Wikipedia:Reference desk/Archives/Mathematics/2012 December 8

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December 8

X chromosomes and statistics

This article (PDF) makes the claims that 1) variance in intelligence among men is higher, and 2) this is due to the fact that men have one X chromosome (which has a disproportionately large number of genes expressed in the brain) and women have two, which get "averaged" during genetic cross-over.

I can believe 1), but I'm having trouble accepting 2). If every man gets his X chromosome from his mother, then would the variance in intelligence among men be the same as that of women? 65.92.7.202 (talk) 01:16, 8 December 2012 (UTC)

Different genes working in different ways. For some genes, one is dominant, and the recessive gene is not expressed at all. Eye color tends to work this way. For others, you get an averaging of the two genes, which seems to be how they claim intelligence works. So, if the woman has two X chromosomes, one of which would give her an IQ of 120, and one of which would give her an IQ of 80, then she ends up with an IQ of 100 (gross oversimplification, of course). However, if she only passes one gene on to her son, he will either have the IQ of 80 or 120. StuRat (talk) 01:32, 8 December 2012 (UTC)

I've fixed the OP's link. I agree fully with the explanation. One does of course have to be aware of the uncertainty in the assumptions on the averaging effect with duplicate genes, and also that there will be contributing factors of an unrelated origin; however, given the assumption, this mechanism can plausibly be invoked as a possible contributor to greater variability of some characteristics in men. — Quondum 10:15, 8 December 2012 (UTC)

Also note that if we use their assumptions, then fathers must not contribute to the intelligence of their sons, as they don't provide an X chromosome to them. I'd think a simple study would show that this is not true. You'd need to study sperm donors, though, to ensure that the males are only providing genetic contributions, as opposed to affecting the environment in which their son is raised. StuRat (talk) 16:45, 8 December 2012 (UTC)

But what about X-inactivation? 65.92.7.202 (talk) 23:35, 8 December 2012 (UTC)

No, their assumptions would only imply that fathers have a smaller genetic contribution to their sons than do mothers.--80.109.106.49 (talk) 21:57, 8 December 2012 (UTC)

Since the OP is aware of X-inactivation, the OP is undoubtedly aware that only one of the two X chromosomes in women is expressed -- the other is inactivated. This makes the claim pretty implausible, unless I am missing something. Looie496 (talk) 00:49, 9 December 2012 (UTC)

Wonderful link, thanks for it. But I don't understand your interpretation of it in this context. My reading of the article is that in any given cell only one of the X chromosomes is expressed, but that each of the X chromosomes is expressed in some cells. To me it would seem then that averaging could occur if intelligence depends on what's happening in many cells. Duoduoduo (talk) 12:39, 9 December 2012 (UTC)

Math of the McEliece cryptosystem

It looked simple enough on this page, but I found out that the matrixes are not normal ones. Can someone explain to me (a person with no knowledge of how a Hamming code works) help me to understand how to do that page's example out by hand? --Melab±1 ☎ 07:28, 8 December 2012 (UTC)

You seem to be asking for a tutorial, which may be more than most would be prepared to do. You have also not shown where you got stuck. You'll have to get a feel for error correction codes before you tackle this. Your comment "the matrixes are not normal ones" might suggest that you have not realized that all arithmetic is done modulo 2. — Quondum 10:29, 8 December 2012 (UTC)

Then if I were to multiply two matrices I would need to apply modulo 2 to every step in calculating the values for each position in the matrix? --Melab±1 ☎ 00:35, 9 December 2012 (UTC)

Yep, or you can also just do standard integer multiplication in the real numbers and then reduce the answer modulo 2 at the very end. Reducing at every step will keep the numbers smaller throughout the multiplication. - Looking for Wisdom and Insight! (talk) 06:37, 10 December 2012 (UTC)

Or alternately regard every element as a boolean value. Addition then is replaced with exclusive or, and multiplication with logical and. Inverting a matrix is quite fun – Gaussian elimination still works, but the only value you ever have to divide by is 1. — Quondum 08:05, 10 December 2012 (UTC)

Pump capacity formulas

HI, I'M LOOKING FOR MATH FORMULAS CONCERNING RECIPROCATING PUMP CAPACITY (FOR U.S. COAST GUARD MERCHANT MARINE UPGRADE TEST). A SIMPLEX SINGLE/DOUBLE ACTING RECIPROCATING PUMP MAKING 180 STROKES/MINUTE, WITH A 5" DIAMETER CYLINDER, AN 8" STROKE AND OPERATING WITH 87% VOLUMETRIC EFFICIENCY, WHAT IS THE CAPACITY OF THE PUMP? ${\displaystyle }$ ESB — Preceding unsigned comment added by Edgarbarrios (talk • contribs) 15:43, 8 December 2012 (UTC)

The volume of a cylinder is:

V = hπr2

They gave you a diameter of 5 inches, so the radius is half that, or 2.5 inches. Presumably you want the figures in cubic feet, so we convert that to 2.5/12 (or 5/24) foot. Similarly, the stroke is the same as the height, so 8 inches is 2/3 foot. We could just use 3.14 as a reasonable approximation for pi. Do the substitutions:

V = (2/3)(3.14)(5/24)2

You will then need to multiply by the volumetric efficiency, and the strokes per minute:

180(0.87)(2/3)(3.14)(5/24)2

The answer should be in cubic feet per minute. I assume there is only one cylinder. If "double acting" means that both sides are pumping at once, then multiply the above number by 2. Do the math and show us your results, and we will check your work. StuRat (talk) 16:26, 8 December 2012 (UTC)