dire new semester, indeed…

Le Monde puzzle [#1152]

The weekly puzzle from Le Monde is a tournament classic:

An even number of teams play one another once a week with no tie allowed and have played all other teams. Four weeks into the tournament, A has won all its games, B,C, and D have won three games, the other teams have won at least one games. What is the minimum number of teams? Show an instance.

By sheer random search

tnmt=function(K=10,gamz=4){
 t1=t0=matrix(1,K,K)
tnmt=function(K=10,gamz=4){
 tnmt=t0=matrix(0,K,K)
 while (!prod(apply(tnmt^2,1,sum)==4)){
   tnmt=t0
   for (i in 1:(K-2)){
     if((a<-gamz-sum(tnmt[i,]^2))> K-i-1) break()
     if(a>0){
      j=sample((i+1):K,a)
      tnmt[i,j]=sample(c(-1,1),a,rep=TRUE)
      tnmt[j,i]=-tnmt[i,j]}}}
 tnmt}
chck=function(1,gamz=4){
    sumz=apply(tnmt,1,sum)
    max(sumz)==gamz&
    sum(sumz==2)>2&
    min(sumz)>-gamz}

I found that 8 teams were not producing an acceptable game out of 10⁶ tries. Here is a solution for 9 teams:

       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
 [1,]             -1   -1         1             -1
 [2,]             -1         1        -1        -1
 [3,]    1    1                   1             -1
 [4,]    1                   1         1   -1     
 [5,]        -1        -1                   1   -1
 [6,]   -1        -1                  -1    1     
 [7,]         1        -1         1         1     
 [8,]                   1   -1   -1   -1     
 [9,]    1    1    1         1

where team 9 wins all four games, 7,4 and 3, win three games, and the other 4 teams win one game. Which makes sense since this is a zero sum game, with a value of 10 over the four top teams and 2(N-4)=10 if no team has two wins (adding an even number of such teams does not change the value of the game).

Notre-Dame-de-Paris analysed by Andrew [not a book review]

As reported in Le Monde, Alexander van Geen, Yuling Yao, Tyler Ellis, and Andrew Gelman wrote a paper analysing the impact of the destruction of Notre-Dame last year in terms of lead concentration in the ground. As 460 tons of lead from the roof melted overnight. Based on  100 samples of surface soil collected by one author (not Andrew!) from tree pits, parks, and other sites in all directions within 1 km of the cathedral. Here is a plain language summary of the findings.

“This study attempts to estimate the extent to which the population of Paris was exposed to lead as a result of the Notre‐Dame cathedral fire of April 15, 2019. The concern stems from the large quantity of lead that covered the cathedral, some of which was injected into the air by the fire for several hours. In order to evaluate how much lead rising from the fire was redeposited nearby, surface soil samples were collected in all directions within a 1 km radius of the cathedral. Elevated levels of lead observed downwind of the cathedral indicate that surface soil preserved the mark of lead fallout from the fire. Although the estimated amount of lead redeposited within 1 km corresponds to only a small fraction of the total covering the cathedral, it could have posed a health hazard to children located downwind for a limited amount of time. Environmental testing on a larger scale immediately after the fire could have provided a more timely assessment of the scale of the problem and resulted in more pointed advice to the surrounding population on how to limit exposure to the fallout of lead.”

The statistical modelling is one of a spatial pattern of the lead distribution, using a mean-zero Gaussian process prior. And of a discretisation of the neighbourhood of the cathedral into uniform 30×30 locations. Without any further input, the model identifies properly the direction of the wind on that fateful evening. And logically concludes to a higher exposure than measured weeks after the fire. (Minor quibbles: a bias in self-declared test toward “a more educated, wealthier segment of the population” is unlikely in the immediate neighbourhood of Notre-Dame where the average flat sells at 16,000 euros per m², and the LCPP (Laboratoire Central de la Préfecture de Police) is not affiliated with the City of Paris but the Ministry of the Interior.)

a journal of the plague year [deconfited reviews]

Found a copy of Humans by Donald Westlake on the book sharing shelves at Dauphine. And read it within a few hours, as it is very light reading but quite funny nonetheless. If hardly ranking as a mystery novel. Or crime novel, unless the crime is Gaiacide and the criminal God. Reminded me of the equally light Bobby Dollar series by Tad Williams. As the main character is an angel, falling for humans as he tries to steer them towards the Armageddon. The setting is the early 1990s, with the main scares being atomic disaster (Chernobyl) and the AIDS pandemic. Plus the rise of environmental worries and of Chinese autocracy. I put it back on the shelves on my next visit to Dauphine, hopefully for someone else to enjoy!

Baked radish stems with basil for making pesto, with a bit more bitterness than usual. Cooked plenty of fennel since this is fennel season. Continued making my weekly rhubarb preserve. Keeping the garden active, now watching squash vines invading new territory, hopefully with an eatable reward in the Fall. Tomatoes are growing incredibly fast as well..! Saw another fox in the Parc before official opening times, quite close if speeding away from me and barely avoiding bumping in a pair of greyhounds which fortunately sounded completely unconcerned.

Watched Children of Men after an exhausting week online for a grant panel. While a parabola for the coming collapse of civilisation under political, biological and environmental apocalypses [is there any meaning to use apocalyse in the plural tense!?] and a premonitory tale on Brexit and the buttressing of Britain [or Trump and his Big Wall mania] induced by anti-immigrant rethorics, the film is over the top in terms of plot and action, with symbolism taking over realism, even on the slightest degree, every shot being filled with references to religions and arts (like the Pink Floyd flying pig), to previous environmental disasters (with long shots of burning cows reminiscent of the mad cow crisis) and geo-political upheavals (including a Hamas type protest in the refugee camp, with a short appearance of a jeep with a French flag more reminiscent of the liberation of Paris in August 1944). Characters are charicaturesque, with a very Manichean division between very few good ones and mostly bad ones. The most ridiculous part of the scenario may well be the battle scene in the refugee camp [tanks versus pistols!]… Once again stunned by all the awards and praise piled upon that film.

Read two more volumes of the Witcher [bought during BayesComp for my son!]. One being Sword of Destiny and a series of short stories, like the first volume. The second Blood of Elves and the beginning of the novels. The first season on TV borrows mostly from the first two collections of short stories. Which are somewhat better than the novel, as the latter is very slow paced and overly sentimental. Not terrible, mind.

Completed with uttermost reluctance the Horde du Contrevent [translating as the windwalkers] by Alain Damasio (no English translation available, but an Italian version, l’Orda del Vento,  is). Book that I again picked for figuring in Le Monde 100 bes&tc list! And felt like constantly fronting a strong, icy wind when going through the pages of that unusual book. The style is unpleasant and rather pretentious, with numerous puns in French.. The story is one of a (religious? mystical?) group walking against the wind(s) for decades to reach the source of these winds and to find the last types of wind no one has ever met. Their dreary pilgrimage is described by the 23 membres of the group, called the Horde, with a heavy-handed typographical symbol at the start of each paragraph identifying who’s speaking (and a convenient page marker with all these symbols). A bit heavy handed as a polyphonic novel (appropriately composed in a Corsican retreat!) and even more in the crypt-Nietschean philosophy it carries… The background universe there is somehow eco-steam-punk, with the wind producing most of the energy. The most exciting part involves rather realistic ice climbing. However, I clearly stand in the small minority of those less than impressed by the book as it is highly popular among French readers, one of the highest printings in the Folio collection, with side products a BD (above) and a movie (in the making?). (And enough votes from fans to almost reach the 10 most favourite novels in Le Monde list. )

Le Monde puzzle [#1149]

The weekly puzzle from Le Monde is a leaking variant on an old puzzle:

Three buckets have capacities of 8, 5 and 3 litres, respectively. At the start of the game, the 8 litre bucket is full and both others are empty. Aiming at reaching exactly 4 litres in one bucket, water is transferred between buckets. However, a fraction 1/k is lost with each transfer. If k=9, it is possible to reach 4 litres in three operations? If k=7, is it at all possible to reach 4 litres?

By sheer random search

k=1/5
z=c(8,5,3)
m<-function(s){
  i=sample(1:3,2)
  s[i]=s[i]+ifelse(
   rep((a<-z[i[1]]-s[i[1]])<(b<-s[i[2]])*(1-k),2),
   a*c(1,-1-k),b*c(1-k,-1))
  s}

I found that most fractions allow to reach 4 litres starting with k=2. (And am unsure the missing ones, like 18 or 21 are not due to a lack of luck… In particular, for k=9, the shortest path is

 8.000    0 0
 2.375    5 0
 0.000    5 2.11
 0.000    4 3