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stephanie lee
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‫محمود عساکره‬‎'s profile photoprantik bhattacharjee's profile photo
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Hello dear ,I am Prantik ,how are you? In search of company I pray to Jehovah .Truly do you ?please know to be in whats app+8801771475116 or you may Hangout me at Google Plus https://plus.google.com/114917580377004814083 .I am from Asia near India,A bible student.Wish you a happy life in love of Jehovah Thank you
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+KANISHKA BOSE 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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+stephanie lee  Thanks .......it is my pleasure.
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+Daniel Tao 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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ok, back at the hotel (i was at clinicals earlier).  also one of the big flaws about pinyin is that it helps (or conversely impacts, depending on your point of view) simplify spoken mandarin.  pinyin effectively removed a lot of the complexity of the language by the way that it is written out.  and the chinese government is encouraging the simplification to help with mandarin being the official language of china vs the regional dialects.  

pinyin eliminates gluttoral stops, initial stops, and final stops.  and for the most part, it kinda combined the tones and simplified them down to the 5.  for example, my name, Tao, in pinyin is Cao.  In the old wade-giles, its T'sao. (missing the tone makrs, but you get the idea).  you got Szechwan, then you got sichuan.  etc etc :)


http://en.wikipedia.org/wiki/Dongpo_pork also, this is spectacular.   i think i'll only have it once a week tho, lol.
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Genius. Physics. :))) +Terence Tao
 
Volume I of the Feynman Lectures on Physics have now been made available online by Caltech.
Preface to the New Millennium Edition · Feynman's Preface · Foreword · Chapter 1. Atoms in Motion · 1-1 Introduction · 1-2 Matter is made of atoms · 1-3 Atomic processes · 1-4 Chemical reactions · Chapter 2. Basic Physics · 2-1 Introduction · 2-2 Physics before 1920 · 2-3 Quantum physics ...
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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  
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Great article (tips)
Happy monday +Terence Tao

Instead of reading line by line. :)
 
[Google Buzz closed down for good recently, so I will be reprinting a small number of my articles from that platform to Google+, starting with this one, in order to have a working public link to these articles. This article was originally written on Mar 3, 2011.]

Computers are notorious for interpreting language in an overly literal fashion; a single misplaced parenthesis in an otherwise flawless piece of software code can cause a computer to halt in utter incomprehension halfway through the compilation of that code.

Humans, when reading natural language, tend to be far more robust at this; once one is fluent in, say, English, one can usually deal with a reasonable number of spelling or grammatical errors in a text, particularly when the writing style is clear and organised, and the themes of the text are familiar to the reader.

However, when, as a graduate student, one encounters the task of reading a technical mathematical paper for the first time, it is often the case that one loses much of one's higher reading skills, reverting instead to a more formal and tedious line-by-line interpretation of the text. As a consequence, a single typo or undefined term in the paper can cause one's comprehension of the paper to grind to a complete halt, in much the same way that it would to a computer.

In many cases, such "compilation errors" can be resolved simply by reading ahead in the paper. In some cases, just reading the next one or two lines can shed a lot of light on the mysterious term that was just introduced, or the unexplained step in the logic. In other cases, one has to read a fair bit further ahead; if, for instance, the conclusion of Lemma 15 was difficult to understand, one can read ahead to the end of the proof of that Lemma (in which, presumably, the conclusion is obtained), or search ahead to, say, Proposition 23, in which Lemma 15 is invoked, to get more clues as to what Lemma 15 is trying to say. (The use of search functions in, say, a PDF reader, is particularly useful in this regard.)

It is also good to keep in mind that no author is infallible, and that in some cases, the simplest explanation for incomprehension is that there is a typo in the text. For instance, suppose a paper states that "Since A is true, B is true", but when one works things out, one cannot quite deduce B from A, but instead can only achieve a slightly different conclusion B'. A bit later on in the text, the paper states that "Since B is true, then C is true", but again one has difficulty deducing C from B. Here, the most likely diagnosis is that the author actually meant to write B' instead of B in both places.

Another useful trick is to "project" the paper down to a simpler and shorter paper by restricting attention to a simpler special case, or by adopting some heuristic that allows one to trivialise some technical portions of the paper (or at least make some steps of the paper plausible enough to the reader that one is willing to skip over the details of proof for those steps). For instance, if the paper is dealing with a result in general dimension, one might first specialise the paper to one dimension (even if this means that the main results are no longer new, but consequences of previous literature). Or, if the paper has to analyse both the main term in an expression as well as error terms, one can adopt the heuristic that all error terms are negligible and only focus on the main term (or dually, one can accept that the main term is always going to compute out to the correct answer, and only focus on controlling error terms). If one is aware of a near-counterexample to the main result, specialising the paper to that near-counterexample (or to a hypothetical perturbation of that near-counterexample that is trying to be a genuine counterexample) is often quite instructive. Ideally, one should project away roughly half of the difficulties of the paper, leaving behind a paper which is twice as simple, and thus presumably much easier to understand; once this is done, one can undo the projection, and return to the original paper, which is now already half understood, and again much easier to understand than before one understood the projected paper. (The difficulty of reading a paper usually increases in a super-linear fashion with the complexity of the paper, so factoring the paper into two sub-papers, each with half the complexity, is often an efficient way to proceed.)

Finally, and perhaps most importantly, reading becomes much easier when one can somehow "get into the author's head", and get a sense of what the author is trying to do with each statement or lemma in the paper, rather than focusing purely on the literal statements in the text. A good author will interleave the mathematical text with commentary that is designed to do exactly this, but even without such explicit clues, one can often get a sense of the purpose of each component of the paper by comparing it with similar components in other papers, or by seeing how such a component is used in the rest of the paper. In extreme cases, one may have to go to a large blackboard and diagram all the logical dependencies of a paper (e.g. if Lemma 6 and Lemma 8 are used to prove Theorem 10, one can draw arrows between boxes bearing these names accordingly) to get some sense of what the key steps in the paper are.
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stephanie lee

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:)) resharing +Scirp Jmp

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

anything good come out of not believing in yourself?

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:)) excited to see it!

Great Thursday everyone
 
And here is my film review. Anyone check it out yet?
Ender's Game is a movie adaptation written by Orson Scott Card, that stars Asa Butterfield, Harrison Ford, Abigail Breslin
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Fantastic movie. I'm glad I didn't read the book
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+Terence Tao had to reshare
 
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, Perez-Garca, 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
Selected Papers Network
Probably the most famous of Grothendieck's contributions to Banach space theory is the result that he himself described as "the fundamental theorem in the metric theory of tensor products". That is now commonly referred to as "Grothendieck's theorem" (GT in short), or sometimes as ...
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What is your favorite desktop environment?
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I'm simple... Windows.  I havent been able to adapt too well to Mac, and I never really played around with Linux enough to give a solid opinion on it.
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A great article +Lifehacker
 
Need to meet with an important contact but keep getting turned down? Try this.
As soon as a deal goes up on Groupon, it is listed with the words “Limited Time Remaining.” An hourglass shows how much time is left before the deal disappears from the site while other banners remind you of the “Limited Quantity Available.” Why all the reminders about the limited time and quantity?
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Mind Controlled Machines

What if you could use you mind to control your environment?? What if everyone could have telekinesis??

Had a chance yesterday to chat with Ariel Garten and Chris Aimone, CEO and CTO of InteraXon, and to try out their streamlined - even fashionable - EEG sysem, called the Muse. These guys have allowed people in Vancouver to use their minds to control the lighting on some of +Canada 's most notable landmarks, thousands of km away - Parliament in Ottawa, the CN Tower in Toronto, and even the Niagara Falls.

They've also got a lighthearted side, creating thought controlled beer taps for their office parties (and you thought +Google was a fun place to work...).

Now they are turning their minds to enabling us to see inside our minds in real-time to learn to control our own minds, which, if it works out, could be incredibly useful to people of all ages (e.g., as Ariel describes in the video below, imagine the impact it might have on kids with ADD - increased self-control with decreased pharmaceuticals). .

It sounds a bit like Star Trek - there's a lot of that in my stream this week, including the earlier post about +Michael Kolios 's hope of creating a tricorder like device to eavesdrop on cells - but it's based on a strong scientific grounding.

Essentially, there are different rhythms in the ways our neurons fire depending on our state. For example, increased alpha wave activity usually corresponds to an increased state of relaxation - so the idea is that you can learn to control your stares by controlling your brain waves.

Of course, it's a bit more complicated than that, since every individual has a unique neural signature and traditional systems to measure EEG (like the one in our lab at +McMaster University ) use dozens or even hundreds of electrodes connected to wires spread across the head to enable us to see what's happening in our participants' brains.

The innovation here is in creating a relatively innocuous, wireless, portable device that can adapt to each individual and be used to interact reliably with objects like computers, phone apps, lights, and even levitating chairs.

The future may not be entirely here now - there definitely is much more work to be done - but after seeing and using the system myself, I'm starting to think the future is coming faster than we think.

You can see more about Muse here: http://www.interaxon.ca/muse/ and see Ariel describe the work in the TEDx talk below.

#ScienceSunday #ScienceEveryday
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