## a first 5k [since last one]

Posted in pictures, Running with tags , , , , , , , , on June 15, 2022 by xi'an

## value of a chess game

Posted in pictures, Statistics, University life with tags , , , , , , , , , , , , on April 15, 2020 by xi'an

In our (internal) webinar at CEREMADE today, Miguel Oliu Barton gave a talk on the recent result his student Luc Attia and himself obtained, namely a tractable way of finding the value of a game (when minimax equals maximin), result that got recently published in PNAS:

“Stochastic games were introduced by the Nobel Memorial Prize winner Lloyd Shapley in 1953 to model dynamic interactions in which the environment changes in response to the players’ behavior. The theory of stochastic games and its applications have been studied in several scientific disciplines, including economics, operations research, evolutionary biology, and computer science. In addition, mathematical tools that were used and developed in the study of stochastic games are used by mathematicians and computer scientists in other fields. This paper contributes to the theory of stochastic games by providing a tractable formula for the value of finite competitive stochastic games. This result settles a major open problem which remained unsolved for nearly 40 years.”

While I did not see a direct consequence of this result in regular statistics, I found most interesting the comment made at one point that chess (with forced nullity after repetitions) had a value, by virtue of Zermelo’s theorem. As I had never considered the question (contrary to Shannon!). This value remains unknown.

## too many marginals

Posted in Kids, Statistics with tags , , , , , , , on February 3, 2020 by xi'an

This week, the CEREMADE coffee room puzzle was about finding a joint distribution for (X,Y) such that (marginally) X and Y are both U(0,1), while X+Y is U(½,1+½). Beyond the peculiarity of the question, there is a larger scale problem, as to how many (if any) compatible marginals h¹(X,Y), h²(X,Y), h³(X,Y), …, need one constrains the distribution to reconstruct the joint. And wondering if any Gibbs-like scheme is available to simulate the joint.

## Prairie chair

Posted in pictures, Statistics, University life with tags , , , , , , , , , , , on October 2, 2019 by xi'an

Today is the launching day of PRAIRIE, one of the four Instituts Interdisciplinaires d’Intelligence Artificielle (3IA) supported by the French government. Taking place in Paris Dauphine, with Yann Le Cun as guest speaker. I have been fortunate to be endowed with one of these chairs for the coming years, along with my CEREMADE colleagues Laurent Cohen and Irène Waldspurger.

## 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.