Network Theory

John Baez

May 22, 2018

Scientists and engineers use diagrams of networks in many different ways. The Azimuth Project is investigating these, using the tools of modern mathematics. You can read articles about our research here:

You can navigate forwards and back through these using the blue arrows. By clicking the links that say "on Azimuth", you can see blog entries containing these articles. Those let you read comments about my articles—and also make comments or ask questions of your own!

You can watch 4 lectures, an overview of network theory, here:

Chemical reaction networks and Petri nets

Parts 1 to 26 are about chemical reaction networks and Petri nets. These parts have been made into a book:

I also expanded some parts into self-standing papers:

Here are the blog articles for parts 1-26:

This was the official end of the series of posts on stochastic Petri nets and chemical reaction networks... but there is more to read:

Electrical circuits, control theory and Markov processes

Starting in part 27, the network theory series changed topics to electrical circuits and related engineering problems. The series of blog posts sort of fizzled out, since my students and I got busy writing papers. I did, however, write blog articles about these papers:


Electrical circuits:

Control theory:

Markov processes and reaction networks:

The mathematics of networks - decorated cospans:

The mathematics of networks - props:

Here is the series of blog posts:

These ended rather prematurely when I decided to focus on writing papers instead. So, read some of the papers listed above — or at least Brendan Fong's thesis, which is a good overview!

To understand ecosystems, ultimately will be to understand networks. - B. C. Patten and M. Witkamp

Text © 2018 John Baez
Diagram on top by Nicolas Le Novere, illustrating SBGN: Entity Relationship Language