The BBC and Scientific American report on a paper looking, “in an exploratory manner,” at the limiting shape of metro systems serving large cities. The BBC linked to the actual paper, which is nice of them. The Scientific American article goes into a bit more detail, though.
The authors contend that rather than the shape of subway networks being decided by central planning, which would produce a variety of shapes, the eventual shape of a subway network converges on an emergen structure consisting of a dense core with branches radiating from it.
Unhelpful framing news, now. A University of Michigan of press release begins:
A hidden facet of a math problem that goes back to timeworn Sanskrit manuscripts has just been exposed by nanotechnology researchers at the University of Michigan and the University of Connecticut.
We love hearing about new maths but keeping up with the literature is difficult. It’s also quite hard to tell if something outside your field of expertise is noteworthy or not. So we want your help directing our attention towards new and noteworthy research, whether it’s on the arXiv or in peer-reviewed journals or just a rumour someone’s worked out something big.
We’re going to call the column Phil. Trans. Aperiodic., and Nathan Barker, who is currently finishing his PhD at Newcastle University, has kindly offered to run it. He’s going to do a fairly regular, fairly serious round-up of the articles you submit.
So, if you’ve seen some good research lately (or you’ve written some, and you’re really really sure it’s good), please go over to the Phil. Trans. Aperiodic. submission page and fill in our form.
One of the many annoying thing about academic paywalls, leaving aside whether you think they should exist or not, is that unless you can log in with Athens or Shibboleth, you can only get access through a PC at your university or workplace. If you try to catch up on reading once you’re back at home, it’s often difficult or impossible to get access to journals and other resources your institution subscribes to. This has become a much bigger problem with the advent of the iPad, which is increasingly the device on which people do their reading, often over mobile networks.
The AMS has come up with a solution called “mobile pairing” – if you log in to their site once through your institution’s network, the device you used will then be granted the same access to journals and things like MathSciNet, no matter where you’re connecting from. It just uses browser cookies, so doesn’t require any yucky apps to be installed.
I’ve shaken my fist at my laptop’s screen many a time while trying to look up references on MathSciNet from home, so I think this is great news.
Information: AMS Mobile Pairing
Source: Peter Krautzberger on Twitter
French researchers Vincent Borrelli, Saïd Jabrane, Francis Lazarus and Boris Thibert have described an isometric embedding of the flat torus in 3D space, using the convex integration theory developed by Gromov in the 1970s. That means they’ve produced a surface which is topologically a torus – it has a single hole — which preserves distances between points in the 4D flat torus. Interestingly, the tangent plane is defined everywhere — the surface is in a sense smooth — but the normal vector is not defined, so it’s also a fractal. This is impossible in higher dimensions
I’ve recorded a short video explaining in a handwavey fashion, with a few props made from things I had lying around, just what has been done.
Some cognitive scientists have done an experiment on some people in Papua New Guinea to test the hypothesis that the number line is based on an in-built intuition that all humans share. They concluded that it isn’t, and that you can use cardinal numbers without placing them mentally on a line.