Archive for Montpellier

Le Monde puzzle [#1083]

Posted in Books, Kids, R, Travel with tags , , , , , , on February 7, 2019 by xi'an

A Le Monde mathematical puzzle that seems hard to solve without the backup of a computer (and just simple enough to code on a flight to Montpellier):

Given the number N=2,019, find a decomposition of N as a sum of non-trivial powers of integers such that (a) the number of integers in the sum is maximal or (b) all powers are equal to 4.  Is it possible to write N as a sum of two powers?

It is straightforward to identify all possible terms in these sums by listing all powers of integers less than N

pool=(1:trunc(sqrt(2019)))^2
for (pow in 3:11)
  pool=unique(c(pool,(2:trunc(2019^(1/pow)))^pow))

which leads to 57 distinct powers. Sampling at random from this collection at random produces a sum of 21 perfect powers:

 1+4+8+9+16+25+27+32+36+49+64+81+100+121+125+128+144+169+196+243+441

But looking at the 22 smallest numbers in the pool of powers leads to 2019, which is a sure answer. Restricting the terms to powers of 4 leads to the sequence

1⁴+2⁴+3⁴+5⁴+6⁴ = 2019

And starting from the pools of all possible powers in a decomposition of 2019 as the sum of two powers shows this is impossible.

Grange Thieri [Pic Saint-Loup]

Posted in Wines with tags , , , , , on December 20, 2018 by xi'an

Grès de Montpellier [Mas de Lunès]

Posted in Kids, pictures, Travel, Wines with tags , , , , , , on September 20, 2018 by xi'an

Pic Saint Loup [Clos Marie]

Posted in Travel, Wines with tags , , , , , , on July 20, 2018 by xi'an

Domaine Mortiès

Posted in pictures, Wines with tags , , , , , on April 20, 2018 by xi'an

Domaine de Montcalmès

Posted in Statistics with tags , , , , , , , , on November 20, 2017 by xi'an

crowd-based peer review

Posted in Statistics with tags , , , , , , , , , , on June 20, 2017 by xi'an

In clear connection with my earlier post on Peer Community In… and my visit this week to Montpellier towards starting a Peer Community In Computational Statistics, I read a tribune in Nature (1 June, p.9) by the editor of Synlett, Benjamin List, describing an experiment conducted by this journal in chemical synthesis. The approach was to post (volunteered) submitted papers on a platform accessible to a list of 100 reviewers, nominated by the editorial board, who could anonymously comment on the papers and read others’ equally anonymous comments. With a 72 hours deadline! According to Benjamin List (and based on  a large dataset of … 10 papers!), the outcome of the experiment is one of better quality return than with traditional reviewing policies. While Peer Community In… does not work exactly this way, and does not aim at operating as a journal, it is exciting and encouraging to see such experiments unfold!