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Quantum equation provides a mathematical short-cut for PageRank calculation
Technology
EVEN images from the most expensive cameras don’t yet rival the view of the world we get from our own eyes. The secret lies in the curved retina at the back of the eyeball – and now there is an artificial equivalent. “The human eye is a spectacular camera, but its imaging optics are very simple,” says John Rogers from the University of Illinois at UrbanaChampaign, a member of the team that created the new camera. The eye only needs a cornea and lens to form an image – thanks to the curvature of the retina, which means that the focus and brightness of an image are relatively uniform whether it falls at the centre of the retina or the edge. It’s also why we have a
Search engines quicken with a quantum touch
QUANTUM theory has a reputation for obscuring things as much as for pinning them down. But its underlying mathematics could help internet search engines to assess web pages more efficiently. One reason for Google’s enormous success is PageRank, an algorithm that measures the importance of a web page by examining the other web pages that link to it. To calculate 26 | NewScientist | 9 August 2008
they pulled the form tight, so that it flattened like a drumhead, then pressed the mesh against it. When they released the tension on the form, it relaxed back into a dome shape, along with the mesh (Nature, DOI: 10.1038/ nature07113). Finally, they removed the mesh from the dome and glued it onto a rigid support, leaving them with an artificial retina that can be turned into an electronic eye by adding a plastic cover with a central lens that correspond to the eye’s cornea and lens, and an “optic nerve” – cables connecting it to a computer. “It’s a really nice piece of work,” says Emma Johnson of the Centre for Biomimetics at the University –”There’s a reason we have eyeballs, not eyecubes”– of Reading, UK. “The hemispherical shape does carry a purpose – shapes without tearing. wide field of vision and suffer there’s a reason we have eyeballs The researchers overcame this and not eyecubes.” relatively few geometric by slicing off the image-detecting distortions in our sight. The artificial retina could be surface of a conventional flat By contrast, the CCD image ideal for defence applications detector used in a digital camera – detector and cutting holes in it to or prosthetic eyes. “This form an ultra-thin mesh. The thin hemispherical shape would the electronic equivalent of a wires between the holes bend retina – is flat and requires a much more naturally integrate when the mesh is deformed, complex system of lenses to with the human eye,” says Rogers. making it flexible enough to obtain a clear image. Making The technology could prove be reshaped into a hemisphere. curved CCDs from scratch has just as useful for the compact To do this, the team used a proven difficult, while flat CCDs camera that takes your holiday are too rigid to stretch into curved dome-shaped rubber form. First snapshots. Flora Graham ● IMAGE DJ/JUPITER
Curves give electronic eye a finer view
a page’s ranking, Google’s software bots crawl the web, gathering information on which pages are linked to each other. It then performs a demanding computation to get the PageRank. The process is repeated frequently to keep it up to date. Now a team of physicists led by Nicola Perra at the University of Cagliari in Italy may have found a better way to calculate a page’s rank. They say PageRank’s mathematical basis bears an uncanny similarity to the Schrödinger equation of quantum theory, meaning that mathematical short-cuts used in quantum physics can also be applied to the web (www.arXiv.org/abs/0807.4325). In physics, solutions to the Schrödinger equation yield “wave functions” linked to the probability of a quantum object – an electron, for example – being found in various
places. Interactions with other particles influence the properties of the wave function and where the particle is likely to be found. Perra and her colleagues argue that links between web pages play a role akin to particle interactions. And since web surfers are more likely to be found on the
“Links between web pages play a role akin to particle interactions” most highly ranked pages, they claim that PageRank can be expressed in terms of a wave function. The team reckons the analogy has practical uses. In quantum physics, it is often easiest to calculate the wavefunction solution for one problem by thinking of it as a small correction to a solution already known for a
similar problem. Similarly, today’s PageRank can be calculated by making a small correction to yesterday’s value, based on changes in the web’s structure reported by the web-crawling bots. Sample calculations carried out by the researchers show that this can be significantly faster than redoing the entire calculation from scratch. Andrei Broder of Yahoo Research in Burbank, California, offers qualified support. “It seems they can compute some approximations faster than by traditional methods,” he says. But he warns that further tests are needed to see if the technique offers genuine practical advantages, and notes that it only provides a partial solution in any case. “Analyses like PageRank are now just one of maybe hundreds of factors used to rank pages,” he says. Mark Buchanan ● www.newscientist.com
EVEN images from the most expensive cameras don’t yet rival the view of the world we get from our own eyes. The secret lies in the curved retina at the back of the eyeball – and now there is an artificial equivalent. “The human eye is a spectacular camera, but its imaging optics are very simple,” says John Rogers from the University of Illinois at UrbanaChampaign, a member of the team that created the new camera. The eye only needs a cornea and lens to form an image – thanks to the curvature of the retina, which means that the focus and brightness of an image are relatively uniform whether it falls at the centre of the retina or the edge. It’s also why we have a
Search engines quicken with a quantum touch
QUANTUM theory has a reputation for obscuring things as much as for pinning them down. But its underlying mathematics could help internet search engines to assess web pages more efficiently. One reason for Google’s enormous success is PageRank, an algorithm that measures the importance of a web page by examining the other web pages that link to it. To calculate 26 | NewScientist | 9 August 2008
they pulled the form tight, so that it flattened like a drumhead, then pressed the mesh against it. When they released the tension on the form, it relaxed back into a dome shape, along with the mesh (Nature, DOI: 10.1038/ nature07113). Finally, they removed the mesh from the dome and glued it onto a rigid support, leaving them with an artificial retina that can be turned into an electronic eye by adding a plastic cover with a central lens that correspond to the eye’s cornea and lens, and an “optic nerve” – cables connecting it to a computer. “It’s a really nice piece of work,” says Emma Johnson of the Centre for Biomimetics at the University –”There’s a reason we have eyeballs, not eyecubes”– of Reading, UK. “The hemispherical shape does carry a purpose – shapes without tearing. wide field of vision and suffer there’s a reason we have eyeballs The researchers overcame this and not eyecubes.” relatively few geometric by slicing off the image-detecting distortions in our sight. The artificial retina could be surface of a conventional flat By contrast, the CCD image ideal for defence applications detector used in a digital camera – detector and cutting holes in it to or prosthetic eyes. “This form an ultra-thin mesh. The thin hemispherical shape would the electronic equivalent of a wires between the holes bend retina – is flat and requires a much more naturally integrate when the mesh is deformed, complex system of lenses to with the human eye,” says Rogers. making it flexible enough to obtain a clear image. Making The technology could prove be reshaped into a hemisphere. curved CCDs from scratch has just as useful for the compact To do this, the team used a proven difficult, while flat CCDs camera that takes your holiday are too rigid to stretch into curved dome-shaped rubber form. First snapshots. Flora Graham ● IMAGE DJ/JUPITER
Curves give electronic eye a finer view
a page’s ranking, Google’s software bots crawl the web, gathering information on which pages are linked to each other. It then performs a demanding computation to get the PageRank. The process is repeated frequently to keep it up to date. Now a team of physicists led by Nicola Perra at the University of Cagliari in Italy may have found a better way to calculate a page’s rank. They say PageRank’s mathematical basis bears an uncanny similarity to the Schrödinger equation of quantum theory, meaning that mathematical short-cuts used in quantum physics can also be applied to the web (www.arXiv.org/abs/0807.4325). In physics, solutions to the Schrödinger equation yield “wave functions” linked to the probability of a quantum object – an electron, for example – being found in various
places. Interactions with other particles influence the properties of the wave function and where the particle is likely to be found. Perra and her colleagues argue that links between web pages play a role akin to particle interactions. And since web surfers are more likely to be found on the
“Links between web pages play a role akin to particle interactions” most highly ranked pages, they claim that PageRank can be expressed in terms of a wave function. The team reckons the analogy has practical uses. In quantum physics, it is often easiest to calculate the wavefunction solution for one problem by thinking of it as a small correction to a solution already known for a
similar problem. Similarly, today’s PageRank can be calculated by making a small correction to yesterday’s value, based on changes in the web’s structure reported by the web-crawling bots. Sample calculations carried out by the researchers show that this can be significantly faster than redoing the entire calculation from scratch. Andrei Broder of Yahoo Research in Burbank, California, offers qualified support. “It seems they can compute some approximations faster than by traditional methods,” he says. But he warns that further tests are needed to see if the technique offers genuine practical advantages, and notes that it only provides a partial solution in any case. “Analyses like PageRank are now just one of maybe hundreds of factors used to rank pages,” he says. Mark Buchanan ● www.newscientist.com