Happy New Year! We’ve got some fun guest posts lined up for next year, including:
• Marc Harper, Relative entropy in evolutionary dynamics.
Marc Harper uses ideas from information theory in his work on bioinformatics and evolutionary game theory. This article explains some of his new work. And as a warmup, it explains how relative entropy can serve as a Lyapunov function in evolution!
This includes answering the question:
“What is a Lyapunov function, and why should I care?” 
The brief answer, in case you’re eager to know, is this. A Lyapunov function is something that always increases—or always decreases—as time goes on. Examples include entropy and free energy. So, a Lyapunov function can be a way of making the 2nd law of thermodynamics mathematically precise! It’s also a way to show things are approaching equilibrium.
The overall goal here is applying entropy and information theory to better understand the behavior of biological and ecological systems. And in April 2015, Marc Harper and I are helping run a workshop on this topic! We’re doing this with John Harte, an ecologist who uses maximum entropy methods to predict the distribution, abundance and energy usage of species. It should be really interesting!
But back to blog articles:
• Manoj Gopalkrishnan, Lyapunov functions for complex-balanced systems.
Manoj Gopalkrishnan is a mathematician at the Tata Institute of Fundamental Research in Mumbai who works on problems coming from chemistry and biology. This post will explain his recent paper on a Lyapunov function for chemical reactions. This function is closely related to free energy, a concept from thermodynamics. So again, one of the overall goals is to apply entropy to better understand living systems.
Since some evolutionary games are isomorphic to chemical reaction networks, this post should be connected to Marc’s. But there’s some mental work left to make the connection—for me, at least. It should be really cool when it all fits together!
• Alastair Jamieson-Lane, Stochastic cross impact balance analysis.
Alastair Jamieson-Lane is a mathematician in the master’s program at the University of British Columbia. Very roughly, this post is about a method for determining which economic scenarios are more likely. The likely scenarios get fed into things like the IPCC climate models, so this is important.
This blog article has an interesting origin. Vanessa Schweizer has a bachelor’s degree in physics, a masters in environmental studies, and a PhD in engineering and public policy. She now works at the University of Waterloo on long-term decision-making problems.
A while back, I met Vanessa at a workshop called What Is Climate Change and What To Do About It?, at the Balsillie School of International Affairs, which is in Waterloo. She described her work with Alastair Jamieson-Lane and the physicist Matteo Smerlak on stochastic cross impact balance analysis. It sounded really interesting, something I’d like to work on. So I solicited some blog articles from them. I hope this is just the first!
So: Happy New Year, and good reading!
Also: we’re always looking for good guest posts here on Azimuth, and we have a system for helping you write them. So, if you know something interesting about environmental or energy issues, ecology, biology or chemistry, consider giving it a try!
If you read some posts here, especially guest posts, you’ll get an idea of what we’re looking for. David Tanzer, a software developer in New York who is very active in the Azimuth Project these days, made an organized list of Azimuth blog posts here:
You can see the guest posts listed by author. This overview is also great for catching up on old posts!
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