Archive for Le Monde

“À l’université, j’étais le matheux qui savait parler aux statisticiens.”

Posted in Books, pictures, University life with tags , , , , , , , on February 19, 2018 by xi'an

This weekend edition of Le Monde had [most of] Cédric Villani as its cover story. Mostly about his new career as a representative of Orsay at the French Parliament. And a member of the presidential majority. But the weekend edition being the weekend edition, it cannot escape its glossy tendencies and rather than focussing on the political agenda and achievements of the député, including a radical restructuring of the maths curriculum in French high schools, or maybe even his position on the harsh stance of the Macron government on migrants and refugees, Le Monde spends most of the article on the extra-ordinary personality of Villani.  Paris-Match-like. Which leads to quote as the one below, where I find myself at a loss on how to interpret this “ability to speak to statisticians”…!

impossible estimation

Posted in Books, Statistics with tags , , , , , , , , , , , on January 29, 2018 by xi'an

Outside its Sciences & Médecine section that I most often read, Le Monde published last weekend a tribune by the anthropologist Michel Naepels [who kindly replied to my email on his column] on the impossibility to evaluate the number of deaths in Congo due to the political instability (a weak and undemocratic state fighting armed rebel groups), for lack of a reliable sample. With a huge gap between two estimations of this number, from 200,000 to 5.4 million excess deaths. In the later, IRC states that “only 0.4 percent of all deaths across DR Congo were attributed directly to violence”. Still, diverging estimates do not mean numbers are impossible to produce, just that more elaborate methods like those developed by Rebecca Steorts for Syrian deaths must be investigated. Which requires more means than those available to the local States (assuming they are interested in the answer) or to NGOs. This also raises the question whether or not “excess deaths” has an absolute meaning, since it refers to an hypothetical state of the world that has not taken place.

On the same page, another article written by geographers shed doubt on predictive policing software, not used in France, if not so clearly as in the Significance article by Kristian Lum and William Isaac last year.

science tidbits

Posted in Books, Kids, pictures, Travel, University life with tags , , , , , , , , , , on January 28, 2018 by xi'an

Several interesting entries in Le Monde Science & Médecine of this week (24 Jan 2018):

  1. This incredible report in the Journal of Ethnobiology of fire-spreading raptors, Black Kite, Whistling Kite, and Brown Falcon, who carry burning material to start fires further away and thus expose rodents and insects. This behaviour was already reported in some Aboriginal myths, as now backed up by independent observations.
  2. A report by Etienne Ghys of the opening of a new CNRS unit in mathematics in… London! The Abraham de Moivre Laboratory is one of the 36 mixed units located outside France to facilitate exchanges and collaborations. In the current case, in collaboration with Imperial. And as a mild antidote to Brexit and its consequences on exchanges between the UK and the EU. (When discussing Martin Hairer’s conference, Etienne forgot to mention his previous affiliation with Warwick.)
  3. A good-will-bad-stats article on the impact of increasing the number of urban bicycle trips to reduce the number of deaths. With the estimation that if 25% of the daily trips over 167 European (and British!) cities were done by bike, 10,000 deaths per year could be avoided! I have not read the original study, but I wonder at the true impact of this increase. If 25% of the commutes are made by bike, the remaining 75% are not and hence use polluting means of transportation. This means more citizens travelling by bike are exposed to the exhausts and fumes of cars, buses, trucks, &tc. Which should see an increase in respiratory diseases, including deaths, rather than a decrease. Unless this measure is associated with banning all exhaust emissions from cities, which does not sound a very likely outcome, even in Paris.
  4. An incoming happening at Cité internationale des Arts in Paris, on Feb 2-3, entitled “we are not the number we believe we are” (in French), based on the universe(s) of Ursula Le Guin who most sadly passed away the day the journal came out.
  5. A diffusion of urban riots in the suburbs of Paris in 2005 that closely follows epidemiological models of flu epidemics, using “a single sociological variable characterizing neighbourhood deprivation”. (Estimation of the SIR model is apparently done by maximum likelihood and model comparison by AIC, given the ODE nature of the models, ABC would have been quite appropriate for a Bayesian modelling!)

Le Monde puzzle [#1037]

Posted in Books, Kids, R with tags , , , , , , , on January 24, 2018 by xi'an

lemondapariA purely geometric Le Monde mathematical puzzle this (or two independent ones, rather):

Find whether or not there are inscribed and circumscribed circles to a convex polygon with 2018 sides of lengths ranging 1,2,…,2018.

In the first (or rather second) case, the circle of radius R that is tangential to the polygon and going through all nodes (assuming such a circle exists) is such that a side L and its corresponding inner angle θ satisfy

L²=R²2(1-cos(θ))

leading to the following R code

R=3.2e5
step=1e2
anglz=sum(acos(1-(1:2018)^2/(2*R^2)))
while (abs(anglz-2*pi)>1e-4){
R=R-step+2*step*(anglz>2*pi)*(R>step)
anglz=sum(acos(1-(1:2018)^2/(2*R^2))) 
step=step/1.01}

and the result is

> R=324221
> sum(acos(1-(1:2018)^2/(2*R^2)))-2*pi
[1] 9.754153e-05

(which is very close to the solution of Le Monde when replacing sin(α) by α!). The authors of the quoted paper do not seem to consider the existence an issue.

In the second case, there is a theorem that states that if the equations

x¹+x²=L¹,…,x²⁰¹⁸+x¹=L²⁰¹⁸

have a solution on R⁺ then there exists a circle such that the polygon is tangential to this circle. Quite interestingly, if the number n of sides is even there are an infinitude of tangential polygons if any.  Now, and rather obviously, the matrix A associated with the above system of linear equations is singular with a kernel induced by the vector (1,-1,…,1,-1). Hence the collection of the sides must satisfy

L¹-L²…+L²⁰¹⁷-L²⁰¹⁸ =0

which puts a constraint on the sequence of sides, namely to divide them into two groups with equal sum, 2018×2019/4, which is not an integer. Hence, a conclusion of impossibility! [Thanks to my office neighbours François and Julien for discussing the puzzle with me.]

death notice from Bourbaki

Posted in Statistics with tags , , , , , on January 21, 2018 by xi'an

Le Monde puzzle [#1036]

Posted in Books, Kids, R with tags , , , , on January 4, 2018 by xi'an

lemondapariAn arithmetic Le Monde mathematical puzzle to conclude 2017:

Find (a¹,…,a¹³), a permutation of (1,…,13) such that

a¹/a²+a³=a²+a³/a³+a⁴+a⁵=b¹<1
a⁶/a⁶+a⁷=a⁶+a⁷/a⁷+a⁸+a⁹=a⁷+a⁸+a⁹/a⁵+a⁹+a¹⁰=b²<1
a¹¹+a¹²/a¹²+a¹³=a¹²+a¹³/a¹³+a¹⁰=b³<1

The question can be solved by brute force simulation, checking all possible permutations of (1,…,13). But 13! is 6.6 trillion, a wee bit too many cases. Despite the problem being made of only four constraints and hence the target function taking only five possible values, a simulated annealing algorithm returned a solution within a few calls:

(a¹,…,a¹³)=(6,1,11,3,10,8,4,9,5,12,7,2,13)
(b¹,b²,b³)=(1/2,2/3,3/5)

using the following code:

checka=function(a){ #target to maximise
 return(1*(a[1]/sum(a[2:3])==sum(a[2:3])/sum(a[3:5]))+
  1*(sum(a[6:7])/sum(a[7:9])==a[6]/sum(a[6:7]))+
  1*(sum(a[7:9])/(a[5]+sum(a[9:10]))==a[6]/sum(a[6:7]))+
  1*(sum(a[11:12])/sum(a[12:13])==sum(a[12:13])/
    (a[10]+a[13])))}
parm=sample(1:13)
cheka=checka(parm)
beta=1
for (t in 1:1e6){
  qarm=parm
  idx=sample(1:13,sample(2:12))
  qarm[idx]=sample(qarm[idx])
  chekb=checka(qarm)
  if (log(runif(1))<beta*(chekb-cheka)){
     cheka=chekb;parm=qarm}
  beta=beta*(1+log(1.00001))
  if (cheka==4) break()}

Le Monde puzzle [#1033]

Posted in Books, Kids, R with tags , , , , on December 19, 2017 by xi'an

lemondapariA simple Le Monde mathematical puzzle after two geometric ones I did not consider:

  1. Bob gets a 2×3 card with three integer entries on the first row and two integer entries on the second row such that (i) entry (1,1) is 1, (ii) summing up subsets of adjacent entries produces all integers from 1 to 21. (Adjacent means sharing an index.) Deduce Bob’s voucher.
  2.  Alice gets Bob’s voucher completed into a 2×4 card with further integer entries. What is the largest value of N such that all integers from 1 to N are available through summing up all subsets of entries?

The first question only requires a few attempts but it can be solves by brute force simulation. Here is a R code that leads to the solution:

alsumz<-function(sol){return( 
  c(sol,sum(sol[1:2]),sum(sol[2:3]),sum(sol[4:5]),
  sum(sol[c(1,4)]), sum(sol[c(1,5)]),sum(sol[1:3]),
  sum(sol[c(1,4,5)]),sum(sol[c(1,2,5)]),
  sum(sol[c(2,4,5)]), sum(sol[c(1,2,3,5)]),sum(sol[2:5]), 
  sum(sol[c(1,2,4)]),sum(sol[c(1,2,4,5)]),sum(sol[1:4]),
  sum(sol)),sum(sol[c(2,3,5)]))}

produces (1,8,7,3,2) as the only case for which

(length(unique(alsum(sol)))==21)

The second puzzle means considering all sums and checking there exists a solution for all subsets. There is no constraint in this second question, hence on principle this could produce N=2⁸-1=255, but I have been unable to exceed 175 through brute force simulation. (Which entitled me to use the as.logical(intToBits(i) R command!)