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Mathematics of biodiversity

From 18 June to 7 July 2012, I'll be attending a research program on the Mathematics of Biodiversity at the Centre de Recerca Matemàtica in Barcelona, organized by Tom Leinster and others. There will be a conference from the 2nd to the 6th and I'll leave on the 7th. I will give a talk, and right now the abstract looks like this:

Diversity, information geometry and learning

Abstract: As well known, some measures of biodiversity are formally identical to measures of information developed by Shannon and others. Further, the replicator equation in evolutionary game theory is formally identical to a process of Bayesian inference studied in the field of machine learning. In this simple model, a population of organisms can be thought of as a 'hypothesis' about how to survive, and natural selection acts to update this hypothesis according to Bayes' rule. This idea has been studied by Marc Harper and elaborated using ideas of information geometry. The question thus arises to what extent natural changes in biodiversity can be usefully seen as analogous to a form of learning. However, some of the same mathematical structures arise in the study of chemical reaction networks, where the increase of entropy, or more precisely decrease of free energy, is not usually considered a form of 'learning'. We report on some preliminary work on these issues.

It's a bit risky because I haven't written up all my ideas yet, but I think I can manage something interesting for 40 minutes.

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