p2pnet - rss feed: Google page ranking and Schröedinger
p2pnet news view | Cool Stuff:- A field of study inspired by Google’s PageRank algorithm looks set for a shake up following the publication of an entirely new formulation of the problem of ranking web pages, writes KFC in the physics arXiv blog.
“Nicola Perra at the University of Cagliari in Italy and colleagues have discovered that when they re-arrange the terms in the PageRank equation the result is a Schröedinger-like wave equation,” says the post.
Schroedinger-like wave equation?
“In physics, especially quantum mechanics, the Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time,” says the Wikipedia.
“It is as central to quantum mechanics as Newton’s laws are to classical mechanics.”
“So what, I hear you say,” the post goes on, “that’s just a gimmick.”Maybe, but, “What the wave equation allows is a study of the dynamic behaviour of PageRanking, how the rankings change and under what conditions, says KFC, adding:
“One of the key tools for this is called perturbation theory. “It’s no understatement to say that perturbation theory revolutionised our understanding of the universe when it was applied to quantum theory in the 1920s and 1930s.
“The promise is that it could do the same to our understanding of the web and if so, this field is in for an interesting few years ahead.”
Say Perra et al: »»»
The WorldWide Web is one of the most important communication systems we use in our everyday life. Despite its central role, the growth and the development of the WWW is not controlled by any central authority. This situation has created a huge ensemble of connections whose complexity can be fruitfully described and quantified by network theory. One important application that allows to sort out the information present in these connections is given by the PageRank alghorithm. Computation of this quantity is usually made iteratively with a large use of computational time. In this paper we show that the PageRank can be expressed in terms of a wave function obeying a Schroedinger-like equation. In particular the topological disorder given by the unbalance of outgoing and ingoing links between pages, induces wave function and potential structuring. This allows to directly localize the pages with the largest score. Through this new representation we can now compute the PageRank without iterative techniques. For most of the cases of interest our method is faster than the original one. Our results also clarify the role of topology in the diffusion of information within complex networks.
“The whole approach opens the possibility to novel techniques inspired by quantum physics for the analysis of the WWW properties,” they add.
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.Stumble It!
physics arXiv blog - Schroedinger-like PageRank wave equation could revolutionise web rankings, August 7, 2008 Schroedinger-like wave equation -Schroedinger-like PageRank equation and localization in the WWW, July 28,2008
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August 8th, 2008 at 11:20 am
Since quantum mechanics is dying of it deserved death I don’t see the point for still using the Schröedinger equation on anything except for fun.
The problem with quantum mechanic is the uncertainty principle that turn every equation into rubber.
This flexibility is extremely small indeed but is enough to make the theory fit any BS you can through at it.
The quantum mechanic advocate has made the universe fuzzy at a very very small scale, at a scale so small in fact that we can not prove it or unprove it for the time being because it require an energy scale we can not probe yet.
How convenient!
August 8th, 2008 at 5:57 pm
someone care to translate that into something a NORMAL geek can understand?
August 9th, 2008 at 6:17 pm
hey, certainly it’s not dying. Quantum mechanics describes too many important things. For example tunneling. Without this effect no transistors would work and in particular microprocessors would not exist. So you would not have an ability to post your message at all.
BTW, if you have another good theory to replace quantum mechanics, that will describe all the effects and suggest new ones, feel free to publish it and get Nobel prize (or two)