it will be big. Tom suggested I could get more money for grad students. The other is a small "seedling" program, just $500,000, for Metron to help develop autonomous vehicles for the Navy. 3) Blake noticed that Jason Erbele's paper Categories in control was cited by Dominique Luzeaux in a paper on the category-theoretic foundations of systems engineering. The main interesting thing about this paper is that Lzueaux is the Deputy Director of the Joint Directorate for Networks, Infrastructure and Information Systems, part of the French defense department. It may seem weird that the military is interested in category theory and operads, but it makes sense. They have a lot of money, they're willing to experiment to stay ahead of other countries, and they have huge organizational/strategic problems that involve complex networked systems. Thus, they've traditionally been at the forefront of "systems of systems engineering". Comment Source:14 February 2017: 1) I gave a talk called [Biology as Information Dynamics](http://math.ucr.edu/home/baez/bio_asu/) at a workshop called [Biological Complexity: Can it be Quantified?](https://beyond.asu.edu/workshop/biological-complexity-can-it-be-quantified) at the [Beyond Center](https://beyond.asu.edu/) at Arizona State University. The last result in my talk is new: it's an improved version of Fisher's fundamental theorem of natural selection, which is more general than the usual version, and phrased in terms of information geometry. I talked about gene regulatory networks with Sara Walker, who works there. A gene regulatory network is a very simple thing: a finite set of 'genes' with two kinds of arrows from some genes to some other genes: 'express' and 'repress'. It would be nice to study 'open' gene regulatory networks using the decorated cospan formalism. There seems to be a fairly simple semantics for these networks where time goes in integer steps and at each time each gene is either on (expressed) or off (repressed). I also had some conversations with Jim Crutchfield, who wants Blake Pollard to visit him up at U.C. Davis. 2) Tom Mifflin of Metron said that DARPA likes our work so much that they're starting two new programs related to these ideas. One will be at the Strategic Technology Office, and it will be big. Tom suggested I could get more money for grad students. The other is a small "seedling" program, just$500,000, for Metron to help develop autonomous vehicles for the Navy. 3) Blake noticed that Jason Erbele's paper [Categories in control](http://www.tac.mta.ca/tac/volumes/30/24/30-24abs.html) was cited by [Dominique Luzeaux](https://scholar.google.com/citations?user=8G2BKfEAAAAJ&hl=en) in a paper on the category-theoretic foundations of systems engineering. The main interesting thing about this paper is that Lzueaux is the Deputy Director of the Joint Directorate for Networks, Infrastructure and Information Systems, part of the French defense department. It may seem weird that the military is interested in category theory and operads, but it makes sense. They have a lot of money, they're willing to experiment to stay ahead of other countries, and they have huge organizational/strategic problems that involve complex networked systems. Thus, they've traditionally been at the forefront of "[systems of systems engineering](https://en.wikipedia.org/wiki/System_of_systems_engineering)".
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11.

27 February 2017:

Four pieces of news:

1) Brendan and Brandon made all the required changes to their paper "Corelations are the prop for extraspecial commutative Frobenius monoids", so this paper has now been published by Theory and Applications of Categories. You can see it here:

http://www.tac.mta.ca/tac/index.html#vol32

It's in the same issue as two papers by Voevodsky, inventor of homotopy type theory, along with papers by Clemens Berger, Michael Batanin and Jiri Adamek — all famous category theorists! So, congratulations!

2) Blake applied to give a talk on his work at the American Physical Society March Meeting in New Orleans on March 13-17. They asked him to present a poster. He applied to the Grad Student Association for funding to go on this trip, but it looks like he'll have to foot some of the bill himself. (Sadly, while the Metron project he and I are working on pays him enough money so he doesn't have to be a teaching assistant, it doesn't give us any travel money, and the Grad Student Association gives rather limited funds.)

3) Blake has also gotten an invitation from the famous information theorist Jim Crutchfield to speak about our work at U. C. Davis. I mentioned this earlier, but now it's really come true! I forget when Blake is going up there.

4) Not exactly academic, but: the Azimuth Climate Data Backup Project's Kickstarter campaign has succeeded! Our original goal was $5000. We got$20,427 of donations, and after Kickstarter took its cut we received $18,590.96. I wrote thank-you notes to all 627 contributors, and compiled a list thanking everyone who was okay with having their name made public. We are close to reaching our goal of backing up 40 terabytes of data. The next step will be to put copies in several secure locations. 3 places have volunteered to hold copies: the Princeton math department, a UNESCO center in France, and the U. C. Riverside department of computing and communications. It will take a while to accomplish these transfers. It looks like I'll be interviewed about this tomorrow by Amy Harmon of the New York Times. But reporters are often busy and distracted, so I'll believe it when it happens. Comment Source:27 February 2017: Four pieces of news: 1) Brendan and Brandon made all the required changes to their paper "Corelations are the prop for extraspecial commutative Frobenius monoids", so this paper has now been published by Theory and Applications of Categories. You can see it here: [http://www.tac.mta.ca/tac/index.html#vol32](http://www.tac.mta.ca/tac/index.html#vol32) It's in the same issue as two papers by Voevodsky, inventor of homotopy type theory, along with papers by Clemens Berger, Michael Batanin and Jiri Adamek &mdash; all famous category theorists! So, congratulations! 2) Blake applied to give a talk on his work at the American Physical Society March Meeting in New Orleans on March 13-17. They asked him to present a poster. He applied to the Grad Student Association for funding to go on this trip, but it looks like he'll have to foot some of the bill himself. (Sadly, while the Metron project he and I are working on pays him enough money so he doesn't have to be a teaching assistant, it doesn't give us any travel money, and the Grad Student Association gives rather limited funds.) 3) Blake has also gotten an invitation from the famous information theorist [Jim Crutchfield](http://csc.ucdavis.edu/~chaos/) to speak about our work at U. C. Davis. I mentioned this earlier, but now it's really come true! I forget when Blake is going up there. 4) Not exactly academic, but: the Azimuth Climate Data Backup Project's [Kickstarter campaign](https://www.kickstarter.com/projects/592742410/azimuth-climate-data-backup-project) has succeeded! Our original goal was$5000. We got $20,427 of donations, and after Kickstarter took its cut we received$18,590.96. I wrote thank-you notes to all 627 contributors, and compiled [a list thanking everyone who was okay with having their name made public](https://johncarlosbaez.wordpress.com/2017/02/18/azimuth-backup-project-part-4/). We are close to reaching our goal of backing up 40 terabytes of data. The next step will be to put copies in several secure locations. 3 places have volunteered to hold copies: the Princeton math department, a UNESCO center in France, and the U. C. Riverside department of computing and communications. It will take a while to accomplish these transfers. It looks like I'll be interviewed about this tomorrow by [Amy Harmon](https://www.nytimes.com/by/amy-harmon) of the _New York Times_. But reporters are often busy and distracted, so I'll believe it when it happens.
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12.

John, Congratulations on such a great response at Kickstarter and all the other good news!

Comment Source:John, Congratulations on such a great response at Kickstarter and all the other good news!
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13.

Thanks!

Comment Source:Thanks!
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14.

8 March 2017:

1) Jason Erbele and Daniel Cicala have applied to attend the AMS workshop on homotopy type theory in the “breathtaking mountain setting” of Snowbird Resort in Utah, June 4th to 10th. It's being run by my friends Dan Christensen, Mike Shulman and Emily Riehl along with Chris Kapulkin and Dan Licata (who I don't know so well).

2) Next week Blake Pollard is going to the American Physical Society meeting in New Orleans and presenting a poster on his work on open systems.

3) My book with Jacob Biamonte, Quantum Techniques for Stochastic Processes, seems to have been accepted for publication by World Scientific Press.

4) Less significant, but fun: the Australian science fiction writer Greg Egan and I proved an interesting equation expressing pi in terms of the golden ratio:

Comment Source:8 March 2017: 1) Jason Erbele and Daniel Cicala have applied to attend the AMS workshop on homotopy type theory in the “breathtaking mountain setting” of Snowbird Resort in Utah, June 4th to 10th. It's being run by my friends Dan Christensen, Mike Shulman and Emily Riehl along with Chris Kapulkin and Dan Licata (who I don't know so well). 2) Next week Blake Pollard is going to the American Physical Society meeting in New Orleans and presenting a poster on his work on open systems. 3) My book with Jacob Biamonte, _[Quantum Techniques for Stochastic Processes](http://math.ucr.edu/home/baez/stoch_stable.pdf)_, seems to have been accepted for publication by World Scientific Press. 4) Less significant, but fun: the Australian science fiction writer Greg Egan and I proved an interesting equation expressing pi in terms of the golden ratio: * [Pi and the golden ratio](https://johncarlosbaez.wordpress.com/2017/03/07/pi-and-the-golden-ratio/), _Azimuth_, 7 March 2017. 
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15.
edited March 2017

27 March 2017:

1) On Friday, Blake and John Foley and I finished off two essays for our Complex Adaptive Composition and Design Environment project.

The first is called "Compositional Tasking: an operad-based approach to adaptive behaviors for distributed systems-of-systems and planning under uncertainty." This is a general overview of our plan to use operads to design and "task" (boss around) networks while moving up and down levels of abstraction as desired. I find this really exciting! With luck the folks at Metron will create some software to illustrate these ideas

The second, called "Compositional Tasking", has more of the mathematical details. Joseph played a key role in this by checking that the Grothendieck construction can create the operads we need. I hope we continue to improve this essay and publish it in one or more papers, which I hope to write this summer.

2) Prakash Panangaden, an expert in categories and computer science at McGill University in Montreal, has come out with a paper which takes the category-theoretic characterization of relative entropy that Tobias Fritz and I found and extends it from finite sets to more general measurable spaces (sets with a sigma-algebra of subsets):

Abstract. The inspiration for the present work comes from two recent developments. The first is the beginning of a categorical understanding of Bayesian inversion and learning, the second is a categorical reconstruction of relative entropy. The present paper provides a categorical treatment of entropy in the spirit of Baez and Fritz in the setting of Polish spaces, thus setting the stage to explore the role of entropy in learning.

"Polish spaces" are a nice class of measurable spaces, loved by the analysts who lived in Poland before the Nazis invaded.

3) Prakash has also written a paper about a bicategory where the morphisms are open Markov processes. This is based on a paper that Brendan, Blake and I wrote:

Abstract. We construct bicategories of Markov processes where the objects are input and output sets, the morphisms (one-cells) are Markov processes and the two-cells are simulations. This builds on the work of Baez, Fong and Pollard, who showed that a certain kinds of finite-space continuous-time Markov chain (CTMC) satisfying a detailed-balance condition can be viewed as morphisms in a category. This view allows a compositional description of their CTMCs. Our contribution is to develop a notion of simulation between processes and construct a bicategory where the two-cells are simulation morphisms. Our version is for processes that are essentially probabilistic transition systems with discrete time steps and which do not satisfy a detailed balance condition. We have also extended the theory to continuous space processes.

In short, Prakash is moving in and starting to offer competition in our field of work. A lot of people in computer science respect his work, so they will start to read our stuff and explore similar ideas. This means we can't laze around when it comes to publishing ideas we have... but it's basically good, because it means more people will be inclined to hire my grad students!

Comment Source:27 March 2017: 1) On Friday, Blake and John Foley and I finished off two essays for our [Complex Adaptive Composition and Design Environment](https://johncarlosbaez.wordpress.com/2016/10/02/complex-adaptive-system-design-part-1/) project. The first is called "Compositional Tasking: an operad-based approach to adaptive behaviors for distributed systems-of-systems and planning under uncertainty." This is a general overview of our plan to use operads to design and "task" (boss around) networks while moving up and down levels of abstraction as desired. I find this really exciting! With luck the folks at Metron will create some software to illustrate these ideas The second, called "Compositional Tasking", has more of the mathematical details. Joseph played a key role in this by checking that the Grothendieck construction can create the operads we need. I hope we continue to improve this essay and publish it in one or more papers, which I hope to write this summer. 2) Prakash Panangaden, an expert in categories and computer science at McGill University in Montreal, has come out with a paper which takes the category-theoretic characterization of relative entropy that Tobias Fritz and I found and extends it from finite sets to more general measurable spaces (sets with a sigma-algebra of subsets): > **Abstract**. The inspiration for the present work comes from two recent developments. The first is the beginning of a categorical understanding of Bayesian inversion and learning, the second is a categorical reconstruction of relative entropy. The present paper provides a categorical treatment of entropy in the spirit of Baez and Fritz in the setting of Polish spaces, thus setting the stage to explore the role of entropy in learning. "Polish spaces" are a nice class of measurable spaces, loved by the analysts who lived in Poland before the Nazis invaded. 3) Prakash has also written a paper about a bicategory where the morphisms are open Markov processes. This is based on a paper that Brendan, Blake and I wrote: > **Abstract**. We construct bicategories of Markov processes where the objects are input and output sets, the morphisms (one-cells) are Markov processes and the two-cells are simulations. This builds on the work of Baez, Fong and Pollard, who showed that a certain kinds of finite-space continuous-time Markov chain (CTMC) satisfying a detailed-balance condition can be viewed as morphisms in a category. This view allows a compositional description of their CTMCs. Our contribution is to develop a notion of simulation between processes and construct a bicategory where the two-cells are simulation morphisms. Our version is for processes that are essentially probabilistic transition systems with discrete time steps and which do not satisfy a detailed balance condition. We have also extended the theory to continuous space processes. In short, Prakash is moving in and starting to offer competition in our field of work. A lot of people in computer science respect his work, so they will start to read our stuff and explore similar ideas. This means we can't laze around when it comes to publishing ideas we have... but it's basically good, because it means more people will be inclined to hire my grad students! 
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16.

John, congratulations to you and your colleagues/students for inspiring others with your work!

Comment Source:John, congratulations to you and your colleagues/students for inspiring others with your work!
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17.

Thanks!

Comment Source:Thanks!
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18.
edited May 2017

5 April 2017:

1) Gheorghe Craciun visited UCR and gave a talk today on his proof of the Global Attractor Conjecture, 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 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 and A universal construction for (co)relations. I need to blog about these!

4) Brendan also gave an expository talk about "The mathematics of system composition" at 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 and Representing operational semantics with enriched Lawvere theories.

6) My student Daniel Cicala got invited to the American Mathematical Society conference on Homotopy Type Theory that will take place in Snowbird, Utah on June 4-10.

Comment Source: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. 
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19.

24 April 2017:

1) This week Blake and I visited Metron Scientific Solutions. I only visited for a few hours, but Blake stayed for several days, including a hackathon where the Metron team tried to solve a search and rescue problem posed by DARPA!

One thing I did during my short stay was try to sell people on the vision of using operads to design systems 'a bit at a time'. Here 'a bit at a time' is meant in two ways. The basic idea is that a 'system' is an element of some algebra $A$ of some operad $O$. Then:

a) We can design small systems and stick them together using the operations of $O$ to get bigger systems, and

b) We can design systems at a high level of abstraction (meaning: not much detail) and then move to a lower level of abstraction (meaning: add extra details) with the help of a map of operads $O' \to O$. We do this by starting with an element of some algebra $A$ of $O$, and then choosing a way to 'lift' it to an element of some algebra $A'$ of $O'$. Here the primed guys are the ones with more detail.

The second point here is subtler than the first and I'm not really trying to explain it here, so don't feel bad if it doesn't make enough sense!

There were a lot of interesting discussions after I left. Blake summarized them for me... but very very briefly, it seems that:

a) we need to think harder about how to model "levels of abstraction", because this phrase means several different things,

b) we need to think more about how our "operads of communication networks" are connected to Spivak's "operad of wiring diagrams",

c) we should continue thinking about Petri nets. The operad of wiring diagrams has an algebra whose elements are open Petri nets. These have a bit of computational power, at least if we equip the Petri nets with suitable bells and whistles. Thus, we can use them to model many real-world gadgets, which may be handy as we move forwards in this project.

Comment Source:24 April 2017: 1) This week Blake and I visited Metron Scientific Solutions. I only visited for a few hours, but Blake stayed for several days, including a hackathon where the Metron team tried to solve a search and rescue problem posed by DARPA! One thing I did during my short stay was try to sell people on the vision of using operads to design systems 'a bit at a time'. Here 'a bit at a time' is meant in two ways. The basic idea is that a 'system' is an element of some algebra $A$ of some operad $O$. Then: a) We can design small systems and stick them together using the operations of $O$ to get bigger systems, and b) We can design systems at a high level of abstraction (meaning: not much detail) and then move to a lower level of abstraction (meaning: add extra details) with the help of a map of operads $O' \to O$. We do this by starting with an element of some algebra $A$ of $O$, and then choosing a way to 'lift' it to an element of some algebra $A'$ of $O'$. Here the primed guys are the ones with more detail. The second point here is subtler than the first and I'm not really trying to explain it here, so don't feel bad if it doesn't make enough sense! There were a lot of interesting discussions after I left. Blake summarized them for me... but very very briefly, it seems that: a) we need to think harder about how to model "levels of abstraction", because this phrase means several different things, b) we need to think more about how our "operads of communication networks" are connected to Spivak's "operad of wiring diagrams", c) we should continue thinking about Petri nets. The operad of wiring diagrams has an algebra whose elements are open Petri nets. These have a bit of computational power, at least if we equip the Petri nets with suitable bells and whistles. Thus, we can use them to model many real-world gadgets, which may be handy as we move forwards in this project. 
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20.

28 April 2017:

1) Kenny Courser passed his oral exam! He gave a talk called A bicategory of decorated cospans, based on his paper with the same title. He survived my questions and also the fact that two members of committee didn't remember to come until he went and grabbed them. (One them was me.)

Congratulations, Kenny!

2) I gave a talk at the Stanford Complexity Group, called Biology as information dynamics. You can see the slides by clicking on the link, and you can also see a video here.

It went a lot better than my similar talk Arizona State University, probably because this audience was more interested in the subject, I covered more ground, and I was more confident.

Marc Harper attended - he came up with some of the math I discussed, and now he's working at Google. So did Vaughn Pratt - the computer scientist who helped come up with Pratt certificates and the Knuth-Morris-Pratt algorithm. He used to be very active on the category theory mailing list, but not much lately.

3) Daniel Cicala put a paper on the arXiv:

Abstract. This paper presents a symmetric monoidal and compact closed bicategory that categorifies the zx-calculus developed by Coecke and Duncan. The 1-cells in this bicategory are certain graph morphisms that correspond to the string diagrams of the zx-calculus, while the 2-cells are rewrite rules.

He is submitting this to CALCO, the Conference on Algebra and Coalgebra in Computer Science. After he put it on the arXiv, Duncan asked him to submit it to QPL, the conference on Quantum Physics and Logic run by Duncan, Coecke and others. (Even I am involved in it, slightly, and Jason Erbele spoke there in 2015.) Luckily he can submit an "extended abstract" to QPL and have the best of both worlds.

Comment Source:28 April 2017: 1) Kenny Courser passed his oral exam! He gave a talk called A bicategory of decorated cospans, based on his paper with the same title. He survived my questions and also the fact that two members of committee didn't remember to come until he went and grabbed them. (One them was me.) Congratulations, Kenny! 2) I gave a talk at the Stanford Complexity Group, called [Biology as information dynamics](http://math.ucr.edu/home/baez/bio_asu/). You can see the slides by clicking on the link, and you can also [see a video here](https://www.youtube.com/watch?v=IKetDJof8pk). It went a lot better than my similar talk Arizona State University, probably because this audience was more interested in the subject, I covered more ground, and I was more confident. Marc Harper attended - he came up with some of the math I discussed, and now he's working at Google. So did Vaughn Pratt - the computer scientist who helped come up with Pratt certificates and the Knuth-Morris-Pratt algorithm. He used to be very active on the category theory mailing list, but not much lately. 3) Daniel Cicala put a paper on the arXiv: * [Categorifying the zx-calculus](https://arxiv.org/abs/1704.07034). > **Abstract.** This paper presents a symmetric monoidal and compact closed bicategory that categorifies the zx-calculus developed by Coecke and Duncan. The 1-cells in this bicategory are certain graph morphisms that correspond to the string diagrams of the zx-calculus, while the 2-cells are rewrite rules. He is submitting this to [CALCO](http://coalg.org/mfps-calco2017/), the Conference on Algebra and Coalgebra in Computer Science. After he put it on the arXiv, Duncan asked him to submit it to [QPL](http://qpl.science.ru.nl/), the conference on Quantum Physics and Logic run by Duncan, Coecke and others. (Even I am involved in it, slightly, and Jason Erbele spoke there in 2015.) Luckily he can submit an "extended abstract" to QPL and have the best of both worlds.
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21.

3 May 2017:

This week's progress is all about the virtues of initiative: finding opportunities and seizing them.

1) Blake found an interesting ad on MathJobs for a research position at the Bay Area Complexity Institute. The institute is so new that it doesn't even exist yet, but the job description looks like it was written specially for Blake:

You must have a working knowledge of graduate-level category theory, measure theory, and probability theory. Bonus points if you are experienced with any of: statistical mechanics, dynamical systems, Markov chains, various theories and models of computation, organismal evolution, or complexity in any formal setting. You must also enjoy research and writing, and have the personality traits of a theory builder rather than a problem solver, but have the skills of both. Perhaps most importantly, you should be excited and passionate about working on a small team to pursue the connection between information-theoretic complexity, thermodynamics and entropy, and the evolution of complexity in cosmology and living systems.

He applied, and they sound interested! He's going to meet the people running this institute on May 11th, right after his talk to Crutchfield's group at U.C. Davis.

Moral: look around for jobs. Apply for jobs that sound cool.

2) Jason had been invited by Tobias Fritz to a conference at the Perimeter Institute, in Canada. That's where I used to hang out when I worked on quantum gravity - and indeed, my former student Derek Wise is giving a talk at this conference about his wonderful work on Hopf algebras and quantum gauge theories!

One problem: Tobias didn't offer him travel money. An invitation without money is a sad thing. But Jason hustled and overcame this problem:

I initially asked Tobias Fritz and his group if I could get any travel funds through the Perimeter Institute. The answer was a fairly definite "probably not." I tried various avenues at Victor Valley College, where I am currently teaching, all of which came back No. So I bought my plane tickets, reserved a hotel and rental car, etc. and informed Lucy Zhang, the person in Tobias' group with whom I have been primarily in contact. Two days later I had a sponsor: Daniel Gottesman. So I cancelled my hotel and rental car reservations, the cost of the plane tickets will be reimbursed, the entry fee is waived, and more. I think the only thing that isn't covered is parking at LAX. There is still some time, so I am looking into alternatives to that.

Daniel Gottesman is a bigshot in quantum computation at the Perimeter Institute.

Moral: it pays to ask for help - you just might get it!

3) As for me, I'm not doing anything useful - just hanging out in Hong Kong, checking out temples. But I got here because I wrote about Guowu Meng's amazing work connecting special relativity to Newton's inverse square force law... and he's here in Hong Kong, so he invited me here!

Moral: blog about cool stuff. If you explain it well, people will pay attention.

Comment Source:3 May 2017: This week's progress is all about the virtues of initiative: finding opportunities and seizing them. 1) Blake found an interesting ad on MathJobs for a [research position at the Bay Area Complexity Institute](https://www.mathjobs.org/jobs/jobs/10174). The institute is so new that it doesn't even exist yet, but the job description looks like it was written specially for Blake: > You must have a working knowledge of graduate-level category theory, measure theory, and probability theory. Bonus points if you are experienced with any of: statistical mechanics, dynamical systems, Markov chains, various theories and models of computation, organismal evolution, or complexity in any formal setting. You must also enjoy research and writing, and have the personality traits of a theory builder rather than a problem solver, but have the skills of both. Perhaps most importantly, you should be excited and passionate about working on a small team to pursue the connection between information-theoretic complexity, thermodynamics and entropy, and the evolution of complexity in cosmology and living systems. He applied, and they sound interested! He's going to meet the people running this institute on May 11th, right after his talk to Crutchfield's group at U.C. Davis. **Moral: look around for jobs. Apply for jobs that sound cool.** 2) Jason had been invited by Tobias Fritz to a conference at the Perimeter Institute, in Canada. That's where I used to hang out when I worked on quantum gravity - and indeed, my former student Derek Wise is giving a talk at this conference about his [wonderful work on Hopf algebras and quantum gauge theories](https://arxiv.org/abs/1512.03966)! One problem: Tobias didn't offer him travel money. An invitation without money is a sad thing. But Jason hustled and overcame this problem: > I initially asked Tobias Fritz and his group if I could get any travel funds through the Perimeter Institute. The answer was a fairly definite "probably not." I tried various avenues at Victor Valley College, where I am currently teaching, all of which came back No. So I bought my plane tickets, reserved a hotel and rental car, etc. and informed Lucy Zhang, the person in Tobias' group with whom I have been primarily in contact. Two days later I had a sponsor: Daniel Gottesman. So I cancelled my hotel and rental car reservations, the cost of the plane tickets will be reimbursed, the entry fee is waived, and more. I think the only thing that isn't covered is parking at LAX. There is still some time, so I am looking into alternatives to that. Daniel Gottesman is a bigshot in quantum computation at the Perimeter Institute. **Moral: it pays to ask for help - you just might get it!** 3) As for me, I'm not doing anything useful - just hanging out in Hong Kong, checking out temples. But I got here because I wrote about [Guowu Meng's amazing work connecting special relativity to Newton's inverse square force law](http://math.ucr.edu/home/baez/gravitational.html)... and he's here in Hong Kong, so he invited me here! **Moral: blog about cool stuff. If you explain it well, people will pay attention.** 
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22.

6 May 2017:

1) You may recall that Daniel Cicala got into the Kan Extension Seminar, which is an advanced online course on category theory run by Emily Riehl, Alexander Campbell and our very own Brendan Fong. Participants read famous papers on category theory, discuss them and blog about them. Daniel recently blogged about the paper he read:

2) Blake got offered a 3-month internship at the Princeton branch of Siemens, a big engineering firm! The advertisement was pretty interesting:

PhD Intern – Next-Generation Engineering with Category Theory and Sheaves

Responsibilities

• Develop concepts for unifying different engineering formalisms that describe different domains and aspects of complex systems using Category Theory.
• Implement the developed concepts in software prototypes to demonstrate novel languages and algorithms to represent and extract knowledge across engineering disciplines.
• Investigate the use of Sheaves for the creation of hybrid engineering models that combine data-driven and physics-based representations.
• Participate in the preparation of scientific publications.

Required Knowledge/Skills, Education, and Experience

• PhD student in Mathematics or Physics.
• Programming skills in Python and/or JavaScript and ability to quickly prototype in these languages.
• Good written and verbal communication skills in English are required, as well as excellent interpersonal skills in multi-cultural environments.
• Team player who can also be independent, prioritize work and thrive in a fast-paced dynamic environment.
• The successful candidate must be able to work with controlled technology in accordance with US Export Control Law.

The guy in charge is named Arquimedes Canedo, and he seems potentially interested in hiring Blake or other applied category theory people (hint hint!) for a longer-term project.

Comment Source:6 May 2017: 1) You may recall that Daniel Cicala got into the [Kan Extension Seminar](https://golem.ph.utexas.edu/category/2016/10/the_kan_extension_seminar_retu.html), which is an advanced online course on category theory run by Emily Riehl, Alexander Campbell and our very own Brendan Fong. Participants read famous papers on category theory, discuss them and blog about them. Daniel recently blogged about the paper he read: * [A discussion on notions of Lawvere theory](https://golem.ph.utexas.edu/category/2017/05/a_discussion_on_notions_of_law.html). 2) Blake got offered a 3-month internship at the Princeton branch of Siemens, a big engineering firm! The [advertisement](https://jobs.siemens-info.com/jobs/207833/PhD+Intern+%E2%80%93+Next-Generation+Engineering+with+Category+Theory+and+Sheaves?lang=en-US) was pretty interesting: > **PhD Intern – Next-Generation Engineering with Category Theory and Sheaves** > **Responsibilities** > * Develop concepts for unifying different engineering formalisms that describe different domains and aspects of complex systems using Category Theory. > * Implement the developed concepts in software prototypes to demonstrate novel languages and algorithms to represent and extract knowledge across engineering disciplines. > * Investigate the use of Sheaves for the creation of hybrid engineering models that combine data-driven and physics-based representations. > * Participate in the preparation of scientific publications. > **Required Knowledge/Skills, Education, and Experience** > * PhD student in Mathematics or Physics. > * Programming skills in Python and/or JavaScript and ability to quickly prototype in these languages. > * Good written and verbal communication skills in English are required, as well as excellent interpersonal skills in multi-cultural environments. > * Team player who can also be independent, prioritize work and thrive in a fast-paced dynamic environment. > * The successful candidate must be able to work with controlled technology in accordance with US Export Control Law. The guy in charge is named [Arquimedes Canedo](https://scholar.google.com/citations?user=r2zo9HQAAAAJ&hl=en), and he seems potentially interested in hiring Blake or other applied category theory people (hint hint!) for a longer-term project.
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23.

That first paper by Canedo is context-modeling, which is something we worked on via a DARPA project a few years ago

https://www.researchgate.net/publication/283579370_C2M2L_Final_Report

Basically covering the same territory and I recognize all the players

Comment Source:That first paper by Canedo is context-modeling, which is something we worked on via a DARPA project a few years ago https://www.researchgate.net/publication/283579370_C2M2L_Final_Report Basically covering the same territory and I recognize all the players 
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24.
edited June 2017

Interesting, WebHubTel! I will tell my student Blake Pollard about this, since he is going to do that 3-month internship with Canedo this summer.

Comment Source:Interesting, WebHubTel! I will tell my student Blake Pollard about this, since he is going to do that 3-month internship with Canedo this summer.
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25.

28 May 2017:

Lots of good news:

1) Brandon Coya got a "dissertation year fellowship" which offers him $7200 of funding for one quarter next year. All of you UCR grad students should apply for this at the appropriate time. 2) Blake also got one! He'll use it this summer. 3) I gave a plenary talk at the Hong Kong Mathematical Society, on the dodecahedron, the icosahedron and E8. Check it out - it's fun! I'm coming back to the US now. Comment Source:28 May 2017: Lots of good news: 1) Brandon Coya got a "dissertation year fellowship" which offers him$7200 of funding for one quarter next year. All of you UCR grad students should apply for this at the appropriate time. 2) Blake also got one! He'll use it this summer. 3) I gave a plenary talk at the Hong Kong Mathematical Society, on [the dodecahedron, the icosahedron and E8](https://johncarlosbaez.wordpress.com/2017/05/16/the-dodecahedron-the-icosahedron-and-e8/). Check it out - it's fun! I'm coming back to the US now.
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26.
edited June 2017

2 June 2017:

More good news:

1) Adam Yassine passed his oral exam, speaking on "Open systems in classical mechanics".

2) Blake Pollard passed his thesis defense, speaking on "Open Markov processes and reaction networks".

Comment Source:2 June 2017: More good news: 1) Adam Yassine passed his oral exam, speaking on "Open systems in classical mechanics". 2) Blake Pollard passed his thesis defense, speaking on "[Open Markov processes and reaction networks](http://math.ucr.edu/home/baez/thesis_defense_pollard.pdf)". 
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27.

9 June 2017:

More good news:

1) Kenny Courser's paper A bicategory of decorated cospans got accepted for publication in Theory and Applications of Categories!

He had to go through a couple rounds of revisions demanded by the referee. In the last round, the referee demanded that Kenny explain the difference between his use of double categories and Lerman and Spivak's use of double categories to study dynamical systems. Kenny wrote and explanation and sent a new version of his paper to the editor. He didn't hear back for many weeks. Finally, it turned out that the editor had never sent the new version to the referee! When Kenny discovered this, the matter was quickly resolved.

Moral: if you sent an email to a journal editor and don't hear back, it's possible they haven't read your email, or forgot to do anything about it. Don't be too shy to politely ask them what's up.

2) Daniel Cicala's paper on Categorifying the zx-calculus, rejected by CALCO, was accepted by QPL.

In computer science conference papers are considered more important than papers in journals - the opposite from math. It really helps your career to get papers accepted by important conferences. CALCO is the Category on Algebra and Coalgebra in Computer Science. QPL is Quantum Physics and Logic. Daniel's paper is a good fit for QPL since that conference is organized by people like Bob Coecke and Ross Duncan, who helped develop the zx-calculus (a diagrammatic method for dealing with certain categories that come up in quantum computation). So, if you write any sort of paper on diagrammatic methods for dealing with categories that show up in physics or engineering - signal flow diagrams, bond graphs, electrical circuits, etc. - you should consider submitting it to QPL. It comes around once every summer, but papers can be submitted earlier.

(I helped referee a bunch of papers for QPL, but I'm not allowed to referee papers by my own students.)

3) Daniel Cicala is now at Snowbird, Utah, learning about homotopy type theory.

It turns out two of the organizers of this workshop are friends of mine - Mike Shulman and Dan Christensen. Furthermore, they helped me answer a question that came up in a paper Daniel and Kenny are writing: is any functor from a groupoid to itself equivalent to an isofibration? It turns out the answer is yes and that this was not previously known (at least not by them).

Comment Source:9 June 2017: More good news: 1) Kenny Courser's paper [A bicategory of decorated cospans](https://arxiv.org/abs/1605.08100) got accepted for publication in _Theory and Applications of Categories_! He had to go through a couple rounds of revisions demanded by the referee. In the last round, the referee demanded that Kenny explain the difference between his use of double categories and Lerman and Spivak's use of double categories to study dynamical systems. Kenny wrote and explanation and sent a new version of his paper to the editor. He didn't hear back for many weeks. Finally, it turned out that the editor had never sent the new version to the referee! When Kenny discovered this, the matter was quickly resolved. Moral: if you sent an email to a journal editor and don't hear back, it's possible they haven't read your email, or forgot to do anything about it. Don't be too shy to politely ask them what's up. 2) Daniel Cicala's paper on [Categorifying the zx-calculus](https://arxiv.org/abs/1704.07034), rejected by CALCO, was accepted by QPL. In computer science conference papers are considered more important than papers in journals - the opposite from math. It really helps your career to get papers accepted by important conferences. [CALCO](http://coalg.org/mfps-calco2017/cfp-calco.html) is the Category on Algebra and Coalgebra in Computer Science. [QPL](http://qpl.science.ru.nl/) is Quantum Physics and Logic. Daniel's paper is a good fit for QPL since that conference is organized by people like Bob Coecke and Ross Duncan, who helped develop the zx-calculus (a diagrammatic method for dealing with certain categories that come up in quantum computation). So, if you write any sort of paper on diagrammatic methods for dealing with categories that show up in physics or engineering - signal flow diagrams, bond graphs, electrical circuits, etc. - you should consider submitting it to QPL. It comes around once every summer, but papers can be submitted earlier. (I helped referee a bunch of papers for QPL, but I'm not allowed to referee papers by my own students.) 3) Daniel Cicala is now at Snowbird, Utah, learning about [homotopy type theory](https://homotopytypetheory.org/2016/10/04/hott-mrc/). It turns out two of the organizers of this workshop are friends of mine - Mike Shulman and Dan Christensen. Furthermore, they helped me answer a question that came up in a paper Daniel and Kenny are writing: is any functor from a groupoid to itself equivalent to an isofibration? It turns out the answer is yes and that this was not previously known (at least not by them). 
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28.

14 June 2017:

1) It looks like we'll be having a new member on our team this fall! Christina Vasilakopoulou is being offered a visiting assistant professorship at UCR, and seems likely to accept. She was a student of Martin Hyland, the category theorist at Cambridge University who also advised Tom Leinster, Eugenia Cheng and Aaron Lauda (who worked with me when he was an undergrad at UCR). Since then she's worked with various people including David Spivak. She's done a mix of "pure" category theory (applied to algebra, actually) and "applied" category theory such as this:

I'm sure she'll bring a lot of energy and new ideas to our team.

2) Blake and I gave talks here:

You can see my talk slides here:

There are a lot of interesting people here, including Luca Peliti, who talked about an analogy I'm really interested in:

• Luca Peliti, On the value of information in gambling, evolution and thermodynamics.

Abstract. The connection between the information value of a message and capital gain was made by Kelly in 1953. In 1965 Kimura tried to evaluate the rate of information intake by a population undergoing Darwinian evolution by equating it with the substitutional load. Recently, the analogy between Kelly’s scheme and work extraction was pointed out in the context of stochastic thermodynamics. I shall try to connect these threads, highlighting analogies and differences between the meaning of information and its value in the different contexts.

and Hong Qian - Blake kept running into his work while working on his thesis:

• Hong Qian, The mathematical foundation of a landscape theory for living matter and life.

Abstract. The physicists’ notion of energy is derived from Newtonian mechanics. The theory of thermodynamics is developed based on that notion, and the realization of mechanical energy dissipation in terms of heat. Since the work of L. Boltzmann, who trusted that atoms were real as early as in 1884, the heat became intimately related to the stochastic motion of the invisible atoms and molecules. In this talk, starting from a stochastic description of a class of rather general dynamics that is not limited to mechanics, we show a notion of energy can be derived mathematically, in the limit of vanishing stochasticity, based on the Kullback-Leibler divergence, or relative entropy associated with the stochastic, Markov processes. With the emergent notion of an energy function, e.g., “landscape”, a mathematical structure inherent to the stochastic dynamics, which is akin to thermodynamics, is revealed. This analysis implies that an abstract “mathematicothermodynamics” structure exists, and can be formulated, for dynamics of complex systems independent of classical thermal physics, for example, in ecology.

I've gotten a bunch of ideas for new projects, which I'm listing in a notebook.

Comment Source:14 June 2017: 1) It looks like we'll be having a new member on our team this fall! [Christina Vasilakopoulou](https://arxiv.org/find/math/1/au:+Vasilakopoulou_C/0/1/0/all/0/1) is being offered a visiting assistant professorship at UCR, and seems likely to accept. She was a student of Martin Hyland, the category theorist at Cambridge University who also advised Tom Leinster, Eugenia Cheng and Aaron Lauda (who worked with me when he was an undergrad at UCR). Since then she's worked with various people including David Spivak. She's done a mix of "pure" category theory (applied to algebra, actually) and "applied" category theory such as this: * David I. Spivak, Christina Vasilakopoulou, Patrick Schultz, [Dynamical systems and sheaves](https://arxiv.org/abs/1609.08086). * Patrick Schultz, David I. Spivak, Christina Vasilakopoulou, Ryan Wisnesky, [Algebraic databases](https://arxiv.org/abs/1602.03501). I'm sure she'll bring a lot of energy and new ideas to our team. 2) Blake and I gave talks here: * [Dynamics, Thermodynamics and Information Processing in Chemical Networks](https://luxcnworkshop.wordpress.com/), 13-16 June 2017, Complex Systems and Statistical Mechanics Group, University of Luxembourg. Organized by Massimiliano Esposito and Matteo Polettini. You can see my talk slides here: * [The mathematics of open reaction networks](http://math.ucr.edu/home/baez/networks_luxembourg/open_reaction_networks_web.pdf). There are a lot of interesting people here, including Luca Peliti, who talked about an analogy I'm really interested in: * [Luca Peliti](http://www.peliti.org/), On the value of information in gambling, evolution and thermodynamics. > **Abstract.** The connection between the information value of a message and capital gain was made by Kelly in 1953. In 1965 Kimura tried to evaluate the rate of information intake by a population undergoing Darwinian evolution by equating it with the substitutional load. Recently, the analogy between Kelly’s scheme and work extraction was pointed out in the context of stochastic thermodynamics. I shall try to connect these threads, highlighting analogies and differences between the meaning of information and its value in the different contexts. and Hong Qian - Blake kept running into his work while working on his thesis: * [Hong Qian](https://arxiv.org/find/math-ph/1/au:+Qian_H/0/1/0/all/0/1), The mathematical foundation of a landscape theory for living matter and life. > **Abstract.** The physicists’ notion of energy is derived from Newtonian mechanics. The theory of thermodynamics is developed based on that notion, and the realization of mechanical energy dissipation in terms of heat. Since the work of L. Boltzmann, who trusted that atoms were real as early as in 1884, the heat became intimately related to the stochastic motion of the invisible atoms and molecules. In this talk, starting from a stochastic description of a class of rather general dynamics that is not limited to mechanics, we show a notion of energy can be derived mathematically, in the limit of vanishing stochasticity, based on the Kullback-Leibler divergence, or relative entropy associated with the stochastic, Markov processes. With the emergent notion of an energy function, e.g., “landscape”, a mathematical structure inherent to the stochastic dynamics, which is akin to thermodynamics, is revealed. This analysis implies that an abstract “mathematicothermodynamics” structure exists, and can be formulated, for dynamics of complex systems independent of classical thermal physics, for example, in ecology. I've gotten a bunch of ideas for new projects, which I'm listing in a notebook.
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29.

22 June 2017:

Here is this week's progress, as far as I know:

1) I'm visiting the University of Genoa. It's home to 3 well-known category theorists:

• Marco Grandis (who works on double and n-tuple categories),
• Giuseppe Rosolini (who does functorial semantics for programming languages) and
• Eugenio Moggi (the guy who introduced monads in computer science - a big deal in Haskell and some other languages).

Marco Grandis told me something very interesting. His advisor, Gabriele Darbo, introduced a "theory of devices" in 1970, based on the category of corelations! He applied it to linear electrical circuits using the "add currents, duplicate voltages" rule. All this is VERY similar to Brendan's thesis work and also some of my work with Blake. But it's also different!

Yesterday I summarized the ideas here:

I haven't had time yet to think hard about how his formalism connects to ours. Darbo's work was mostly ignored, perhaps because it's all in Italian. I think we can still learn something from it, even though we've gone further.

2) Today I gave a general talk for the math and science faculty here at Genoa:

3) I also gave a talk to the math department:

Comment Source:22 June 2017: Here is this week's progress, as far as I know: 1) I'm visiting the University of Genoa. It's home to 3 well-known category theorists: * Marco Grandis (who works on double and n-tuple categories), * Giuseppe Rosolini (who does functorial semantics for programming languages) and * Eugenio Moggi (the guy who introduced monads in computer science - a big deal in Haskell and some other languages). Marco Grandis told me something very interesting. His advisor, Gabriele Darbo, introduced a "theory of devices" in 1970, based on the category of corelations! He applied it to linear electrical circuits using the "add currents, duplicate voltages" rule. All this is VERY similar to Brendan's thesis work and also some of my work with Blake. But it's also different! Yesterday I summarized the ideas here: * [The theory of devices](https://johncarlosbaez.wordpress.com/2017/06/20/the-theory-of-devices/). I haven't had time yet to think hard about how his formalism connects to ours. Darbo's work was mostly ignored, perhaps because it's all in Italian. I think we can still learn something from it, even though we've gone further. 2) Today I gave a general talk for the math and science faculty here at Genoa: * [Tales of the dodecahedron: from Pythagoras to Plato to Poincar&eacute;](http://math.ucr.edu/home/baez/dodecahedron/genoa_talk/1.html). 3) I also gave a talk to the math department: * [Applied category theory](http://math.ucr.edu/home/baez/control/applied_category_theory.pdf). 
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30.
edited July 2017

24 June 2017:

1) Daniel Cicala submitted an abstract for my AMS special session on Applied Category Theory:

• A bicategorical syntax for pure state qubit quantum mechanics

Abstract. We begin by constructing a framework used to study open networks modeled by graphs and their rewritings. This consists of a symmetric monoidal compact closed bicategory built by combining spans and cospans inside a topos. Into this bicategorical framework, we fit Coecke and Duncan’s zx-calculus, a graphical language used to reason about pure state qubit quantum mechanics. After viewing the zx-calculus through this lens, we highlight several benefits over the 1-categorical approach: the presence of a symmetric monoidal compact closed structure and a better representation of rewriting information. (Received June 22, 2017)

2) So did Brendan Fong:

• Black boxes and decorated corelations

Abstract. Consider an electric circuit. Suppose this circuit has chosen terminals, which we may connect with the terminals of another circuit. That is to say, consider that we may compose two circuits to obtain another circuit. This suggests we might model circuits as morphisms in a category. Next, suppose I want to compose a circuit with a resistor of resistance 2 ohms. If I have no such resistors, I could substitute with a pair of 1 ohm resistors in series. This suggests a coarser representation of circuits, one that keeps track of only how the circuit behaves, and not their [its] constituent components. In this talk I shall introduce decorated corelations as a tool for constructing categories that model circuits, and constructing ‘black box’ functors that shift between these models. This framework is applicable not only to circuits, but to open systems in general. (Received June 23, 2017)

Comment Source:24 June 2017: 1) Daniel Cicala submitted an abstract for my AMS special session on Applied Category Theory: * A bicategorical syntax for pure state qubit quantum mechanics > **Abstract.** We begin by constructing a framework used to study open networks modeled by graphs and their rewritings. This consists of a symmetric monoidal compact closed bicategory built by combining spans and cospans inside a topos. Into this bicategorical framework, we fit Coecke and Duncan’s zx-calculus, a graphical language used to reason about pure state qubit quantum mechanics. After viewing the zx-calculus through this lens, we highlight several benefits over the 1-categorical approach: the presence of a symmetric monoidal compact closed structure and a better representation of rewriting information. (Received June 22, 2017) 2) So did Brendan Fong: * Black boxes and decorated corelations > **Abstract.** Consider an electric circuit. Suppose this circuit has chosen terminals, which we may connect with the terminals of another circuit. That is to say, consider that we may compose two circuits to obtain another circuit. This suggests we might model circuits as morphisms in a category. Next, suppose I want to compose a circuit with a resistor of resistance 2 ohms. If I have no such resistors, I could substitute with a pair of 1 ohm resistors in series. This suggests a coarser representation of circuits, one that keeps track of only how the circuit behaves, and not their [its] constituent components. In this talk I shall introduce decorated corelations as a tool for constructing categories that model circuits, and constructing ‘black box’ functors that shift between these models. This framework is applicable not only to circuits, but to open systems in general. (Received June 23, 2017) 
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31.
edited July 2017

27 June 2017:

More abstracts for our AMS special session on Applied Category Theory on November 4-5.

1) Kenny Courser:

• A bicategory of coarse-grained Markov processes.

Abstract. If C is a category with finite colimits, D is a symmetric monoidal category and F is a lax symmetric monoidal functor from C to D, Fong has developed a theory of F-decorated cospans which are suitable for representing open dynamical systems. Indeed, Fong has shown the existence of a symmetric monoidal category consisting of objects of C and isomorphism classes of F-decorated cospans in C as morphisms. One application of this result is given by Baez, Fong and Pollard in which they construct a symmetric monoidal category whose morphisms are given by isomorphism classes of open Markov processes. Using a result of Shulman, we present a symmetric monoidal bicategory consisting of finite sets as objects,open Markov processes as morphisms and coarse-grainings of open Markov processes as 2-morphisms. (Received June 25, 2017)

Comment Source:27 June 2017: More abstracts for our AMS special session on Applied Category Theory on November 4-5. 1) Kenny Courser: * A bicategory of coarse-grained Markov processes. > **Abstract.** If C is a category with finite colimits, D is a symmetric monoidal category and F is a lax symmetric monoidal functor from C to D, Fong has developed a theory of F-decorated cospans which are suitable for representing open dynamical systems. Indeed, Fong has shown the existence of a symmetric monoidal category consisting of objects of C and isomorphism classes of F-decorated cospans in C as morphisms. One application of this result is given by Baez, Fong and Pollard in which they construct a symmetric monoidal category whose morphisms are given by isomorphism classes of open Markov processes. Using a result of Shulman, we present a symmetric monoidal bicategory consisting of finite sets as objects,open Markov processes as morphisms and coarse-grainings of open Markov processes as 2-morphisms. (Received June 25, 2017) 2) Adam Yassine: * Open systems in classical mechanics > **Abstract.** Using the framework of category theory, we formalize the heuristic principles that physicists employ in constructing the Hamiltonians for open classical systems as sums of Hamiltonians of subsystems. First we construct a category where the objects are symplectic manifolds and the morphisms are spans whose legs are surjective Poisson maps. Using a slight variant of Fong’s theory of ”decorated” cospans, we then decorate the apices of our spans with Hamiltonians. This gives a category where morphisms are open classical systems, and composition allows us to build these systems from smaller pieces. (Received June 26, 2017) Keep 'em coming! I'm still hoping that Brandon, Joseph and Christina will submit abstracts. John Foley may submit one too: it would be great to have him give a talk about how our Metron project is using operads for "compositional tasking". This would be a nice sequel to a talk by Joseph on the underlying math - namely, "network models" and the operads they give rise to.