Archive for stochastic algorithms

Le Monde puzzle [#1068]

Posted in Books, Kids, R with tags , , , , , , on October 3, 2018 by xi'an

A purely (?) algorithmic Le Monde mathematical puzzle

For the table below, what is the minimal number of steps required to reach equal entries when each step consists in adding ones to three entries sitting in a L, such as (7,11,12) or (5,6,10)? Same question for the inner table of four in yellow.

For the inner table, this is straightforward as there are four possible L’s, three equations like 6+n⁶=7+n⁷,  and two degrees of freedom leading to a unique entry of N=13 (impossible!)  or 16 (feasible). Hence adding 10 L’s. For the entire table, summing up all entries after completion leads to 16N, which is also equal to 1+3+3+…+16+M, where M is the number of added L’s, itself equal to 138+3O, if O denotes the number of ones added. Hence M can only take the values 18, 21, … It took me quite a while to R code an approach to complete the table into 16 18’s, as my versions of simulated annealing did not seem to converge. In the end, I used a simplified version where the table was completed by multinomial draws, like a M(17;3⁻¹,3⁻¹,3⁻¹) for the upper left corner, corresponding to random draws of one of the 36 available L’s, which should be used 50 times in total, and then augmented or reduced of one L depending on the value at a randomly selected entry. Leading to the result

> aneal(grid=c(1,3,3:13,15,15,16),maxT=1e5)
 [1] 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18

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journée algorithmes stochastiques à Dauphine vendredi

Posted in Statistics, University life with tags , , , , , , , , , , on November 28, 2017 by xi'an

A final reminder (?) that we hold a special day of five talks around stochastic algorithms at Dauphine this Friday, from 10:00 till 17:30. Attendance is free, coffee and tea are free (while they last!), come and join us!

Journée algorithmes stochastiques

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , on September 27, 2017 by xi'an

On December 1, 2017, we will hold a day workshop on stochastic algorithms at Université Paris-Dauphine, with the following speakers

 Details and abstracts of the talks are available on the workshop webpage. Attendance is free, but registration is requested towards planning the morning and afternoon coffee breaks. Looking forward seeing ‘Og’s readers there, at least those in the vicinity!

And while I am targetting Parisians, crypto-Bayesians, and nearly-Parisians, there is another day workshop on Bayesian and PAC-Bayesian methods on November 16, at Université Pierre et Marie Curie (campus Jussieu), with invited speakers

and a similar request for (free) registration.