My plan now is to continue adding text to the various sections in the blog, and to make sure that the sections are all well connected with each other. My goal is a step-by-step progression. Comments are always welcome and can be posted on this forum page.

]]>Here are the blogs:

- [[Blog - Meet the operads]] (part 1)

As a point of departure and reference, I am using this talk:

- David I. Spivak, A mathematical language for modular systems.

- Matteo Smerlak and Ahmed Youssef, Statistical patterns of Darwinian evolution.

Abstract.In the most general terms, Darwinian evolution is a flow in the space of fitness distributions. In the limit where mutations are infinitely frequent and have infinitely small fitness effects (the "diffusion approximation", Tsimring et al. have showed that this flow admits "fitness wave" solutions: Gaussian-shape fitness distributions moving towards higher fitness values at constant speed. Here we show more generally that evolving fitness distributions are attracted to a one-parameter family of distributions with a fixed parabolic relationship between skewness and kurtosis. Unlike fitness waves, this statistical pattern encompasses both positive and negative (a.k.a. purifying) selection and is not restricted to rapidly adapting populations. Moreover we find that the mean fitness of a population under the selection of pre-existing variation is a power-law function of time, as observed in microbiological evolution experiments but at variance with fitness wave theory. At the conceptual level, our results can be viewed as the resolution of the "dynamic insufficiency" of Fisher's fundamental theorem of natural selection. Our predictions are in good agreement with numerical simulations.

I asked him if he could write a blog article summarizing this paper, and he gladly agreed! I hope he will write it here on the wiki.

If you see this, Matteo, you can announce any progress you make here! Or, if you have questions, you can ask them here.

]]>I'm trying to stay out of partisan politics, but I think these subnational efforts are important and I want to get involved. I'll be talking about this more!

]]>`(((1)))`

style because I'm working off a master version in LaTeX at this stage and those don't get screwed up by the conversion software; when complete they'll be changed to `[1]`

style references.)
If anyone feels like reading it and letting me know of any bits that are incomprehensible, etc, that'd be much appreciated.

]]>I just reworked my latest forum post into a short blog article. It's a combination of math and biography.

John, I recall that Andrew told you how to turn on Markdown on the blog, so that we don't have to convert the markdown to html by hand. If that's not working right, just let us know, so that can continue to do the conversions.

]]>- [[Blog - statistical laws of Darwinian evolution]].

Please give it a look and put corrections and comments here!

]]>• John Baez, Categories in control, *Azimuth Blog*, 23 April 2015.

He has put drafts on the Azimuth Wiki for us to read them and comment on them:

• Brendan Fong, Categories in control (part 2).

• Brendan Fong, Categories in control (part 3).

• Brendan Fong, Categories in control (part 4).

Only the first is close to done - he may be "over-promising", the way beginning bloggers often do.

]]>Here are the next scheduled posts. You can't actually see them until the dates listed.

Information geometry (part 15), 11 January 2016. Reviving a dormant series, I explain some of Blake Pollard's new paper Open Markov processes: A compositional perspective on non-equilibrium steady states in biology. Short version: they

*don't*obey the principle of minimum entropy production; they obey another minimum principle!Information geometry (part 16), 14 January 2016. Some more about Blake Pollard's new work and how it's related to Schnakenberg's work on entropy production.

Salar de Uyuni, 22 January 2016. This is about an interesting ecosystem in Bolivia. Mainly just for fun.

I would also like to post a followup to my article about the IEA underestimating renewables. They came out with a new report in August 2015, discussed here:

If any of you would like to take a look at their new report and tell me something interesting about it, that would be great!

]]>John Baez, Categorical foundations of network theory - an introduction to the workshop and what it's about.

David Spivak, A networked world, part 1 - the problem, part 2 - creating a knowledge network and part 3 - from parts to wholes.

Tobias Fritz, Resource convertibility, part 1, part 2 and part 3 - an introduction to the mathematics of 'resources'.

John Baez, Categories in control - about my paper with Jason Erbele on the use of categories to study signal flow diagrams.

John Baez, A compositional framework for passive linear networks - about my paper with Brendan Fong on the use of categories to study electrical circuit diagrams.

John Baez, Decorated cospans - about Brendan Fong's paper providing mathematical infrastructure for the study of networks.

John Baez and Brendan Fong, Cospans, wiring diagrams, and the behavioral approach - an attempt to reflect on how our work connects to that of David Spivak.

There's one more coming up, about the work of my student Nick Woods.

]]>- [[Blog - a networked world]].

It explains how he got interested in the things he'll be discussing at our meeting in Turin on 25-28 May 2015.

I've set the three parts to be published on Friday 27 March, Monday 30 March and Thursday 2 April 2015. Since he doesn't read the Azimuth Forum I'm not asking for suggestions on how to improve the articles... though I'd be happy to hear about typos.

]]>- [[Blog - stationary stability in finite populations]]

It's a followup to his earlier one, [[Blog - relative entropy in evolutionary dynamics]]. Time to finish this mini-series!

Give it a read and ask questions if there's stuff that you don't understand!

]]>A question: is it really wise to use $\psi_+$ as the name for the state whose energy is $E_0 - \Delta$, and $\psi_-$ as the name for the state whose energy is $E_0 + \Delta$? I guess I know why Piotr is doing this, but it could be a bit confusing. Maybe I'll add an explanation.

By the way, the term 'superposition' is never defined. I'll also add a definition of that, since that's the topic of the post!

]]>I have an idea for a series of 3 posts on quantum community detection:

- Quantum superposition vs statistical mixtures (draft here + some notes on the next parts
- Community detection in (classical) complex networks
- Quantum community detection

First two topic are standalone, general introduction to these topics. And I believe that they are of the general interest and benefit of the readers. The third one is about a paper arXiv:1310.6638, in which we are trying to predict the scale of quantum effects in a light-harvesting complex of green plants. It is an investigation in the same team (Jake Biamonte, Tomi Johnson and Mauro Faccin, Ville Bergholm and me) as the previous quantum network posts:

John, what do you think about it?

That is, is the concept of these blog post nice? Do you like the introduction to quantum superposition?

]]>I would like the images to be included from the randform blog article here on Azimuth. John is there a possibility to download them?

]]>Notes on the transition from Stacey to Tanzer, the new forum address, and a small plug for the forum.

]]>- [[Blog - El Nino project (part 9)]]

This will contain a lot of the nice graphics [[Graham Jones]] put on [[Experiments in El Nino analysis and prediction]], showing correlations and covariances of sea surface air temperatures in the Pacific.

]]>- [[Blog - El Nino project (part 8)]].

I edited her English, added links, and added a short section of links to discussions of the effects of missing data on HadCRUT4. Everyone - especially Nad - should take a look and see if they like this post.

**Note: this version has been superseded and will not be posted to the blog. For a discussion of the new version, go here.**

I'm giving a seminar on Network Theory, as described here:

and I'll try to write course notes as blog articles, starting here:

I also hope to make videos of the seminar, perhaps in the form of "Hangouts on Air". This is one of the things that has been distracting me.

However, now that these things are underway, and the book with Jacob is close to done, I plan to return to the climate network business and start working very hard on that.

]]>The graphing program I'm using is sometimes getting some corner details of the contours wrong, and in general the graphs could probably be made a little bit nicer if I work some more on them. I'll probably try to do that when more of the other stuff is finished.

I need to figure out clearer language.

I actually need to write the program and run it on some cloud platform to get results, which is the much bigger task!

A couple of practical questions for John:

- There are some 3-side-by-side graphs, but maybe given the blog is so narrow they ought to be 3 stacked vertically?
- After the last blog article you and Andrew Stacey seemed to figure out how to do markdown blogs on wordpress. Is it the case I can write everything other than hyperlinks/images in markdown format now, or should I html-ize things?

EDIT: looks like the forum didn't like the [ [ link ] ] to the blog, so changed it to a longer link.

]]>- [[Exploring climate data (part 2)]]

It's probably best if you save interesting questions or comments for when the article appears! Unless there's a serious mistake here, the only thing that really needs to be done is to get Blake to enter some information about himself into a page on the Azimuth Wiki.

I want to keep this series going, and perhaps the next thing should be some of the interesting temperature graphics Daniel Mahler created.

]]>This is not yet ready to go, but quite close -- the whole intent and flow of the article is spelled out here.

I still need to work on the intro, the conclusion, and to actually check the coding steps that I describe.

]]>- [[Blog - time inversion symmetry breaking]]

I think I'll nominate the quantum network theory posts by Tomi. But there are so many good ones, I'm not sure which to pick!

]]>- [[Blog - El Nino project (part 7)]]

It's a bit dry so far, mainly about the definition of El Niño. But I may also include a bit about "different flavors of El Niño". I will send a bunch of an article about that - Graham Jones already has it. If you don't get it from me in a few minutes, and want it, let me know.

]]>- [[Blog - Petri net software]]

This will be based on the research Jim Stuttard has been compiling at Petri net - software. However, it won't replace this article because I'll focus on a subset of the software tools - the ones that seem best, or best-documented.

There's nothing much in this article yet except a copy of what Jim Stuttard wrote - I'll say when I write something!

This article could be part of David Tanzer's blog series on Petri net programming, or a standalone.

]]>To get started, let's try this:

- Dara O Shayda, Darwin Tahiti SOI comparison.

Dara: could you

Give me the figures that are included in this file?

Say where you got the Darwin and Tahiti data?

Say anything you can to explain how these figures were generated? (I understand how the Gabor transform works - is that all you are using here, or something more complicated? A Gabor transform needs a certain parameter that describes the width of the "window" - what are you using there?)

Ideally people will learn to write these posts themselves; right now we're limited by the fact that I'm doing most of the writing. But I'll try to write this one. There's nothing here yet, but this is where I'll write it:

- [[Blog - exploring climate data (part 1)]]

This is a thread to discuss the article that we are writing for the MPE blog (Mathematics of Planet Earth).

I'll post a note when I have a draft up on the wiki.

This thread is a spinoff from this forum thread: Helping JB write for Azimuth.

There John said:

Jinqiao Duan of IPAM invited me to write an article on the Mathematics of Planet Earth blog

Here are the requirements for the post:

We encourage personal commentary on any topic associated with MPE2013. A contribution can be a report on a meeting, a pointer to important research results or educational material, a website recommendation, a short essay on a key issue, a book review, a news item, or any other material that might be of interest to a broad audience. A contribution can be as short as a couple of paragraphs and may include a photo or illustration or even an audio or video clip. We recommend no more than about 1,000 words of text. In case you are a newcomer to the blogosphere, here is a link to a helpful web site: http://www.maa.org/pubs/FOCUSfeb-mar12_blogroll.html.

Here are some initial thoughts that I sent to John by email.

John,

Your slides on Energy, the Environment, and What Mathematicians Can Do already contain a lot of great material. Just converting some of that material into an expository and honestly persuasive essay could go along way. I'd be happy to make a pass at writing a draft. In doing so I would end up processing the ideas for myself, and clarifying where I stand on the points of discussion -- both in terms of my understanding of the scientific content, and my assessments about what should/can be done by mathematicians.

There is another major facet to the story, which is not unrelated to your stated goal of ending innumeracy and illogic. Our abuse of the environment is driven by societal processes. So environmental science really can't omit from the picture economics and politics as major components of the objective reality. Yet this has been a terrible quagmire for science because it is a battleground of vested interests. Much more clarity is needed here, and mathematicians are by nature truth seekers.

There is a great spiritual challenge here: how to fearlessly pursue the truth, in these most complex and heated of areas -- the social sciences -- without unwittingly becoming a doctrinaire ideologist.

I don't have answers here, but I do see a lot of questions that have yet to be addressed in a truly scientific manner.

If you think that there is room for some discussion along these lines, I could continue to write up this thread of thought.

]]>