John C. Baez's Blog, page 88

Programming with Chemical Reaction Networks

There will be a 5-day workshop on Programming with Chemical Reaction Networks: Mathematical Foundation at BIRS from Sunday, June 8 to Friday June 13, 2014 It’s being organized by

• Anne Condon (University of British Columbia)

• David Doty (California Institute of Technology)

• Chris Thachuk (University of Oxford).

BIRS is the Banff International Research Station, in the mountains west of Calgary, in Alberta, Canada.

Description

Here’s the workshop proposal on the BIRS website. It’s a pretty inte...

Networks of Dynamical Systems

guest post by Eugene Lerman

Hi, I’m Eugene Lerman. I met John back in the mid 1980s when John and I were grad students at MIT. John was doing mathematical physics and I was studying symplectic geometry. We never talked about networks. Now I teach in the math department at the University of Illinois at Urbana, and we occasionally talk about networks on his blog.

A few years ago a friend of mine who studies locomotion in humans and other primates asked me if I knew of any math that could be usefu...

Network Theory III

In the last of my Oxford talks I explain how entropy and relative entropy can be understood using certain categories related to probability theory… and how these categories also let us understand Bayesian networks!

The first two parts are explanations of these papers:

• John Baez, Tobias Fritz and Tom Leinster, A characterization of entropy in terms of information loss

• John Baez and Tobias Fritz, A Bayesian characterization of relative entropy.

Somewhere around here the talk was interrupted by...

Network Theory II

Chemists are secretly doing applied category theory! When chemists list a bunch of chemical reactions like

C + O₂ → CO₂

they are secretly describing a ‘category’.

That shouldn’t be surprising. A category is simply a collection of things called objects together with things called morphisms going from one object to another, often written

f: x → y

The rules of a category say:

1) we can compose a morphism f: x → y and another morphism g: y → z to get an arrow gf: x → z,

2) (hg)f = h(gf), so we don’t ne...

Markov Models of Social Change (Part 2)

guest post by Vanessa Schweizer

This is my first post to Azimuth. It’s a companion to the one by Alaistair Jamieson-Lane. I’m an assistant professor at the University of Waterloo in Canada with the Centre for Knowledge Integration, or CKI. Through our teaching and research, the CKI focuses on integrating what appears, at first blush, to be drastically different fields in order to make the world a better place. The very topics I would like to cover today, which are mathematics and policy design...

Network Theory I

Here’s a video of a talk I gave last Tuesday—part of a series. You can see the slides here:

• Network Theory I: electrical circuits and signal-flow graphs.

Click on items in blue, or pictures, for more information.

One reason I’m glad I gave this talk is because afterwards Jamie Vicary pointed out some very interesting consequences of the relations among signal-flow diagrams listed in my talk. It turns out they imply equations familiar from the theory of complementarity in categorical quantum me...

Markov Models of Social Change (Part 1)

guest post by Alastair Jamieson-Lane

The world is complex, and making choices in a complex world is sometimes difficult.

As any leader knows, decisions must often be made with incomplete information. To make matters worse, the experts and scientists who are meant to advise on these important matters are also doing so with incomplete information—usually limited to only one or two specialist fields. When decisions need to be made that are dependent on multiple real-world systems, and your vari...