HDTenEightyP/NetNews huggingface dataset:
From: chasman@athena.mit.edu (David Chasman)
Subject: QUESTION FROM AN IGNORANT CHEMIST
Organization: Massachusetts Institute of Technology
Date: Thu, 12 Nov 1992 15:44:10 GMT

This is probably a silly question, but I can't learn if I don't ask
questions:

I have the following data analysis problem:

I have a set on values: { y_i }

I hypothesize that these values are related to some x's
by

	y_i = sum_{n=1}^D x_n(i) 

x_n(i) are just some values and more than 2 y_i may have an x_n(i) in common.
Generally, D will be 1-10 :

For example :

  x_1(1) = 1   x_1(2) = 1
  x_2(1) = 1   x_2(2) = 2
  x_3(1) = 2   x_3(2) = 1
  x_4(1) = 2   x_4(2) = 2

so: y_1 = 2    y_2 = 3    y_3 = 3    y_4 = 4

The questions are : (1) can I figure out what D is ?
                    (2) can I giure out the x_n(i) ?

Answers to either question are appreciated

Thankyou --David Chasman








Newsgroups: sci.math.stat
From: nmm1@cus.cam.ac.uk (Nick Maclaren)
Subject: Re: bug in fortran RNG
Organization: U of Cambridge, England
Date: Fri, 6 Nov 1992 17:23:24 GMT

In article <1992Nov5.205359.29733@cbfsb.cb.att.com>, rizzo@cbnewsf.cb.att.com (anthony.r.rizzo) writes:
|> Some time ago, during a discussion of random number generators,
|> at least one individual mentioned that the RNG in "Numerical Recipes,"
|> perhaps the fortran version, had a bug in it.  Does anyone recall
|> what that bug was and how to correct it?  Does anyone recall
|> which of the various RNGs in "Numerical Recipes" has the bug?
|> Thanks!

I might have been the person, but I didn't say that there was a bug in any of
the basic generators in Numerical Recipes.  I said that most of them were
ghastly, and fail several of the standard tests very badly.  The only one
that is any good is the DES-based one, and I suggest using more efficient
code (such as Eric Young's).  Alternatively, use a reliable traditional
generator, such as Wichmann and Hill's.


Nick Maclaren
University of Cambridge Computer Laboratory,
New Museums Site, Pembroke Street,
Cambridge CB2 3QG, England.
Email:  nmm1@cus.cam.ac.uk
Tel.:   +44 223 334761
Fax:    +44 223 334679
Newsgroups: sci.math.stat
From: richman@reepicheep.gcn.uoknor.edu (Mike Richman)
Subject: Re: Factor Analysis& Rotation
Originator: usenet@midway.ecn.uoknor.edu
Date: Wed, 4 Nov 1992 23:05:42 GMT
Reply-To: richman@reepicheep.gcn.uoknor.edu (Mike Richman)
Organization: Engineering Computer Network, University of Oklahoma, Norman, OK, USA

In article <1992Nov3.113547.3959@memstvx1.memst.edu>, rajagopa@memstvx1.memst.edu writes:
|> Dear friends,
|> 	      Could some of you stat buffs let me know the concept of
|> factor analysis and rotation in plain english. I do not quite get the hang 
|> of it. I thank your responses and will post the compiled version on the net.
|> Thanks/Raj
|> 

There are several ways of approaching the rotation issue.  One is to
view it historically from a "simple structure" standpoint. In this
case, a decent text to read is Thurstone's "Multiple Factor Analysis".
What he says is that simple structure rotation attempts to find a
linear transformation ("rotation") which results in repositioning the
initial (unrotated) factors in hyperspace such that the variable
configuration is simplified as much as possible.  He lists 5 rules to
help the graphical rotators of the 1940's achieve this by using the
concept of a hyperplane.  In doing simple structure rotation, one
typically isolates subsets of highly interrelated variables which
covary similarly.  There is some overlap with the concepts of cluster
analysis.  With the advent of computers, hand rotation has become
nearly a lost art and most analysts depend upon some algebraic
expression which attempts to fulfill some of Thursone's concepts (ie,
Varimax).

Another way of looking at factor rotation is from a quasi-confirmatory
view.  In such a situation, one might wish to look for a predetermined
factor loading structure by finding a least-squares fit between a low
dimensional subset of factors and some preconceived loadings.  This
type of rotation is known as target rotation.  The most straightforward
description of the concepts behind rotation is probably Rummel's (1970)
text, Applied Factor Analysis, Northwestern U. Press.  I also have a
review article on rotation of principal components, which includes a
Monte Carlo test of the accuracy of available algorithms, should that
interest you.
---
Mike Richman                        !CIMMS/The University of Oklahoma
richman@reepicheep.gcn.uoknor.edu   !100 East Boyd, Room 1110
405-325-3460 (office) 325-7614 (fax)!Norman, OK  73019-0628  USA
From: rick@daffodil.tymnet.com (Rick McFarland)
Newsgroups: sci.math.stat
Subject: Fermat
Date: 6 Nov 92 15:42:20 GMT
Organization: BT North America, San Jose, CA

Perhaps this news group can help ....

There is  a  lot of discussion in another news group about

    Fermat's "Final?"  Theorem

For all integers  n > 2,  there is NO integer  solution  for
         n           n              n
      A    +    B     =      C    

I have  heard  conflicting stories that 
1)  A  proof does not exist and  Fermat died leaving behind a message
     "remarkable proof!"  implying that he found a simple proof.
2)  A  proof DOES exist but it is very complex.  Thus, Fermat's simple
     proof either  eludes us  or  his "remarkable" proof was flawed.

Can anyone in this news group help?  Any recent news about this?

THANKS in advance!




"omne ignotum pro magnifico"
Newsgroups: sci.math.stat
From: mokaba@binah.cc.brandeis.edu
Subject: multi-colinearity in full lisrel models
Reply-To: mokaba@binah.cc.brandeis.edu
Organization: Brandeis University
Date: Thu, 5 Nov 1992 18:26:58 GMT

Could someone help the novice!!
I am working on estimatic both structural and measurement parameter using
LISREL. I used 19 indicators of 6 latent varible, three of which are
eta's (endogenous) and the other three are ksi's (exogenous). 

Problem :
In estimating this model I get negative beta coefficients where i expected
positive ones. Some one suggested that I could be have a mulcolinearity
problem. How do I test for it in LISREL? How do I resolve it short of 
eliminating one of the varibales from the model? 
e-mails appreciated.
Benny
From: P.G.Hamer@bnr.co.uk
Newsgroups: sci.math.stat
Subject: distance measures for reverse engineering
Date: 12 Nov 1992 10:52:20 GMT
Organization: BNR Europe Ltd, London Road, Harlow, England.
NNTP-Posting-Host: 128.199.202.209

Has anybody thought about suitable distance/similarity/dis-similarity
measures for reverse engineering large s/w systems.

I am thinking of taking inter-module reference information,
building a distance matrix then using clustering and/or
2D projection techniques (eg metric scaling).

The question is: how do you produce a distance matrix that
will reveal a *layered* software architecture [if it exists]?
Presumably the modules in a layer may well have little 
inter-communication; the commonality is, presumably, in their
callers and who they call.

Any ideas?

Regards, Peter (P.G.Hamer@bnr.co.uk)
Newsgroups: sci.math.stat,comp.lang.fortran
From: u235@rex.chb.uokhsc.edu (Yung-Jin Lee)
Subject: Algorithms for model discrimination
Originator: usenet@essex.ecn.uoknor.edu
Date: Wed, 11 Nov 1992 22:24:33 GMT
Organization: University of Oklahoma Health Sciences Center, OKC
	I'm a grudate student of a College of Pharmacy.  In my

Yung-jin
From: hauser@statrix2.wu-wien.ac.at (Michi Hauser)
Newsgroups: sci.math.stat
Subject: Re: Mean Square Convergence: A Necessary Condition?
Date: 6 Nov 1992 18:49:56 GMT
Organization: University of Economics and Business Administration Vienna
Distribution: world
Reply-To: hauser@wu-wien.ac.at
NNTP-Posting-Host: statrix2.wu-wien.ac.at


-- 
Michael Hauser

University of Economics and Business Adminstration
Department for Applied Statistics and Data Processing
Augasse 2-6, 1090 Vienna, Austria

Tel. *43/1/31336 4759
email: hauser@wu-wien.ac.at

Spanos,A.(1986): Statistical foundations of econometric 
modelling, Cambridge Univ. press, p.190, 
Chp. Introduction to asymptotic theory :

If X_n converges in the r-th mean to X for some r>=1 then 
X_n converges in the l-th mean to X for 0<l<r. 

Your r=2 and l=1 .


Best wishes Michael
Newsgroups: sci.math.stat
From: hrubin@mentor.cc.purdue.edu (Herman Rubin)
Subject: Re: Gallup Polls and Curving Grades
Organization: Purdue University Statistics Department
Date: Mon, 9 Nov 1992 02:03:59 GMT

In article <1992Nov8.121446.44520@kuhub.cc.ukans.edu> christos@kuhub.cc.ukans.edu writes:
>Hello there,

>	I would like to get some information about gallup polls and  curving 
>grades., i.e. the procedure that is followed to collect data and the thoery 
>behind it. Do you have any suggested reference that I should refer to any book 
>in sampling that does not get into too much technicality?

Any fair statistics book will give the distribution theory needed to get the
sampling error for a poll.  The other important thing is to get an accurate
sample, and the pollsters usually use a stratified random sample, with the
"random" being important.  Any fair text on sampling discusses this.

As for curving grades, this is only meaningful if one can assume that the
class is large enough and random enough that it reflects the population,
and that environmental factors, such as the teaching, the quality of class
discussion, etc., are irrelevant.  Even then, there is the question as to
why a particular distribution of grades should occur.  Grades mean little
enough without doing something with as little justification as curving.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
Newsgroups: sci.math.stat
From: mikef@dph1.health.su.OZ.AU
Subject: Is the logarithmic transformation monotonic?
Followup-To: poster
Summary: Question re the nature of the log transformation
Originator: mikef@dph1
Keywords: monotonic transformation, logarithm
Organization: Dept Public Health, Sydney University
Date: Thu, 12 Nov 1992 04:58:20 GMT

I have needed to make comparisons between variances of some
random variable X, var(X). Specifically, I needed to know if 
var(X=a)>var(X=b). However, I was only able to compute var(lnX), 
and have made the comparison between var(ln{X=a}) and var(ln{X=b}).

I thought that this comparison would be valid since: 

(1) I believed the natural logarithm was a monotonic tranformation, and

(2) because, if (1) is true I thought that it then follows that
var(X=a)>var(X=b) implies that var(ln{X=a})>var(ln{X=b}).

Am I correct? If not, any good suggestions?

Thanks in advance.  


-- 
__
Michael Fahey         | Internet: mikef@pub.health.su.oz.au
Dept of Public Health | UUCP: uunet!munnari.oz.au!pub.health.su!mikef
University of Sydney  | Bitnet: mikef%pub.health.su.oz.au@cunyvm.bitnet
Newsgroups: sci.math.stat
From: macq@miguel.llnl.gov (Don MacQueen)
Newsgroups: sci.math.stat
Subject: Median absolute deviation from median
Date: 14 Nov 92 00:39:47 GMT
Organization: Lawrence Livermore National Laboratory

Some members of the environmental monitoring division
here are fond of using the median and the median absolute
deviation from the median (the MAD) as summary statistics for samples
that have some left censoring.

Does anyone know of any good properties the MAD has?
(regardless of whether there is censoring)

For instance, the median minimizes the sum of the absolute
deviations, so perhaps the median absolute deviation makes
sense as a measure of variability. Is there more to it than
that?

Thanks
-- 
---------------------------------------------------
Don MacQueen
preferred                   macq@llnl.gov
o.k.                        macq@alle.llnl.gov
Lawrence Livermore Nat. Lab.
7000 East Ave., L-307          (510) 423-1062
Livermore, CA 94550
---------------------------------------------------
Newsgroups: sci.math.stat
From: kunjin+@pitt.edu (Kun Jin)
Newsgroups: sci.math.stat
Subject: Non-central t distribution routine wanted
Date: 5 Nov 92 23:18:42 GMT
Organization: University of Pittsburgh
Originator: kunjin@unixd1.cis.pitt.edu

I am looking for a routine or S-function that can calculate non central t
distribution.  I would appreciate any suggestion on how to find one.

Thanks.

Kun Jin
Newsgroups: sci.math.stat
From: hunt7551@mach1.wlu.ca (len hunt 9208 U)
Subject: HEYWOOD CASES
Organization: Wilfrid Laurier University
Distribution: na
Date: Fri, 6 Nov 1992 18:54:08 GMT

I was wondering if someone could help me with a problem I have encountered.
While completing a number of principal axis factor analyses several have had
problems with heywood cases, i.e., the final estimate for a communality
exceeds 1.00.

The problem involves the handling of this situation.  First, I do not wish
to alter the data in any way or try different variables; there is a good
reason for this but for sake of brevity I shall not disclose it.  I have
read and heard that one can set the communality of a heywood case to 0.99
instead of the >1.00 that is found.  However, correct me if I am wrong, the
squared factor loadings for this variable by all factors will still exceed
one.  Therefore, I have stopped the iteration at the point before this
heywood case arises instead of setting the value equal to 0.99.  It is true
that the final convergence criteria for the communalities is not met by
doing this, but I think it is a better way to handle these cases.

I would appreciate hearing your comments upon stopping the iteration
beforehand.  Please send your message directly to me, as there is already
enough to read on these news lists.

Thanks Sincerely,

Len Hunt

Wilfrid Laurier University
Waterloo, Canada

E-mail ...hunt7551@mach1.wlu.ca
From: mwande@graunt.qal.berkeley.edu (Mike Anderson)
Newsgroups: sci.math.stat
Subject: modelling distributions
Date: 11 Nov 1992 19:47:23 GMT
Organization: University of California, Berkeley
Distribution: world
NNTP-Posting-Host: graunt.qal.berkeley.edu

Suppose I have data on two variables - age and income of a person. I would like
to estimate income curves by age using spline regression, but my problem is
this: to protect the identity of the individuals, incomes were topcoded, so
that any person reporting incomes of > $100,000 gets coded at $100,000. I am
interested in getting very accurate estimates, and given the long right tail
of the income distribution, these truncated values may be throwing off my
estimates quite a bit.
	So I would like to replace the truncated values with my own "tail". My
question is, how do I go about modelling the income distribution and tacking
on my own tail? Off the top of my head, I would precede thusly: If there are
Nt truncated observations and Nu untruncated observations, N = Nt + Nu, I would
first scale the Nu incomes to mean 0, generate N obs from something like a
log-normal, lop off the top Nt quantiles, and compare the generated data to the
observed data with a Q-Q plot, choosing that level of variance in the log-normal
which gives me the straightest fit. Then I would take the Nt random values I
lopped off from the generated data and randomly assign them to the Nt truncated
values. Does this sound reasonable? I'm sure there is a better way to go about 
this, can someone tell me what it is or where to find it?
Thanks in advance, Mike Anderson
-- 
Mike Anderson    Dept. of Demography   UC Berkeley   mwande@QAL.Berkeley.EDU
"And I would say to those out around the country. 'Take a hard look now.
Don't let that rabbit be pulled out of the hat by one hand and 25 other 
rabbits dumped on you in another.'" - George Bush, 1/24/90 
Newsgroups: sci.math.stat
From: PLY@ECL.PSU.EDU (Pen-Li T Yen)
Subject: SOFEWARE "ACED" WANTED
Organization: Penn State Engineering Computer Lab
Distribution: WORLD
Date: Fri, 13 Nov 92 08:53:39 GMT
X-News-Reader: VMS NEWS 1.24

	I am looking for a statistics package "ACED".  This package is used
for optimal design of experiment.  Can someone tell me how to access the 
public statistic library to get it?  Thank you!
	My E-mail address is " PLY@ECL.PSU.EDU"

Pen-Li Yen
Dept of IE
Penn State Univ.  
Newsgroups: sci.math.stat
From: yaffee@acf3.NYU.EDU (Bob Yaffee,Tisch Hall LC-7,(212) 998-3402,)
Subject: Re: multi-colinearity in full lisrel models
Organization: New York University
Date: Sun, 8 Nov 1992 07:50:00 GMT

/* acf3:sci.math.stat / mokaba@binah.cc.brandeis.edu /  1:26 pm  Nov  5, 1992 */
Could someone help the novice!!
I am working on estimatic both structural and measurement parameter using
LISREL. I used 19 indicators of 6 latent varible, three of which are
eta's (endogenous) and the other three are ksi's (exogenous). 

Problem :
In estimating this model I get negative beta coefficients where i expected
positive ones. Some one suggested that I could be have a mulcolinearity
problem. How do I test for it in LISREL? How do I resolve it short of 
eliminating one of the varibales from the model? 
e-mails appreciated.
Benny

Newsgroups: sci.math
From: phkahler@vela.acs.oakland.edu (KAHLER PAUL H.)
Subject: Re: Trivial
Organization: Oakland University, Rochester MI.
Date: Thu, 5 Nov 1992 17:45:53 GMT

I am the one who posted the original question X^2 == Y mod N.
We can stop yelling at bob for saying it is trivial now, but thanks
for defending me. As for bob, I would expect a little arrogance from
him. After all, he is fairly well known (I have seen many references
to his work) and with a reputation, you just can't help it :-)

    To Bob: No I'm not using a STUPID method to find X when N is prime.
And my problem is NOT trivial, because I don't have the factors of N!

   What I am really trying to do is factor N. I realized that I could do
this quickly if I could take square roots mod N. I found out how to do
it if N is prime, so I thought maybe.... I should have thought that if
anyone knew how to solve this without knowing the factors of N then the
factoring problem would have been solved already (the connection is
obvious, but I havent seen it stated explicitly). For this I am a fool.

Thanks to all those who responded. I should have been more specific.
I'll go crawl back in my hole now. :-)

Paul
From: bret@tfd.COM (Bret Weinraub)
Newsgroups: sci.math
Subject: 4x4 matrix
Keywords: matrix detrminant invers
Date: 4 Nov 92 22:31:09 GMT
Organization: Twenty-First Designs, Wash, DC

Help!

I have the following problem.  Any input on how to solve it is greatly
appreciated.  Please email me.

    job:  Invert the following matrix

                                     3 4 1 8
                                     1 1 2 0
                            [A] =    2 7 3 7
                                     1 0 6 5
        formula 1) first find the determinant of A (det A)
                2) to get the inverse, the formula is (1/det A) * [A]
                           The quotation marks should be brackets.
   For a 3 by 3 matrix

         a b c      the formula for the determinant is:
         d e f
         g h i                     det A = a(ei-fh) + b(fg-di) + c(dh-eg)

                    the formula for the inverse is:

          ei-fh/det A    ch-bi/det A   bf-ce/det A
          fg-di/det A    ai-cg/det A   cd-af/det A
          dh-eg/det A    bg-ah/det A   ae-bd/det A

I don't know how to apply this to a 4 by 4 matrix.  But I am willing to learn.


 ~~~~~~	 	
~~~~~ o	 	
~~~@   > 	
~~~   =         bret d weinraub	        bret@tfd.com
 ~~\__}	     	
 ~~    		
 ~		
		
		
		
Newsgroups: sci.math
From: wrblwski@phoenix.Princeton.EDU (Jaroslaw Tomasz Wroblewski)
Subject: Re: Extended Fermat primes
Originator: news@nimaster
Organization: Princeton University
Date: Thu, 12 Nov 1992 14:13:15 GMT

In article <1992Nov8.183618.25103@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>
>Sticking to exponent 128, replacing 120 by 190 and 234 yields the next
>two primes.  Nothing more out to 500.

The largest prime of the form (2a)^2^n+1 I could find is
852-digit  p=46^512+1 . Primality of p can be proved by verifying that 3 is a
primitive root mod p. 
-- 

Jarek (Jaroslaw Tomasz Wroblewski) ,   E-mail jwr@math.Princeton.EDU
Xref: sparky sci.math:14809 sci.physics:18734
From: tadpole@drysdale.ucr.edu (tad white)
Newsgroups: sci.math
Subject: digit puzzles (was Re: Math puzzles - answer)
Date: 6 Nov 92 18:43:36 GMT
Organization: University of California, Riverside

John Baez (jbaez@riesz.mit.edu) posted two math puzzles
<1992Oct28.170601.19561@galois.mit.edu>, to which he later gave
partial answers. He writes:

> The second question concerned the sum from 1 to infinity of o(2^n)/2^n.
> Here o(2^n) is the number of odd digits in the decimal representation of
> 2^n.  The sum is surprisingly simple - it's 1/9.

Along these lines, I can't resist posting the following (due to
Doug Bowman and myself):

For each nonnegative $n$, let $f(n)$ denote the sum of the Fibonacci
numbers $F_i$, over the integers $i$ such that the $i$th digit of
$2^n$ (counting from the right) is at least 5.  e.g., 2^26=67108864,
so f(26) = 21+13+0+0+3+2+1+0 = 40.

(For you Mathematica types, f[n_] := Block[ {zz},
	(zz=Reverse[Floor[IntegerDigits[2^n]/5]]).Fib[Range[Length[zz]]]]
where Fib is a {Listable} Fibonacci-number function.)

Then the sum of f(n)/2^n, over all nonnegative n, is 20/89.

/********************************************************\
*  Tad White                  UCR Dept. of Mathematics  *      
*  tadpole@ucrmath.ucr.edu    Riverside, CA  92521      *
\********************************************************/
-- 
/********************************************************\
*  Tad White                  UCR Dept. of Mathematics  *      
*  tadpole@ucrmath.ucr.edu    Riverside, CA  92521      *
\********************************************************/
Newsgroups: sci.math
From: macrakis@osf.org (Stavros Macrakis)
Subject: Re: symbolic derivation of polynomial roots
Organization: OSF Research Institute
Date: 9 Nov 92 18:16:48

In article <5412@daily-planet.concordia.ca> mckay@alcor.concordia.ca (John McKay) writes:

   My understanding is that the roots of ANY polynomial in Q[x] 
   can be expressed in terms of radicals. What is the trick?
   You may need infinitely many of them.

This is pretty vacuous.  If you allow infinite expressions (with some
suitable definition), you can write any real number starting with just
the integers and the arithmetic operators.  Consider the closed-form
but infinite "rational" representation of pi:

3 + 1*10^-1 + 4*10^-2 + 1*10^-3 + 5*10^-4 + ...

	-s
Xref: sparky sci.math:14854 sci.physics:18772 sci.astro:11926 sci.bio:4112 sci.chem:4538 misc.education:4266
From: nrswart@phonon.uwaterloo.ca (Nicholas R. Swart)
Subject: Re: NP Completeness Question
Organization: University of Waterloo
Date: Fri, 13 Nov 1992 02:11:06 GMT

In article <1dpkkeINNad2@mizar.usc.edu> tunal@mizar.usc.edu (Tamer Unal) writes:
...
>My guess is that 1. is in of polynomial complexity while 2.
>is NP-complete.
>
>Any pointers, references, appreciated.
>
Professor E.R. Swart of the Computer Science Department at the University
of Guelph, has recently developed a polynomial-sized linear programing
formulation of the graph isomorphism problem and he has been able to show
that with minor modifications, this same formulation can be used to solve
the Hamilton tour, clique and other subgraph isomorphism problems.

This proves that P=NP and all NP-complete and all other NP problems thus
have polynomial time algorithms.

So to answer your question, 1 and 2 are probably both polynomial.

Nicholas
Dept. of Elec. and Comp. Engineering
University of Waterloo
Waterloo, Ontario
CANADA
N2L 3G1

>-- 
>Serdar Boztas
>posting from someone else's account with their permission
>normally at serdar@fawlty8.eng.monash.edu.au
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education