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## Comments

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.

I blogged about ExAMS here:

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.

`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.`

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

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.

`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.`

28 November 2016:

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

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:

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.

`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`

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.

`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.`

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:

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

`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.`

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...

`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...`

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 Categoriessubject 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:

Azimuth Backup Project (Part 1).

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.

`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.`

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 Theoryhas 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.

`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.`