Tuesday, May 22, 2007

An application of non-positive curvature

From http://blog.sciencenews.org/mathtrek/2007/05/a_grove_of_evolutionary_trees.html:
"An oceanographer buys a piece of whale flesh at a market in Japan. The clerk assures her the meat comes from a Baird's beaked whale, which is legal to hunt under certain circumstances. The scientist takes the meat to her lab, performs a DNA analysis of it, and finds that it is in fact an endangered right whale. Killing a right whale is a crime.

When the oceanographer reports her findings to the International Whaling Commission, the commissioners ask her one question: how certain are you?

Until recently, a scientist would not have been able to give a rigorous answer. The analysis depends on the scientist's understanding of the evolutionary relationships among different species of whales, and statisticians didn't know how to analyze the tree-shaped graphs that express those relationships.

Now, mathematicians have developed a new understanding of the mathematics of tree-shaped graphs, which makes possible the statistical analysis of evolutionary trees. The development will help biologists to make sense of the flood of newly available genetic information."
A very interesting article with a number of interesting references which I have yet to read.

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