Summer is a busy time for this site’s hard-working triumvirate, so we haven’t been keeping on top of the news as much as we’d like. There’s been some quite interesting news, so here’s a quick round-up of the most important bits:

Proof News!

Adam Marcus, Dan Spielman, and Nikhil Srivastava have proved a positive answer to the Kadison-Singer conjecture in their paper, Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem. I think Gil Kalai was the first to write about it, but Terry Tao wrote a short Google+ post and Bryan Roberts has written a very nice overview post on his blog.

It’s turning out to be a summer of tumbling conjectures, as Bob Hough solved the Erdős covering congruence conjecture in his paper, The least modulus of a covering system. Terry Tao wrote a short note on Google+ describing the negative result. Aperiodichum Yemon Choi was hip to this before any of us, writing a post in the middle of June complaining that it wasn’t getting any attention.

Yet Another Alternative Method of Scholarly Discourse

You might have noticed the funny hashtags on Terry’s posts. He’s using the Selected Papers Network, which is Yet Another Alternative Method of Scholarly Discourse. I was going to write in depth about it, but it doesn’t look like I have time to do that so I’ll just mention it here. It scans other fora (currently only Google+) for comments about papers (anything on the arXiv or with a PubMed ID or DOI), denoted with some special hashtags, and puts them all together on one page.

The first thing you’ll notice is that they’ve made the layout look a lot like the arXiv. The core of the idea seems to be that refereeing should happen in the open, and shouldn’t be controlled by editorial boards. It’s very heavily linked to Google+ at the moment, because that’s where all the cool people are, but that’s sort of a big problem from a “free information” perspective, though. It doesn’t do much to solve the problem of comments disappearing when selectedpapers.net does, because nobody else is watching and collecting the hashtags, but a good API would solve that problem.

Plenty of people are playing with it at the moment, so it might just take off – it’s quite a low-investment way of sharing your thoughts on new publications. Certainly, people like Tim Gowers and Terry Tao seem to be using it to share quick “here’s a thing, have a look at it” reviews rather than carefully considered referee’s reports.

The Selected Papers Network was announced by John Baez on Google+ – that post’s a good place to find out what it’s all about.

Plants do sums while no-one’s watching

A while ago the BBC posted a story titled Plants ‘do maths’ to control overnight food supplies. It was depressingly short on what the ‘maths’ was, so I did a bit of journalism and emailed the mathematical biologist involved in the project, Martin Howard, directly. He replied to me straight away, but I completely forgot to post it. Here’s what he said (I had guessed from the John Innes Centre press release that their model was a simple dynamical system):

Dear Christian,

Thanks for emailing with your questions! The paper is actually now available from the arxiv, the link is:

http://arxiv.org/abs/1306.5148

All the details are in the Mathematical modelling section. But indeed you are correct that it’s a dynamical system, where the amount of S molecule (which records the total amount of starch) obeys the equation:

\[ \frac{dS}{dt} = \frac{- \gamma S}{t_{day} –t} \]

where $t_{day} =24$ hrs. In the case where $\gamma =1$, the decay of starch levels during the night is of course linear with time. So indeed from a mathematical perspective this is not exactly ground-breaking stuff! Indeed there has been interest already in developing these ideas for the classroom, both at pre-GCSE level (slopes, triangles etc) and at A level (solve the ODE). The important thing is showing that this sort of computation is actually going on at a cellular level, by validating predictions made from the model.

Another important point is that the computation, we think, is done in analogue fashion exploiting appropriate chemical kinetics inside the cell. In other words, it’s not digital, so not like the division implementation in a computer. This ought to have significant implications in synthetic biology.

Hope this is useful to you!
Best wishes,
Martin.

So, sorry to Martin for not putting that out in anything like useful time. Because stars have burned out and glaciers have moved since the press release, the final paper is now online at eLife.

Some physicists claim to have proved Heisenberg’s uncertainty principle – that observing a thing changes it. The paper’s called Proof of Heisenberg’s error-disturbance relation and I have no idea how correct it is, or if it’s even maths. Nobody has written anything on the Selected Papers Network about it. So much for progress!

Finally, Steven Strogatz posted a link on Twitter to a “vigorous, provocative essay” by Ian Stewart about what mathematics really is, in the New Statesman. It’s a good read! Read it!

That’s not all the news we failed to cover recently, but it’s most of the news we meant to cover. Normal service will resume when our madcap city lives cease being so hectic. Have a good summer!