Here’s another power-law.
Apparently the distribution for the interval between epileptic seizures is a power-law. The long intervals are rare. There are lots processes that give rise to a power law distribution. The proposed model in this case involves a cascading failure in the network of neurons.
I don’t think this next paper has undergone peer reviews, but in this paper they look at the interval between a serial killer’s murders. That’s a thin data sample. The interval between his crimes is power-law distributed.
Interesting example of impulse control, will power power, etc.
I wonder if we have other data on brainstorms? Brainstorms of a less horrific kind: interval between blog posts, emails, phone calls, code commits, sales closed, etc. etc. What if we took the top hundred poems Robert Frost wrote and measured the interval between their creation? Would we see that as power law distributed? With enough data we could probably look into the effect of coffee on brainstorms.
Hi Ben,
I can’t say I am terribly impressed by that paper. For one thing, the reason they give for suggesting that serial murder may have a similar distribution to epileptic fits is the discredited theories of Lombroso, a 19th century criminologist. While Lombroso was a humanitarian who worked to improve prison conditions, his discredited theory that crime is due to hereditary defects caused by de-evolution was later used to justify the Holocaust and other eugenic movements. It’s surprising to see his work referenced in an apparently serious paper in 2012…
They also make little effort to show that the data they have collected actually IS a power law other than saying that “{numerical results of their simulation} decently agree with the experimental data.” – or in other words they plotted a log-log graph and decided that their data looked roughly like the straight line from their model. There is no evidence of any attempt to do any statistical significance testing or to consider other distributions that produce roughly straight lines on log-log graphs (eg Poisson, log-normal, exponential). Their limited data set makes this even more risky.
On a more positive note, I think a paper you might find interesting if you haven’t seen it is: http://arxiv.org/abs/0706.1062
It looks at 24 datasets such as emails and phone calls and explains some of the mathematics you can use to see if they are better explained by power laws or one of the other distributions.
Sorry if this comment seems a bit negative but the paper’s comment “Thus, one may speculate that similar processes in the brain may lead to both epileptic seizures and serial killings.” was just a bit too radical for me to ignore!
The author of the paper JH cites applies its methods to this data set: http://cscs.umich.edu/~crshalizi/weblog/857.html