Archive for May 22nd, 2007

HowTo: Find scientific papers for free

May 22, 2007

Sandra Porter at Discovering biology in a digital world gives some pointers in a three part post, first of which is out already. I am looking forward to the other two parts!

Use of topology in biology

May 22, 2007

How distant on the evolutionary tree are two species? A question that mathematicians can answer using topological techniques, apparently, has plenty of uses in biology; via Swarup. There is some stuff about freely available statistical tools too:

In the surface of any three-dimensional space with negative curvature, there is only one shortest line connecting any two points. Had the space been positively curved, it would resemble the surface of a ball. On a ball, there is more than one shortest line connecting two points. For example, the shortest distance between the Earth’s North Pole and the South Pole is traversed by any of the great circles.

The existence of only one shortest line connecting any two points is the key property that allows the mathematicians to compute an “average tree” at the center of a clump of estimates. The confidence of the estimate is then related to the distance from the average tree to each of the estimates. On positively curved surfaces, a single average point might not exist at all, which would make it impossible to pin down the confidence level.

The researchers have used their new methods to develop a freely available statistical software package that augments a statistics program called R. The software was first released two years ago. “Biologists are using it quite a lot,” Holmes says. One of Billera’s graduate students, Megan Owen, is developing more efficient algorithms to calculate the shortest path between a pair of points.

“What this tells me is that you don’t know what kind of mathematics is going to be useful to biology,” Billera says. “It wasn’t clear before this that geometry and topology would be useful to biology. Who would think they had anything to do with each other?”

Take a look!