Some facts about Rubik's cube

posted by @ulaulaman about #RubikCube

Rubik's cube is a 3d puzzle game crated by Ernő Rubik.

In a classic Rubik's Cube, each of the six faces is covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. In currently sold models, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white and blue are arranged in that order in a clockwise arrangement.

On of the first optimal solution is dued to Richard Korf

As far as we have been able to determine, we have found the first optimal solutions to random instances of Rubik's Cube, one of the most famous combinatorial puzzles of its time. The median optimal solution length appears to be 18 moves. The key idea, due to (Culberson and Schaeffer 1996), is to take a subset of the goals of the original problem, and precompute and store the exact number of moves needed to solve these subgoals from all possible initial states. Then the exact solution to the subgoals is used as a lower bound heuristic for an IDA* search of the original problem.⁽¹⁾

Some years before this paper, Korf proposed a self-learning software in order to solve the cube:

This paper describes a program which learns efficient strategies for solving problems such as Rubik’s cube and the eight puzzle. It uses a new general problem solving method based on macro-operators. The strategies learned by the program are equal to or superior to strategies used by humans on these problems, in terms of number of moves required for solution.⁽²⁾

Searching about Rubik's cube, I found a couple of curious papers in which the puzzle is applied to study some deseases:

Like Rubik's Cube, the pancreatic islet is a dynamic puzzle comprised of many interrelated components requiring proper alignment and integration. Phospholipid turnover is one “panel” in the islet; however, an obligate role for phospholipase activation in glucose-induced insulin secretion is not yet rigorously established, despite tantalizing, inferential evidence. It may be that glucose serves principally to potentiate the phospholipase and secretory responses to other signals that act by initiating phospholipid hydrolysis.⁽³⁾

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God's Number is 20
David Joyner. Adventures in Group Theory: Rubik's Cube, Merlin’s Machine, and Other Mathematical Toys (pdf)

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(1) Richard E. Korf (1997). Finding optimal solutions to Rubik's Cube using pattern databases. Proceedings of the fourteenth national conference on artificial intelligence (pdf)
(2) Richard E. Korf (1982). A Program That Learns to Solve Rubik's Cube. Proceedings of the fourteenth national conference on artificial intelligence (pdf)
(3) Metz S.A. (1991). The Pancreatic Islet as Rubik's Cube: Is Phospholipid Hydrolysis a piece of the Puzzle?, Diabetes, 40 (12) 1565-1573. DOI: 10.2337/diab.40.12.1565

From space with love

One year later, Chris Hadfield uploaded a video of his version of Space Oddity performed on the International Space Station. David Bowie had him a permission of one year and so, a couple of days ago, Chris Hadfield deleted the video, but you can see it on the YouTube channel of Sky News:

The most incredible thing is that, following Bowie's request, Hadfield's video is removed from his youtube channel, but it is reuploaded by other users and not only by Sky News...

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via space.com

Analytical Institutions in Four Books

about #MariaGaetanaAgnesi

According to Dirk Jan Struik, Agnesi is "the first important woman mathematician since Hypatia (fifth century A.D.)". The most valuable result of her labours was the Instituzioni analitiche ad uso della gioventù italiana, (Analytical Institutions for the Use of Italian Youth) which was published in Milan in 1748 and "was regarded as the best introduction extant to the works of Euler." In the work, she worked on integrating mathematical analysis with algebra. The first volume treats of the analysis of finite quantities and the second of the analysis of infinitesimals. A French translation of the second volume by P. T. d'Antelmy, with additions by Charles Bossut (1730–1814), was published in Paris in 1775; and Analytical Institutions, an English translation of the whole work by John Colson (1680–1760), the Lucasian Professor of Mathematics at Cambridge, "inspected" by John Hellins, was published in 1801 at the expense of Baron Maseres. The work was dedicated to Empress Maria Theresa, who thanked Agnesi with the gift of a diamond ring, a personal letter, and a diamond and crystal case. Many others praised her work, including Pope Benedict XIV, who wrote her a complimentary letter and sent her a gold wreath and a gold medal.

Simulate the transit of extrasolar planets

by @ulaulaman about #exoplanets #planetary_transit #kepler_mission #nasa #astronomy

The search for extrasolar planets (or exoplanets) had its first success in 1991 with the discovery of some planets orbiting around the pulsar PSR1257+12^{(1, 2, 3)}, measuring the variations of the radio pulses coming from the star. The second important milestone in exoplanet research takes place in 1995, with the discovery around the star 51 Pegasi (a star like our Sun) of a Jupiter-like planet, found at a distance closer than Mercury's orbit in our Solar System⁽⁴⁾.

(51 Pegasi via BBC)

These initial discoveries, and many other up to 2009^{(5, 6)} were made using the method of radial velocity or Doppler oscillation, in practice it is assumed that the radial velocity of a star is affected by the presence of a planet orbiting the star itself. In this way, the frequence from the star will be blue when the planet moves in its orbit toward the Earth, tending to red when the planet moves away⁽⁷⁾. With the radial velocity, however, is rather difficult to determine the exact orbit of a planet (or at least something that comes close), and then effectively allows us to determine the period of rotation around the star and the orbital eccentricity (i.e. the deviation by a circle) of the orbit of the planet itself. And I must remember that the method is effective especially for massive planets.
Luckly, the transit method is a more effective method to discover and study exoplanets: it is based on the examination of the light emitted by the studied star and it is considered by Dimitar Sasselov⁽⁸⁾ the method of observation more fruitful: when this light decreases, this means that the star is passing in front of an object. In this way it is possible to determine the radius of a planet and its orbital period. Using essentially the same tools used for the detection of the planet, it is also possible to study the atmosphere of the planet itself, determining its composition, temperature and the presence and formation of clouds.

(comparison between radial velocity and transit⁽⁷⁾)

The Kepler mission is based just on this latter method: launched on March 6, 2009⁽⁵⁾, has found 3845 candidate planets to April 2014, with the first findings published in Science in 2010⁽⁵⁾ and the first Earth-like planet announced a couple of days ago:

Looking the following plots and the plunet-hunting infographic, we can see that astronomers are looking for a kind of light holes, which allow them to determine a bit of data from the planet candidate as its mass, the orbital period and other typically stuff:

(The first transit of Kepler⁽⁵⁾)

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(Transits of the planets of Kepler-11⁽⁹⁾)

The research about Kepler-11⁽⁹⁾ is interesting because, in addition to combining the data for the studied system, it also collects information on a particular planet, Kepler-11g, and also offers deductions, based on the data, about the composition and formation of the planetary system, thus providing, as well as a number of interesting scientific data, a good example of the potential of the mission in general.
The Kepler mission, therefore, was in the last years, a source of interesting news and it can be didactically interesting to use Kepler to start bringing astronomy into the classroom. The advantages of this approach with regard to the teaching of physics are multiple and we can emphasize some of these rather than others based on the order and degree of the school. For example, we can introduce students to the study of the direct data of astronomical experiments, almost all public and freely available, some even in simple formats to read even with the usual text editor. In this way, for example, they get used to the development of real data and to their statistical processing^{(11, 12)}, but it is also possible to create a sort of miniature Kepler mission⁽¹⁰⁾:

Magical modular furniture

#MIT #design #furniture #technology #Milano

Transform is a magical, modular furniture developed by MIT:

The work is comprised of three dynamic shape displays that move more than one thousand pins up and down in realtime to transform the tabletop into a dynamic tangible display. The kinetic energy of the viewers, captured by a sensor, drives the wave motion represented by the dynamic pins.
The motion design is inspired by the dynamic interactions among wind, water and sand in nature, Escher’s representations of perpetual motion, and the attributes of sand castles built at the seashore. TRANSFORM tells the story of the conflict between nature and machine, and its reconciliation, through the ever-changing tabletop landscape.

They came in Italy during the last design week, but I was busy at school, so I cannot go to see the exhibition and I had to settle with the videos:

It's a hard life...

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(via Wired)

Jurij Gagarin: a dream during an orbit

by @ulaulaman about #YuriGagarin #space_esploration #Russia #ColdWar

He was born in Klušino on the 9th March, 1934; he died on the 27th March 1968, in a plane crash. His death and the controversy that followed and especially the pioneering gesture for which I remembered him today, make me pull over to Hal Jordan, a comic book superhero. In fact, Yuri Alekseevich Gagarin, when he returned home from his space mission, was celebrated as a hero, as a man who was raised on humanity in all its stature: the 12nd April 12 1961 he had become the first man to go in space, completing one orbit around the Earth.

Yuri has thus paved the way for space, marking a key point in the path toward the Moon: at that time Russia was very close to winning that race in space that characterized the Cold War, but thanks to Wernher von Braun, United States conquest the Moon before their opponents. In every case the importance of Gagarin and the Russian space school are now remembered for example with the movie First Orbit:

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Waiting for the beginning

Following a draft published on arXiv a couple of weeks ago, the BICEP2's observations could be explained not only with the cosmic inflation, but also with another mechanism:

The recent claimed observation of primordial gravitational waves provides a dramatic new empirical window on the early universe. In particular, it provides the opportunity, in principle, to de nitively test the inflationary paradigm, and to explore the speci c physics of inflationary models. However, while there is little doubt that inflation at the Grand Unfi ed Scale is the best motivated source of such primordial waves, it is important to demonstrate that other possible sources cannot account for the current BICEP2 data before definitely claiming Inflation has been proved.

A possible contribution to BICEP2's signal could be given by a self ordering scalar field:

Finally we note that while current data cannot de nifitively rule out a SOSF transition as the source of gravitational waves, it nevertheless does imply that the source for such waves is at, or near the Grand Uni ed Scale. Thus, it allows an exploration of physics at a scale far larger than we can currently constrain at terrestrial experiments. This will be very important for constraining physics beyond the standard model, whether or not inflation is responsible for the entire BICEP2 signal, even though existing data from cosmology is strongly suggestive that it does.

About the SOSF I found some interesting paper on arXiv:
A Nearly Scale Invariant Spectrum of Gravitational Radiation from Global Phase Transitions, Probing the Gravitational Wave Signature from Cosmic Phase Transitions at Different Scales, and Gravitational waves from self-ordering scalar fields.

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via AstronomicaMens, The Physics arXiv Blog