Sudoku clues

http://t.co/zk3P3rPjFZ #sudoku #mathematics #arXiv #abstract

The arXiv's paper is published two years ago, but I think that every time is a good time to play sudoku!

The sudoku minimum number of clues problem is the following question: what is the smallest number of clues that a sudoku puzzle can have? For several years it had been conjectured that the answer is 17. We have performed an exhaustive computer search for 16-clue sudoku puzzles, and did not find any, thus proving that the answer is indeed 17. In this article we describe our method and the actual search. As a part of this project we developed a novel way for enumerating hitting sets. The hitting set problem is computationally hard; it is one of Karp's 21 classic NP-complete problems. A standard backtracking algorithm for finding hitting sets would not be fast enough to search for a 16-clue sudoku puzzle exhaustively, even at today's supercomputer speeds. To make an exhaustive search possible, we designed an algorithm that allowed us to efficiently enumerate hitting sets of a suitable size.

In the following video by Numberphile, James Grime discusses the paper results:

From Nash equilibria to collective behavior

https://twitter.com/ulaulaman/status/517303481565458432 by @ulaulaman about #Nash equilibria and their role in collective behavior

The Nash equilibrium is an important tool in game theory:

[It] is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy. If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision, and Will is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others in the game.

Nash equilibria may, for example, be found in the game of coordination, in the prisoner's dilemma, in the paradox of Braess⁽⁶⁾, or more generally in any strategy game. In particular, given a game, we can ask whether it has or not a Nash equilibrium: apparently deciding the existence of Nash equilibria is an intractable problem, if there is no restriction on the relationships among players. In addition for a strong Nash equilibrium, the problem is on the second level of the polynomial hierarchy, which is a scale for the classification problem based on the complexity of resolution⁽¹⁾.
In addition to this study about Nash equilibria, Gianluigi Greco (one of my high school classmates), together with Francesco Scarcello, also studied the Nash equilibria (in this case the forced equilibria) in graphical games, where graphical game is a game represented in a graphical manner, through a graph⁽²⁾.

CERN's 60th Birthday

http://t.co/zU9b7V4idL by @ulaulaman about #CERN60

The day to celebrate CERN's birthday is arrived:

The convention establishing CERN was ratified on 29 September 1954 by 12 countries in Western Europe. The acronym CERN originally stood in French for Conseil Européen pour la Recherche Nucléaire (European Council for Nuclear Research), which was a provisional council for setting up the laboratory, established by 12 European governments in 1952. The acronym was retained for the new laboratory after the provisional council was dissolved, even though the name changed to the current Organisation Européenne pour la Recherche Nucléaire (European Organization for Nuclear Research) in 1954.

The most recent discovery at the laboratories is the Higgs boson (or a particle that seems it), but there are some others successes in the CERN's history:

1973: The discovery of neutral currents in the Gargamelle bubble chamber;
1983: The discovery of W and Z bosons in the UA1 and UA2 experiments;
1989: The determination of the number of light neutrino families at the Large Electron–Positron Collider (LEP) operating on the Z boson peak;
1995: The first creation of antihydrogen atoms in the PS210 experiment;
1999: The discovery of direct CP violation in the NA48 experiment;
2010: The isolation of 38 atoms of antihydrogen;
2011: Maintaining antihydrogen for over 15 minutes;

There are two Nobel Prizes directly connected to the CERN:

1984: to Carlo Rubbia and Simon Van der Meer for

their decisive contributions to the large project which led to the discovery of the field particles W and Z, communicators of the weak interaction

1992: to Georges Charpak for

his invention and development of particle detectors, in particular the multiwire proportional chamber, a breakthrough in the technique for exploring the innermost parts of matter

On CERN's webcast you can see the official ceremony

Foucault and the pendulum

http://t.co/AphFwEZfQ2 #foucaultpendulum #physics #earthrotation

The first public exhibition of a Foucault pendulum took place in February 1851 in the Meridian of the Paris Observatory. A few weeks later Foucault made his most famous pendulum when he suspended a 28 kg brass-coated lead bob with a 67 meter long wire from the dome of the Panthéon, Paris. The plane of the pendulum's swing rotated clockwise 11° per hour, making a full circle in 32.7 hours. The original bob used in 1851 at the Panthéon was moved in 1855 to the Conservatoire des Arts et Métiers in Paris. A second temporary installation was made for the 50th anniversary in 1902.
During museum reconstruction in the 1990s, the original pendulum was temporarily displayed at the Panthéon (1995), but was later returned to the Musée des Arts et Métiers before it reopened in 2000. On April 6, 2010, the cable suspending the bob in the Musée des Arts et Métiers snapped, causing irreparable damage to the pendulum and to the marble flooring of the museum. An exact copy of the original pendulum had been swinging permanently since 1995 under the dome of the Panthéon, Paris until 2014 when it was taken down during repair work to the building. Current monument staff estimate the pendulum will be re-installed in 2017

Idiosyncratic Thinking: a computer heuristics lecture

http://t.co/7JB3CPaQt9 #Feynman

Richard Feynman, Winner of the 1965 Nobel Prize in Physics, gives us an insightful lecture about computer heuristics: how computers work, how they file information, how they handle data, how they use their information in allocated processing in a finite amount of time to solve problems and how they actually compute values of interest to human beings. These topics are essential in the study of what processes reduce the amount of work done in solving a particular problem in computers, giving them speeds of solving problems that can outmatch humans in certain fields but which have not yet reached the complexity of human driven intelligence. The question if human thought is a series of fixed processes that could be, in principle, imitated by a computer is a major theme of this lecture and, in Feynman's trademark style of teaching, gives us clear and yet very powerful answers for this field which has gone on to consume so much of our lives today.

Experiments with inertia

a coulpe of home experiments about #inertia

from Science Comics #2

Witches Kitchen 1971

http://t.co/sHn7nJ4uFj a #funny image about #mathematics by Alexander Grothendieck

Riemann-Roch Theorem: The final cry: The diagram is commutative! To give an approximate sense to the statement about f: X → Y, I had to abuse the listeners' patience for almost two hours. Black on white (in Springer lecture notes) it probably takes about 400, 500 pages. A gripping example of how our thirst for knowledge and discovery indulges itself more and more in a logical delirium far removed from life, while life itself is going to Hell in a thousand ways and is under the threat of final extermination. High time to change our course!

Alexander Grothendieck about the Grothendieck–Riemann–Roch theorem via Math 245

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Read also: how does one understand GRR?