Sunday, April 23, 2006

PageRank algorithm finds physics gems

Several colleagues from Boston University and from Brookhaven have proposed a method

to look for influential papers using the same algorithm that Google uses to rank web pages. This algorithm uses the list of web pages (or papers) and the links between them (or citations) as input. The web pages or papers are nodes of a graph and the citations are oriented links. It works as follows:

You have lots of "random walkers". Each of them sits at some paper XY. In each step, each random walker either jumps to a random paper in the full database, with probability "d", or it jumps to a random paper mentioned in the references of the previous paper XY, with probability "1-d". Once the number of random walkers associated with each paper reaches equilibrium (approximately), the algorithm terminates. The number of walkers at each paper gives you the rank.

As Alex Wissner-Gross has explained me, the algorithm is equivalent to a Monte Carlo approach to the diagonalization of the adjacency matrix.

This method differs from the naive, straightforward sum of all citations in two basic respects:
1. In the PageRank framework, it is better to be cited by influential papers.
2. In the PageRank framework, it is better to be cited by papers with a small number of references i.e. to be rather special among these references.
When the colleagues applied this method to a graph of 300,000+ papers, they discovered the true undercited gems. Two of the four most spectacular ones were

The first paper was written by Eugene Wigner whose statement that particles transform as representations of the Lorentz group has been under a severe attack of algebraic quantum field theorists; and by Frederick Seitz, an eminent scientist who was recently under a heavy and immoral attack of anonymous terrorists, fashionable communists, and envirofascists.

The second paper by Feynman and Gell-Mann has revealed the A-V (axial vector minus vector) structure of the four-fermion weak interactions. The paper is also important as an example how very good theorists are right even if renowned experiments say that the theorists are wrong: the renowned experimenters argued that the weak interactions were S-T (scalar or tensor exchange) but they made an error: their conclusions were based on the last point of their graph which is why Feynman identified them - in an explosion of anger - as morons as soon as he open the experimental article in Phys. Rev. ;-)

Via PhysicsWeb.ORG.