Articles by xi'an

Le Monde puzzle [#1063]

August 8, 2018 | xi'an

A simple (summertime?!) arithmetic Le Monde mathematical puzzle A “powerful integer” is such that all its prime divisors are at least with multiplicity 2. Are there two powerful integers in a row, i.e. such that both n and n+1 are powerful?  Are there odd integers n such that n² – 1 is ...
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Le Monde puzzle [#1062]

July 27, 2018 | xi'an

A simple Le Monde mathematical puzzle none too geometric: Find square triangles which sides are all integers and which surface is its perimeter. Extend to non-square rectangles. No visible difficulty by virtue of Pythagore’s formula: for (a in 1:1e4) for (b in a:1e4) if (a*b==2*(a+b+...
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Le Monde puzzle [#1061]

July 19, 2018 | xi'an

A griddy Le Monde mathematical puzzle: On a 4×5 regular grid, find how many nodes need to be turned on to see all 3×4 squares to have at least one active corner in case of one arbitrary node failing.  Repeat for a 7×9 grid. The question is open to simulated annealing, as in ...
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Hamiltonian tails

July 16, 2018 | xi'an

“We demonstrate HMC’s sensitivity to these parameters by sampling from a bivariate Gaussian with correlation coefficient 0.99. We consider three settings (ε,L) = {(0.16; 40); (0.16; 50); (0.15; 50)}” Ziyu Wang, Shakir Mohamed, and Nando De Freitas. 2013 In an experiment with my PhD student Changye Wu (who wrote all R codes used below), we […]
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a thread to bin them all [puzzle]

July 8, 2018 | xi'an

The most recent riddle on the Riddler consists in finding the shorter sequence of digits (in 0,1,..,9) such that all 10⁴ numbers between 0 (or 0000) and 9,999 can be found as a group of consecutive four digits. This sequence is obviously longer than 10⁴+3, but how long? On my trip to Brittany last weekend, […]
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seven digit addition

July 5, 2018 | xi'an

Another quick riddle from the riddler: solve the equation EXMREEK + EHKREKK = ?K?H?X?E which involves every digit between 0 and 9. While the puzzle can be unravelled by considering first E and K, which must be equal to 6 and 3, a simple R code also leads to the conclusion isok [Read more...]

hitting a wall

July 4, 2018 | xi'an

Once in a while, or a wee bit more frequently (!), it proves impossible to communicate with a contributor of a question on X validated. A recent instance was about simulating from a multivariate kernel density estimate where the kernel terms at x¹,x²,… are Gaussian kernels applied to the inverses ...
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Bayesian GANs [#2]

June 26, 2018 | xi'an

As an illustration of the lack of convergence of the Gibbs sampler applied to the two “conditionals” defined in the Bayesian GANs paper discussed yesterday, I took the simplest possible example of a Normal mean generative model (one parameter) with a logistic discriminator (one parameter) and implemented the scheme (during ...
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Le Monde puzzle [#1053]

June 20, 2018 | xi'an

An easy arithmetic Le Monde mathematical puzzle again: If coins come in units of 1, x, and y, what is the optimal value of (x,y) that minimises the number of coins representing an arbitrary price between 1 and 149?  If the number of units is now four, what is the optimal choice? ...
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a chain of collapses

June 19, 2018 | xi'an

A quick riddler resolution during a committee meeting (!) of a short riddle: 36 houses stand in a row and collapse at times t=1,2,..,36. In addition, once a house collapses, the neighbours if still standing collapse at the next time unit. What are the shortest and longest lifespans of this row? Since ...
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maximal spacing around order statistics [#2]

June 7, 2018 | xi'an

The proposed solution of the riddle from the Riddler discussed here a few weeks ago is rather approximative, in that the distribution of when the n-sample is made of iid Normal variates is (a) replaced with the distribution of one arbitrary minimum and (b) the distribution of the minimum is ...
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Le Monde puzzle [#1051]

May 17, 2018 | xi'an

A combinatoric Le Monde mathematical puzzle of limited size: When the only allowed move is to switch two balls from adjacent boxes, what is the minimal number of moves to return all balls in the above picture to their respective boxes? Same question with six boxes and 12 balls. The question ...
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maximal spacing around order statistics

May 16, 2018 | xi'an

The riddle from the Riddler for the coming weeks is extremely simple to express in mathematical terms, as it summarises into characterising the distribution of when the n-sample is made of iid Normal variates. I however had a hard time finding a result connected with this quantity since most available ...
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the riddle of the stands

May 10, 2018 | xi'an

The simple riddle of last week on The Riddler, about the minimum number of urinals needed for n men to pee if the occupation rule is to stay as far as possible from anyone there and never to stand next to another man,  is quickly solved by an R code: ...
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Imperial postdoc in Bayesian nonparametrics

April 27, 2018 | xi'an

Here is another announcement for a post-doctoral position in London (UK) to work with Sarah Filippi. In the Department of Mathematics at Imperial College London. (More details on the site or in this document. Hopefully, the salary is sufficient for staying in London, if not in South Kensington!) The post ...
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practical Bayesian inference [book review]

April 25, 2018 | xi'an

[Disclaimer: I received this book of Coryn Bailer-Jones for a review in the International Statistical Review and intend to submit a revised version of this post as my review. As usual, book reviews on the ‘Og are reflecting my own definitely personal and highly subjective views on the topic!] It ...
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Le Monde puzzle [#1049]

April 17, 2018 | xi'an

An algorithmic Le Monde mathematical puzzle with a direct Alice and Bob play a game by picking alternatively one of the remaining digits between 1 and 10 and putting it in either one of two available stacks, 1 or 2. Their respective gains are the products of the piles (1 for Alice and 2 for […]
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a [Gregorian] calendar riddle

April 16, 2018 | xi'an

A simple riddle express this week on The Riddler, about finding the years between 2001 and 2099 with the most cases when day x month = year [all entries with two digits]. For instance, this works for 1 January, 2001 since 01=01 x 01. The only difficulty in writing an R code for this question […]
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Masterclass in Bayesian Statistics in Marseilles next Fall

April 8, 2018 | xi'an

This post is to announce a second occurrence of the exciting “masterclass in Bayesian Statistics” that we organised in 2016, near Marseilles. It will take place on 22-26 October 2018 once more at CIRM (Centre International de Recherches Mathématiques, Luminy, Marseilles, France). The targeted audience includes all scientists interested in learning ...
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Le Monde puzzle [#1048]

March 31, 2018 | xi'an

An arithmetic Le Monde mathematical puzzle: A magical integer m is such that the remainder of the division of any prime number p by m is either a prime number or 1. What is the unique magical integer between 25 and 100? And is there any less than 25? The question is dead easy ...
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