Archive for the Kids Category

a book by C.Robert [not a book review]

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , , , on December 10, 2018 by xi'an

the witchwood crown [book review]

Posted in Books, Kids, pictures with tags , , , , , , on December 1, 2018 by xi'an

As Memory Sorrow and Thorn is a favourite fantasy series of mine, despite its imperfections, I pre-ordered the first volume in the new trilogy of Tad Williams, The witchwood crown, which takes place about fifty years after the events recounted in Memory Sorrow and Thorn. With some of the former characters, obviously [for the humans] getting old. Or ending up dead. This new story is thus very much articulated with respect to the original trilogy and could not be read independently. (I was surprised to see I remember so much of Memory Sorrow and Thorn given that I only read it once!) Overall, the first volume mostly sets the scene, brings in new villains and threats on this Osten Ard universe created by Williams, but does not see too much action, except for the constant traveling of most characters, crisscrossing the land so much that one would deem setting an Osten Ard travel agency as an urgent requirement for the next volume! The most annoying part of this articulation is that, while it avoids sketching these old characters from scratch, they keep running in circles about their live, old times, their position in the society, &tc. In particular, the latent antagonism between the three royal generations is poorly done, the future (?) king being turned into an idiot who does not know anything about the running of the kingdom and the specifics of its northern and southern enemies. The continuing low key bickering between the older royals is equally annoying, not to mention the princess stuck in between, whose role remains unclear till the end! While the overall plot unfolding remains captivating and meeting a few new characters worth reading The witchwood crown, I am still disappointed at the lack of depth of most characters and at the poor editing of the story in this heavy volume. Many threads are now open and it remains to be seen how skillfully Williams manages to spin them into the next book!

Le Monde puzzle [#1078]

Posted in Books, Kids, R with tags , , , , , , on November 29, 2018 by xi'an

Recalling Le Monde mathematical puzzle  first competition problem

Given yay/nay answers to the three following questions about the integer 13≤n≤1300 (i) is the integer n less than 500? (ii) is n a perfect square? (iii) is n a perfect cube?  n cannot be determined, but it is certain that any answer to the fourth question (iv) are all digits of n distinct? allows to identify n. What is n if the answer provided for (ii) was false.

When looking at perfect squares less than 1300 (33) and perfect cubes less than 1300 (8), there exists one single common integer less than 500 (64) and one single above (729). Hence, it is not possible that answers to (ii) and (iii) are both positive, since the final (iv) would then be unnecessary. If the answer to (ii) is negative and the answer to (iii) is positive, it would mean that the value of n is either 512 or 10³ depending on the answer to (i), excluding numbers below 500 since there is no unicity even after (iv). When switching to a positive answer to (ii), this produces 729 as the puzzle solution.

Incidentally, while Amic, Robin, and I finished among the 25 ex-aequos of the competition, none of us reached the subsidiary maximal number of points to become the overall winner. It may be that I will attend the reward ceremony at Musée des Arts et Métiers next Sunday.

data is everywhere

Posted in Kids, pictures, Statistics, University life with tags , , , , , , , , on November 25, 2018 by xi'an

Le Monde puzzle [#1075]

Posted in Books, Kids, R with tags , , , , , , , on November 22, 2018 by xi'an

A Le Monde mathematical puzzle from after the competition:

A sequence of five integers can only be modified by subtracting an integer N from two neighbours of an entry and adding 2N to the entry.  Given the configuration below, what is the minimal number of steps to reach non-negative entries everywhere? Is this feasible for any configuration?

As I quickly found a solution by hand in four steps, but missed the mathematical principle behind!, I was not very enthusiastic in trying a simulated annealing version by selecting the place to change inversely proportional to its value, but I eventually tried and also obtained the same solution:

      [,1] [,2] [,3] [,4] [,5]
   -3    1    1    1    1
    1   -1    1    1   -1
    0    1    0    1   -1
   -1    1    0    0    1
    1    0    0    0    0

But (update!) Jean-Louis Fouley came up with one step less!

      [,1] [,2] [,3] [,4] [,5]
   -3    1    1    1    1
    3   -2    1    1   -2
    2    0    0    1   -2
    1    0    0    0    0

The second part of the question is more interesting, but again without a clear mathematical lead, I could only attempt a large number of configurations and check whether all admitted “solutions”. So far none failed.

Þe Norse farce [design #2]

Posted in Kids, Mountains, pictures with tags , , , , , , , , on November 19, 2018 by xi'an

yenorse_3-e1536588941791.png

X entropy

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , on November 16, 2018 by xi'an

Another discussion on X validated related to the maximum entropy priors and their dependence on the dominating measure μ chosen to define the  score. With the same electrical engineering student as previously. In the wee hours at Casa Matematicà Oaxaca. As I took the [counter-]example of a Lebesgue dominating measure versus a Normal density times the Lebesgue measure producing the same maximum entropy distribution [with obviously the same density wrt to the Lebesgue measure] when the constraints involve the second moment, this confused the student and I spent some time constructing another example with different outcomes, when the Lebesgue measure versus the [artificial] dx/√|x| measure.

I am actually surprised at how limited the discussion of that point occurs in the literature (or at least in my googling attempt). Just a mention made in Bayesian Analysis in Statistics and Econometrics.