2 August 2017:
This week's progress:
1) Nina Otter is at Banff International Research Station, the place in Canada where they have tons of math workshops, attending one on [Topological Data Analysis: Developing Abstract Foundations](https://www.birs.ca/events/2017/5-day-workshops/17w5108). Topological data analysis uses things like [persistent homology](https://en.wikipedia.org/wiki/Persistent_homology) to calculate the topology of clouds of data points. It's very fashionable these days.
2) Blake and I gave _Reviews in Mathematical Physics_ a final version of our paper "A compositional framework for reaction networks". I celebrated by blogging about it all over:
* [Category theory in chemistry](https://plus.google.com/u/0/+johncbaez999/posts/hhyzhu1mB7F), on G+, a "pop" explanation that got lots of likes but also lots of interesting comments.
* [A compositional framework for reaction networks](https://johncarlosbaez.wordpress.com/2017/07/30/a-compositional-framework-for-reaction-networks/), on Azimuth, a more technical explanation that also got some good comments.
* [A compositional framework for reaction networks](https://golem.ph.utexas.edu/category/2017/07/a_compositional_framework_for_2.html), on the n-Category Cafe, an almost identical technical explanation that got completely different comments, including a really fascinating one from Mike Shulman: he's been looking at open Petri nets in logic, without knowing that's what they're called! Instead of chemicals reacting to give other chemicals, he's looking at assumptions "reacting" to give conclusions! In other words, he's looking at proofs. /This is the kind of analogy Mike Stay and I really like, and I bet it will produce interesting new ways of looking at both chemistry and logic.
3) Nina and I just sent a revised version of our paper "[Operads and phylogenetic trees](http://math.ucr.edu/home/baez/phylo.pdf)" to Steve Lack, who is an editor at TAC. The referee had wanted tons of big changes, so this was a lot of work. Our reply letter listing what we've done is 11 pages long! I won't be surprised if the referee points out mistakes in this.
But the paper is better now - if you were too scared to read it before, read it now! It's about Markov processes and operads.
The referee had earlier said "Overall, I believe that an improved version of this paper would make an excellent, unusual and interesting contribution to TAC", so I hope they accept it now. We've been working on this paper since December 2013.
**Moral: it sometimes takes insane amounts of persistence to publish things.**