John C. Baez's Blog, page 79

Network Theory in Turin

Here are the slides of the talk I’m giving on Monday to kick off the Categorical Foundations of Network Theory workshop in Turin:

• Network theory.

This is a long talk, starting with the reasons I care about this subject, and working into the details of one particular project: the categorical foundations of networks as applied to electrical engineering and control theory. There are lots of links in blue; click on them for more details!

Information and Entropy in Biological Systems (Part 4)

I kicked off the workshop on Information and Entropy in Biological Systems with a broad overview of the many ways information theory and entropy get used in biology:

• John Baez, Information and entropy in biological systems.

Abstract. Information and entropy are being used in biology in many different ways: for example, to study biological communication systems, the ‘action-perception loop’, the thermodynamic foundations of biology, the structure of ecosystems, measures of biodiversity, and...

Information and Entropy in Biological Systems (Part 3)

We had a great workshop on information and entropy in biological systems, and now you can see what it was like. I think I’ll post these talks one a time, or maybe a few at a time, because they’d be overwhelming taken all at once.

So, let’s dive into Chris Lee’s exciting ideas about organisms as ‘information evolving machines’ that may provide ‘disinformation’ to their competitors. Near the end of his talk, he discusses some new results on an ever-popular topic: the Prisoner’s Dilemma. You may...

PROPs for Linear Systems

Eric Drexler likes to say: engineering is dual to science, because science tries to understand what the world does, while engineering is about getting the world to do what you want. I think we need a slightly less ‘coercive’, more ‘cooperative’ approach to the world in order to develop ‘ecotechnology’, but it’s still a useful distinction.

For example, classical mechanics is the study of what things do when they follow Newton’s laws. Control theory is the study of what you can get them to do.

...

Carbon Emissions Stopped Growing?

In 2014, global carbon dioxide emissions from energy production stopped growing!

At least, that’s what preliminary data from the International Energy Agency say. It seems the big difference is China. The Chinese made more electricity from renewable sources, such as hydropower, solar and wind, and burned less coal.

In fact, a report by Greenpeace says that from April 2014 to April 2015, China’s carbon emissions dropped by an amount equal to the entire carbon emissions of the United Kingdom!

I...

Resource Theories

by Brendan Fong

Hugo Nava-Kopp and I have a new paper on resource theories:

• Brendan Fong and Hugo Nava-Kopp, Additive monotones for resource theories of parallel-combinable processes with discarding.

A mathematical theory of resources is Tobias Fritz’s current big project. He’s already explained how ordered monoids can be viewed as theories of resource convertibility in a three part series on this blog.

Ordered monoids are great, and quite familiar in network theory: for example, a Petri ne...

Cospans, Wiring Diagrams, and the Behavioral Approach

joint with Brendan Fong

We’re getting ready for the Turin workshop on the Categorical Foundations of Network Theory. So, we’re trying to get our thoughts in order.

Last time we talked about understanding types of networks as categories of decorated cospans. Earlier, David Spivak told us about understanding networks as algebras of an operad. Both these frameworks work at capturing notions of modularity and interconnection. Are they then related? How?

In this post we want to discuss some simil...

Decorated Cospans

Last time I talked about a new paper I wrote with Brendan Fong. It’s about electrical circuits made of ‘passive’ components, like resistors, inductors and capacitors. We showed these circuits are morphisms in a category. Moreover, there’s a functor sending each circuit to its ‘external behavior': what it does, as seen by someone who can only measure voltages and currents at the terminals.

Our paper uses a formalism that Brendan developed here:

• Brendan Fong, Decorated cospans.

The idea here...

A Compositional Framework for Passive Linear Networks

Here’s a new paper on network theory:

• John Baez and Brendan Fong, A compositional framework for passive linear networks.

While my paper with Jason Erbele, Categories in control, studies signal flow diagrams, this one focuses on circuit diagrams. The two are different, but closely related.

I’ll talk about their relation at the Turin workshop in May. For now, let me just talk about this paper with Brendan. There’s a lot in here, but let me just try to explain the main result. It’s all about ‘...

Categories in Control

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

A while back I decided one way to apply my math skills to help save the planet was to start pushing toward green mathematics: a kind of mathematics that can interact with biology and ecology just as fruitfully as traditional mathematics interacts with physics. As usual with math, the payoffs will come slowly, but they may be large. It’s not a substitute for doing other, more urgent things—b...