## trick or treat?!

Posted in Kids, pictures, Travel, Wines with tags , , , on September 24, 2016 by xi'an

Two weeks ago, we went to a local restaurant, connected to my running grounds, for dinner. While the setting in a 16th building that was part of the original Sceaux castle was quite nice, the fare was mediocre and the bill more suited for a one star Michelin than dishes I could have cooked myself. The height (or rather bottom) of the meal was a dish of sardines consisting in an half-open pilchard can… Just dumped on a plate with a slice of bread. It could have been a genius stroke from the chef had the sardines been cooked and presented in the can, alas it sounded more like the act of an evil genie! Or more plainly a swindle. As those tasty sardines came straight from the shop!

## an inverse permutation test

Posted in Books, Kids, R, Statistics with tags , , , , on September 23, 2016 by xi'an

A straightforward but probabilistic riddle this week in the Riddler, which is to find the expected order of integer i when the sequence {1,2,…,n} is partitioned at random into two sets, A and B, each of which is then sorted before both sets are merged. For instance, if {1,2,3,4} is divided in A={1,4} and B={2,3}, the order of 2 in {1,4,2,3} is 3. An R rendering of the experiment is

m=rbinom(1,n,.5)
if (m*(n-m)>0){
fist=sort(sample(1:n,m))
return(order(c(fist,sort((1:n)[-fist])))[i])
}else{
return(i)}
[\sourcecode]

It is rather easy to find that the probability that the order of i takes the value j is

${i-1 \choose j-1}(1/2)^i$

if j<i (i is in A) and

${n-i \choose n-j}(1/2)^{n-i+1}$

if $j>i$ (i is in B), the case i=j being the addition of both cases, but the mean can be found (almost) immediately by considering that, when i is in A, its average value is (i+1)/2 and when it is in B, its average value is (n+i)/2 [by symmetry]. Hence a global mean of (2i+n+1)/4….

## snapshots from Nature

Posted in Books, Kids, pictures, University life with tags , , , , , , , , , , on September 19, 2016 by xi'an

Among many interesting things I read from the pile of Nature issues that had accumulated over a month of travelling, with a warning these are mostly “old” news by now!:

• the very special and untouched case of Cuba in terms of the Zika epidemics, thanks to a long term policy fighting mosquitoes at all levels of the society;
• an impressive map of the human cortex, which statistical analysis would be fascinating;
• an excerpt from Nature 13 August 1966 where the Poisson distribution was said to describe the distribution of scores during the 1966 World Cup;
• an analysis of a genetic experiment on evolution involving 50,000 generations (!) of Escherichia coli;
• a look back at the great novel Flowers for Algernon, novel I read eons ago;
• a Nature paper on the first soft robot, or octobot, along with some easier introduction, which did not tell which kind of operations could be accomplished by such a robot;
• a vignette on a Science paper about the interaction between honey hunters and hunting birds, which I also heard depicted on the French National Radio, with an experiment comparing the actual hunting (human) song, a basic sentence in the local language, and the imitation of the song of another bird. I could not understand why the experiment did not include hunting songs from other hunting groups, as they are highly different but just as effective. It would have helped in understanding how innate the reaction of the bird is;
• another literary entry at the science behind Mary Shelley’s Frankenstein;
• a study of the Mathematical Genealogy Project in terms of the few mathematicians who started most genealogies of mathematicians, including d’Alembert, advisor to Laplace of whom I am one of the many descendants, although the finding is not that astounding when considering usual genealogies where most branches die off and the highly hierarchical structure of power in universities of old.

## The Magicians [book review]

Posted in Books, Kids, Travel, Wines with tags , , , , , , , , , on September 17, 2016 by xi'an

While in Melbourne, I heard a recommendation for Lev Grossman’s The Magicians and the next day, while checking the Melbourne Writers Festival bookstore, found the book (rather than the Kristoff volume I was seeking), bought it, and read it within a few days.

‘Brakebills will remind readers of Hogwarts, though with more illicit fondling. Grossman has written what could crudely be labeled a Harry Potter for adults.” , NYT

So is this an Harry Potter for adults?! First, I think Harry Potter can be read by adults (if I qualify as adult!). This remark presumably means the book should not be read by young readers, maybe, due to recurrent sex and alcohol consumption, plus some drugs and an overall depressive tone.

Back to Harry Potter, there is the same magical boarding school feeling, even though it is located in upstate New York on the Hudson river.  And not in Scotland. With an equivalent to Quidditch, an evil magician, exams, surly teens, one or two love triangles, &tc. If in a more modern and American way. The difference with Harry Potter is that it also doubles as Narnia! A Narnia eventually turned wrong and sour, but nonetheless a strong similarity of stories and ideas. Of course, this parallel could be seen as an attempt at deconstruction, exhibiting the inconsistencies in the original novels, but it is so subtle it does not feel like it. There are the same encounters with sentient animal creatures, who never reappear after, the same call for Kings and Queens, as in Narnia. This lack of depth at exploring the connections between Harry Potter, Narnia and even some aspects of the Wheel of Time is frustrating in that something great could have come of it. And then… then… comes the worst literary trick in my list, the call to a subterranean quest with endless monsters and accidents! (I obviously exclude Tolkien’ Moria episode from this list!!!) Concluding with the evil character dumping information in the last battle to explain missing bits and pieces in the story.

So, in conclusion, not such a magical book, even though I read it within a few days thanks to my 39 hour trip back to Paris. The Magicians remains too teeny for my taste, hearing self-deprecating depressive monologues occurs way too often to make the main character congenial, and the story has not enough depth or structure to be compelling. A reviewer rightly pointed out it feels like fandom fiction. Rather than a universe on its own. (As for instance Aaronovitch’ Rivers of London series.)

## random walk on a torus [riddle]

Posted in Books, Kids, pictures with tags , , , , , , , , , on September 16, 2016 by xi'an

The Riddler of this week(-end) has a simple riddle to propose, namely given a random walk on the {1,2,…,N} torus with a ⅓ probability of death, what is the probability of death occurring at the starting point?

The question is close to William Feller’s famous Chapter III on random walks. With his equally famous reflection principle. Conditioning on the time n of death, which as we all know is definitely absorbing (!), the event of interest is a passage at zero, or any multiple of N (omitting the torus cancellation), at time n-1 (since death occurs the next time). For a passage in zero, this does not happen if n is even (since n-1 is odd) and else it is a Binomial event with probability

${n \choose \frac{n-1}{2}} 2^{-n}$

For a passage in kN, with k different from zero, kN+n must be odd and the probability is then

${n \choose \frac{n-1+kN}{2}} 2^{-n}$

which leads to a global probability of

$\sum_{n=0}^\infty \dfrac{2^n}{3^{n+1}} \sum_{k=-\lfloor (n-1)/N \rfloor}^{\lfloor (n+1)/N \rfloor} {n \choose \frac{n-1+kN}{2}} 2^{-n}$

i.e.

$\sum_{n=0}^\infty \dfrac{1}{3^{n+1}} \sum_{k=-\lfloor (n-1)/N \rfloor}^{\lfloor (n+1)/N \rfloor} {n \choose \frac{n-1+kN}{2}}$

Since this formula is rather unwieldy I looked for another approach in a métro ride [to downtown Paris to enjoy a drink with Stephen Stiegler]. An easier one is to allocate to each point on the torus a probability p[i] to die at position 1 and to solve the system of equations that is associated with it. For instance, when N=3, the system of equations is reduced to

$p_0=1/3+2/3 p_1, \quad p_1=1/3 p_0 + 1/3 p_1$

which leads to a probability of ½ to die at position 0 when leaving from 0. When letting N grows to infinity, the torus structure no longer matters and the probability of dying at position 0 implies returning in position 0, which is a special case of the above combinatoric formula, namely

$\sum_{m=0}^\infty \dfrac{1}{3^{2m+1}} {2m \choose m}$

which happens to be equal to

$\dfrac{1}{3}\,\dfrac{1}{\sqrt{1-4/9}}=\dfrac{1}{\sqrt{5}}\approx 0.4472$

as can be [unnecessarily] checked by a direct R simulation. This √5 is actually the most surprising part of the exercise!

## Darwin’s radio [book review]

Posted in Books, Kids, pictures, University life with tags , , , , , , , , , , , , , , , , on September 10, 2016 by xi'an

When in Sacramento two weeks ago I came across the Beers Books Center bookstore, with a large collection of used and (nearly) new cheap books and among other books I bought Greg Bear’s Darwin Radio. I had (rather) enjoyed another book of his’, Hull Zero Three, not to mention one of his first books, Blood Music, I read in the mid 1980’s, and the premises of this novel sounded promising, not mentioning the Nebula award. The theme is of a major biological threat, apparently due to a new virus, and of the scientific unraveling of what the threat really means. (Spoilers alert!) In that respect it sounds rather similar to the (great) Crichton‘s The Andromeda Strain, which is actually mentioned by some characters in this book. As is Ebola, as a sort of contrapoint (since Ebola is a deadly virus, although the epidemic in Western Africa now seems to have vanished). The biological concept exploited here is dormant DNA in non-coding parts of the genome that periodically get awaken and induce massive steps in the evolution. So massive that carriers of those mutations are killed by locals. Until the day it happens in an all-connected World and the mutation can no longer be stopped. The concept is compelling if not completely convincing of course, while the outcome of a new human race, which is to Homo Sapiens what Homo Sapiens was to Neanderthal, is rather disappointing. (How could it be otherwise?!) But I did appreciate the postulate of a massive and immediate change in the genome, even though the details were disputable and the dismissal of Dawkins‘ perspective poorly defended. From a stylistic perspective, the style is at time heavy, while there are too many chance occurrences, like the main character happening to be in Georgia for a business deal (spoilers, spoilers!) at the times of the opening of collective graves, or the second main character coming upon a couple of Neanderthal mummies with a Sapiens baby, or yet this pair of main characters falling in love and delivering a live mutant baby-girl. But I enjoyed reading it between San Francisco and Melbourne, with a few hours of lost sleep and work. It is a page turner, no doubt! I also like the political undercurrents, from riots to emergency measures, to an effective dictatorship controlling pregnancies and detaining newborns and their mothers.

One important thread in the book deals with anthropology digs getting against Native claims to corpses and general opposition to such digs. This reminded me of a very recent article in Nature where a local Indian tribe had claimed rights to several thousand year old skeletons, whose DNA was then showed to be more related with far away groups than the claimants. But where the tribe was still granted the last word, in a rather worrying jurisprudence.

## art brut

Posted in Kids, Mountains, pictures, Travel with tags , , , , , on September 9, 2016 by xi'an