stephanie lee
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Todays doodle﻿
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:)) resharing

i find at times unsure of myself and then comes this lol

anything good come out of not believing in yourself?

﻿
The "four fours" problem. ﻿
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great post

H~anniv chicken butt +1 (applicable 3 ways)﻿
Curiosity:
With rows of Pascal's triangle, you can calculate the natural power of the number 11.

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients. It is named after the French mathematician Blaise Pascal in much of the Western world, although other mathematicians studied it centuries before him in India, Greece, Iran, China, Germany, and Italy.

The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top. The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. A simple construction of the triangle proceeds in the following manner. On row 0, write only the number 1. Then, to construct the elements of following rows, add the number above and to the left with the number above and to the right to find the new value. If either the number to the right or left is not present, substitute a zero in its place. For example, the first number in the first row is 0 + 1 = 1, whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.

Source: http://en.wikipedia.org/wiki/Pascal%27s_triangle

With rows of Pascal's triangle, you can calculate the natural power of the number 11.
Row first  1 => 11^0 = 1
Row second 11 => 11^1=11
Row third 121 => 11^2=121
Row fourth 1331 => 11^3 =  1331
Row fifth 14641 => 11^4 = 14641
beyond  fifth row: we add the numbers from right to left  given by method.﻿
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:)) excited to see it!

Great Thursday everyone﻿
And here is my film review. Anyone check it out yet?﻿
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Grothendieck's inequality ( http://en.wikipedia.org/wiki/Grothendieck_inequality ) asserts that a certain discrete optimisation problem (optimising a quadratic form over inputs that are +1 or -1) is equivalent up to constants to a continuous optimisation problem (optimising the same quadratic form over unit vectors in a Hilbert space).  This is important for theoretical computer science, because the former problem essentially contains NP-hard problems such as MAX-CUT, whereas the latter can be rephrased as a semidefinite program (by writing the problem in terms of the Gram matrix of the unit vectors) and can be solved in polynomial time by algorithms such as the ellipsoid method.  So there are certain NP-hard problems which one can solve "up to constants" in polynomial time: in some sense, the "ratio" between NP and P is bounded!   Furthermore, in a certain technical sense, one cannot achieve a better approximation to such problems by any polynomial-time algorithm than through the Grothendieck inequality, at least if one assumes the Unique Games Conjecture (a result of Raghavendra and Steurer).

Grothendieck's inequality also has a very cute connection to Bell's inequality in quantum mechanics, as observed by Tsirelson; roughly speaking, the ability of quantum mechanics to violate Bell's inequality is logically equivalent to the constant in Grothendieck's inequality being greater than one (basically because the discrete optimisation problem describes the envelope of all possible measurement outcomes of a classical hidden-variable system, and the vector-valued optimisation problem describes the envelope of all possible measurement outcomes of a quantum system).  Or to put it another way, Grothendieck's inequality asserts (in some sense) that Bell's inequality can only be violated "up to a constant", at least when there are only two measurements made.  (For three or more measurements the violation can be much more dramatic, a result of Junge, Navascues, Palazuelos, Perez-Garca, Scholz, and Werner.)

[All this I learned today from a very nice lecture by Pisier on these topics, largely based on his survey article linked to here.]

#spnetwork #recommend arXiv:1101.4195﻿
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Daniel
you know how the mandarin I know is/was from just hearing but I remembered you mentioning 'pinyin' last night when you were told the word for Chinese chess

eh, I Can Teach Myself More In A Formalized way. Cool beans. Thanks doctor!
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?﻿
What is your favorite desktop environment?﻿
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Genius. Physics. :))) ﻿
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A great article ﻿
Need to meet with an important contact but keep getting turned down? Try this.﻿
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Nice﻿
Isn't it too much for  this BMW?
The 2014 BMW i8 will be priced from \$135,700 plus destination and handling fee when it arrives in showrooms across the United States in spring of next year.
The latter links a 1.5-liter 3-cylinder twin-turbocharged petrol engine developing 228hp and 236 lb-ft of torque that drives the rear wheels via a 6-speed automatic gearbox and a synchronous electric motor developing 129hp (96kW) and 184 lb-ft  of torque turning the front wheels via a two-stage automatic transmission. A 5 kWh lithium-ion high-voltage battery with liquid cooling complete the setup.
Overall, the powertrain delivers a combined system output of 357hp and 420 lb-ft of torque for 0 to 62mph sprint in 4.4 seconds and a top speed of 155 mph. Fuel consumption (with the use of the battery)  94 mpg US.

#bmwi8  ﻿