A very quick Riddler’s riddle last week with the question
Find the (integer) fraction with the smallest (integer) denominator strictly located between 1/2020 and 1/2019.
and the brute force resolution
for (t in (2020*2019):2021){
a=ceiling(t/2020)
if (a*2019<t) sol=c(a,t)}
leading to 2/4039 as the target. Note that
I read William McIlvanney’s Laidlaw [in planes last week] after I saw it recommended as a pre-Rankin novel. Which inspired the whole tartan noir literature. Including Rankin’s books, most obviously. The book is set in 1970’s Glasgow, which sounds rougher and grittier than when I was visiting the West End two decades later. The city is described as dominated by thugs, at least in the popular areas, with ultra-violent men running the criminal world, while still maintaining some Calvinist principles. Especially about the place of women and their abhorrence of homosexuality. Besides the very dark atmosphere of the novel, Laidlaw is one of the least conventional crime novels I have read, with more inner dialogues than conversations (an issue with some Rebus novels!) and a strong dose of metaphysics on the nature of crime and justice, guilt and punishment. The style is also much more elaborated, to the point I often had to re-read sentences (some of which eventually escaped my understanding) and not only for the phonetic rendering of the Glaswegian accents (which is much more readable than Irvine Welsh’s Trainspotting). The intellectual detective, Laidlaw, is sometimes drawn in heavy traits (like, why should he keep books by Kierkegaard or Camus and Unamuno in his drawer of his desk), prone to bouts of depression and migraine, and, like Rebus, facing a disintegrating marriage and an addiction to alcohol. Not to mention smoking as most characters are chain-smoking. (This aspect as well as the need to resort to phone booths sets the novel back in time.) His relations with the force are even worse than Rebus’, as his provocations of more traditional colleagues leave him mostly isolated and poorly appreciated by his superiors.
The central character may actually be Glasgow itself, so much do the characters move around it and add permanent descriptions of the feeling of the place(s). Far from pretty, it oozes fear and poverty, desperation and bigotry, but also some form of social link, strongly separated between sexes. The appalling status of women (at least of the women appearing in the novel) is subtly denounced by the novel, even though in an ambiguous way. All in all, an impressive book (and not “just” a crime novel).
On the “All about that Bayes” seminar tomorrow (Tuesday 21 at 3p.m., room 42, AgroParisTech, 16 rue Claude Bernard, Paris 5ième), Scott Sisson, School of Mathematics and Statistics at UNSW, and visiting Paris-Dauphine this month, will give a talk on
Approximate posteriors and data for Bayesian inference
Abstract
For various reasons, including large datasets and complex models, approximate inference is becoming increasingly common. In this talk I will provide three vignettes of recent work. These cover a) approximate Bayesian computation for Gaussian process density estimation, b) likelihood-free Gibbs sampling, and c) MCMC for approximate (rounded) data.
As a visiting professor at Paris-Dauphine next month, Pierre Jacob will give a series of lectures on coupling and Monte Carlo. Next month on Feb. 12, 25, 26, 27, at Université Paris-Dauphine, all starting at 13:45 (room yet to be announced). Attendance is open to all and material will be made available on the lecture webpage.
This morning, I had my first parkrun race in Gainesville, before heading back to Paris. (Thanks to Florence Forbes who pointed out this initiative to me.) Which reminded me of the race I ran in Helsinki a few years ago. Without the “self-transcendance” topping…! While the route was very urban, it was a fun opportunity to run a race with a few other runners. My time of 19.56 is not my best by far but, excuses, excuses, I was not feeling too well and the temperature was quite high (21⁰) and I finished in the first three runners, just seconds behind two young fellows who looked like they were still in high school. (I am now holding the record of that race for my age group as well!) Anyway, this is a great way to join races when travelling and not worry about registration, certificates, &tc.
Parkrun also provides an age-grade adjusted ranking (78.8%), which is interesting but statistically puzzling as this is the ratio of one’s time over the fastest time (ever?) in the age x gender category. Given that fastest times are extreme, this depends on one individual and hence has a high variability. Especially in higher (meaning older!) veteran categories. A quantile in the empirical distribution would sound better. I came across this somewhat statistical analysis of the grade,
A board game as Le weekly Monde current mathematical puzzle:
11 players in a circle and 365 tokens first owned by a single player. Players with at least two tokens can either remove one token and give another one left or move two right and one left. How quickly does the game stall, how many tokens are left, and where are they?
The run of a R simulation like
od=function(i)(i-1)%%11+1
muv<-function(bob){
if (max(bob)>1){
i=sample(rep((1:11)[bob>1],2),1)
dud=c(0,-2,1)
if((runif(1)<.5)&(bob[i]>2))dud=c(2,-3,1)
bob[c(od(i+10),i,od(i+1))]=bob[c(od(i+10),i,od(i+1))]+dud
}
bob}
always provides a solution
> bob [1] 1 0 1 1 0 1 1 0 1 0 0
with six ones at these locations. However the time it takes to reach this frozen configuration varies, depending on the sequence of random choices.
