by gill1109 » Sat Mar 15, 2014 2:16 am
FrediFizzx wrote:Off topic; let's get back on topic here.
Yes please.
The central question of the thread which I started here, is: is the proof of the quoted theorem, correct?
If we come to the conclusion that it seems to be a true theorem, then I will be delighted to open a new topic in which I would like to discuss if and how it can be applied to computer simulation models, QRC and so on.
If the answer is that it seems to be an incorrect theorem, then I will retract the paper in which I planned to publish it. (I have to submit the final version in one week).
The
assumptions of the theorem are given, and I hope they are now completely clear. The
relevance of the theorem can/will be another topic. (Superfluous if the theorem is false).
Richard Gill wrote:Consider a spreadsheet with N = 4 000 rows, and just 4 columns.
Place a +/-1, however you like, in every single one of the 16 000 positions.
Give the columns names: A1, A2, B1, B2.
Independently of one another, and independently for each row, toss two fair coins.
Define two new columns S and T containing the outcomes of the coin tosses, encoded as follows: heads = 1, tails = 2.
Define two new columns A and B defined (rowwise) as follows: A = A1 if S = 1, otherwise A = A2; B = B1 if T = 1, otherwise B = B2.
Our spreadsheet now has eight columns, named: A1, A2, B1, B2, S, T, A, B.
Define four "correlations" as follows:
rho11 is the average of the product of A and B, over just those rows with S = 1 and T = 1.
rho12 is the average of the product of A and B, over just those rows with S = 1 and T = 2.
rho21 is the average of the product of A and B, over just those rows with S = 2 and T = 1.
rho22 is the average of the product of A and B, over just those rows with S = 2 and T = 2.
I claim that the probability that rho11 + rho12 + rho21 - rho22 is larger than 2.5, is smaller than 0.005 (5 pro mille, or half of one percent)
You can find a proof at
http://arxiv.org/abs/1207.5103 (appendix: Proof of Theorem 1 from Section 2), together with remarks by me in the first posting of this thread.
[quote="FrediFizzx"]Off topic; let's get back on topic here.[/quote]
Yes please.
The central question of the thread which I started here, is: is the proof of the quoted theorem, correct?
If we come to the conclusion that it seems to be a true theorem, then I will be delighted to open a new topic in which I would like to discuss if and how it can be applied to computer simulation models, QRC and so on.
If the answer is that it seems to be an incorrect theorem, then I will retract the paper in which I planned to publish it. (I have to submit the final version in one week).
The [b]assumptions[/b] of the theorem are given, and I hope they are now completely clear. The [b]relevance[/b] of the theorem can/will be another topic. (Superfluous if the theorem is false).
[quote="Richard Gill"]
Consider a spreadsheet with N = 4 000 rows, and just 4 columns.
Place a +/-1, however you like, in every single one of the 16 000 positions.
Give the columns names: A1, A2, B1, B2.
Independently of one another, and independently for each row, toss two fair coins.
Define two new columns S and T containing the outcomes of the coin tosses, encoded as follows: heads = 1, tails = 2.
Define two new columns A and B defined (rowwise) as follows: A = A1 if S = 1, otherwise A = A2; B = B1 if T = 1, otherwise B = B2.
Our spreadsheet now has eight columns, named: A1, A2, B1, B2, S, T, A, B.
Define four "correlations" as follows:
rho11 is the average of the product of A and B, over just those rows with S = 1 and T = 1.
rho12 is the average of the product of A and B, over just those rows with S = 1 and T = 2.
rho21 is the average of the product of A and B, over just those rows with S = 2 and T = 1.
rho22 is the average of the product of A and B, over just those rows with S = 2 and T = 2.
I claim that the probability that rho11 + rho12 + rho21 - rho22 is larger than 2.5, is smaller than 0.005 (5 pro mille, or half of one percent)
[/quote]
You can find a proof at [url]http://arxiv.org/abs/1207.5103[/url] (appendix: Proof of Theorem 1 from Section 2), together with remarks by me in the first posting of this thread.