HDTenEightyP/NetNews huggingface dataset:
From: manderse@orion.oac.uci.edu (Mark Andersen)
Subject: CART methods and software?
Summary: Where?
Newsgroups: sci.math.stat
Organization: University of California, Irvine
Date: 14 Sep 92 19:35:14 GMT
Distribution: na

I sure hope this isn't the proverbial FAQ, but does anyone here use CART 
Classification and Regression Tree) methods? I have recently decided that
these methods are worth looking into as spatial predictors, and possibly
for investigating organism-habitat relations (something I do a lot of).

I'm currently reading the CART book (by some permutation of Breiman, Freidman,
Olshen, and Stone), and would like to know if the software they describe
is available anywhere convenient (I know they suggest contacting one of the
authors, but I don't recall seeing a complete address in the book; does
anyone have it?).

Thanks in advance for any help.


Mark Andersen                   manderse@orion.oac.uci.edu
Dept. of Ecology and Evolutionary Biology
UC Irvine, Irvine, CA, 92717
Newsgroups: sci.math.stat
From: ppc1@cec1.wustl.edu (Peter Pui Tak Chiu)
Subject: FULL HOUSE (REVISED)
Organization: Washington University, St. Louis MO
Date: Sun, 13 Sep 1992 18:53:43 GMT



// this previous version of this program assumes that we are drawing from
// an infinite deck.  (which is a bug).

// now this version has no such problem...
// but still the probability is around 0.004...
// which is four times the theoretical value 0.001441

// what's wrong???!!!

#include <iostream.h>
#include <time.h>
#include <stdlib.h>
#include <math.h>

static int hand[5];
long COUNTER=0, GOOD=0;

int getRandom(){
int n,BAD=1;
while(BAD){
n=rand()%52+1;
for(int i=0;i<5;i++){
	int FLAG=0;
	if(n==hand[i])FLAG=1;
	if(!FLAG)BAD=0;
	}}
return(n);
}

void init(){
for(int i=0;i<5;i++)hand[i]=0;
for(i=0;i<5;i++)hand[i]=getRandom();
for(i=0;i<5;i++)hand[i]=hand[i]%13;
}

int fullhouse(){
int counter[13],flag2=0,flag3=0;
for(int i=0;i<13;i++)counter[i]=0;
for(i=0;i<5;i++)counter[hand[i]]++;
for(i=0;i<13;i++){
	if(counter[i]==2)flag2++;
	if(counter[i]==3)flag3++;
	}
return(flag2&&flag3);
}

main(){
randomize();
while(1){
COUNTER++;
init();
if(fullhouse())GOOD++;
if(!fmod(COUNTER,10000))cerr<<COUNTER<<double(GOOD)/COUNTER<<"\n";
}}
From: kc@cs.ucsd.edu (k claffy)
Newsgroups: sci.math.stat
Subject: measure of goodness of sample
Keywords: sampling, estimator, goodness, efficiency
Date: 7 Sep 92 02:45:24 GMT

Can anyone help me with the problem of
assigning a "goodness" grade to a given sample
of a population, for example based on one
or more of the following:
the error of the estimated parameter (mean/median), 
the variance of the sample (as compared with the
variance of the parent population?), and 
taking into account the sample size (so that,
ceterus paribus, smaller samples get better grades?)

i have Cochran but i can't find any universal
measure (right, there probably isn't any).  
i know there are standard formulas for variances 
of means of normal populations, for example, 
but i have a fairly bizarre parent population, 
and i want to assign ranks to 20 samples (taken
with different methods and different
sampling fractions).    
(i want to use the term "efficiency", 
but i assume someone else has defined this
and i'm just not reading the right books.
if so, i wouldn't mind knowing.  One of my
books mentions 'Gaussian efficiency' in passing
but doesn't define it.  argh.)

email appreciated -- i'll summarize if desired,
thanks much,
k
From: jerry@nutmeg.hnrc.tufts.edu (Jerry Dallal)
Newsgroups: sci.math.stat
Subject: Multi-dimensional parameters in Bayesian inference
Date: 13 Sep 92 23:21:42 GMT
Organization: USDA HNRC at Tufts University

In article <BuJ7v8.EKM@mentor.cc.purdue.edu>, hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

> But one thing to keep in mind--the higher the
> dimension, the more important the assumptions.
> -- 

I'm glad to see someone of Prof. Rubin's stature make this statement.  Although
I've spent a good deal of time studying Bayesian methods (I consider myself 
to have mastered the theory up a level represented by Lee's book), I am not
doing mathematical research in this area.  Some very good Bayesians have
made statements similar to Professor Rubin's, namely, that in multi-dimensional
problems the joint behavior of the parameters is more important than their
marginal behavior.  However, I have heard other knowledgeable Bayesians say
that in many problems, the solution is robust to assumptions about joint
behavior.  And I'm willing to admit that I have neither the honed skills nor 
burning interest to investigate the issue for myself.  Intuition tells me Rubin 
is correct.  I would appreciate a brief statement or two from those in the know
about just how serious this problem is.  Is there a wide variety of cases that
are inference robust to assumptions about joint behavior?  Or should I run for
the hills when someone writes, "Assuming *independent* non-informative priors
for theta1 and theta2 . . . "?

(Note:  the use of *non-informative* rather than *improper* or *uniform* was
intentional.  I mean it in the sense of Edwards, Lindman, and Savage where the
priors, while non-informative, are nevertheless, proper.)
Newsgroups: sci.math
From: platt@watson.ibm.com (Daniel E. Platt)
Subject: Re: Lebesgue integral (was: Couple of questions
Date: Fri, 11 Sep 1992 13:00:33 GMT
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM T.J. Watson Research Center

In article <12tnxa#.kmc@netcom.com>, kmc@netcom.com (Kevin McCarty) writes:
|> In article <1992Sep10.173619.24343@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
|> >In article <18neu6INN32k@function.mps.ohio-state.edu> edgar@function.mps.ohio-state.edu (Gerald Edgar) writes:
|> >
|> >>I have been told that the Lebesgue integral is not needed in physics--
|> >>presumably Riemann integral is enough.  Do you agree?
|> >
|> >Last I heard, the Hilbert space of a free particle was L^2(R^3), the
|> >space of all functions whose absolute value squared is LEBSEGUE integrable.
|> 
|> But is this a question of convenience or necessity?
|> In other words, how badly would you miss them if you threw out the
|> non-Riemann-square-integrable functions from L^2(R^3)?
|> Could still you do physics with but a slight limp, or would you be
|> flat on your back?
|> -- 

I think you would end up flat on your back.  The problem is that many (most)
of the techniques revolving around Fourier series and integrals, completeness
of a basis, etc, ultimately involve being able to evaluate 'improper' integrals
as a limit of an integral of a sequence of functions.  They often look like
Dirac-delta functions (the word 'function' is a misnomer, it is more like
a limit of a family of functions) which just hides the complexity under
some notation so that physicists don't have to worry about L^2(R^3).

Dan
From: shoham@ll.mit.edu (Daniel Shoham)
Newsgroups: sci.math
Subject: Re: Chess Problem
Date: 15 Sep 92 03:24:39 GMT
Organization: MIT Lincoln Laboratory

>In article <1992Sep12.174545.23214@ima.isc.com>, karl@ima.isc.com (Karl Heuer) writes:
>
>> Here's a more advanced chessboard question.
>> 
>> A white king, a black king, and a white pawn are randomly placed on an NxN
>> chessboard.  (Independent, uniform distributions.)  What is the limit, as
>> N -> infinity, of the probability that the position is a win for white?
>> 
>> (Note that it doesn't matter what you do about collisions or illegal
>> positions, since they occur with probability zero in the limit.)
>
We will assume optimal players on both sides (otherwise the question is
meaningless).

As stated, the probability is zero. A chess game is declared a draw
after 50 moves without an irreversible one. Even if white manages to get a
queen, the probability of finding the black king within 50 squares of an edge
is -> 0.

Suppose the 50-moves rule has been removed, and all that is needed is to queen
the pawn.

In a very large board, the likelihood of any of the three pieces starting
anywhere near any of the edges or each other is -> 0 so we will ignore it.

As I see it, white has a choice of two stratgies:
1. Run the pawn down and queen it without a king defense.
2. Move the king toward the pawn and defend it. Then advance the two in tandem.

(strategies where the king and pawn move toward each other may save time, but
they work just as well as strategy 2).

We will use an x-y system to describe the position of each square. The last
(queening) row is defined as y=0, whereas the first row is y=1. x, is similarly
ranged between 0 and 1.
(px,py) = pawn's starting position
(bx,by) = black (king) starting position
(wx,wy) = white (king) starting position

px, py, bx, by, wx, wy are iidrv with uniform (0,1) distribution.

Strategy 1 works if:
py < by  or  py < |px-bx|

Strategy 2 works if:
d(p,w) < d(p,b)      where d(i,j)=max(|ix-jx| , |iy-jy|)  (i.e. chess-distance)

We could now use brute force to integrate over all cases, or (if your religion
permits it) do a Monte Carlo simulation.

As my religion does not forbid me from doing a Monte Carlo after I have found
an analytic algorithm (that I am too lazy to integrate), I did it:

P(Draw) =~ 12.5%  (40,000 runs, i.e. +/- .5%)


Dan Shoham
shoham@ll.mit.edu
Newsgroups: sci.math
From: steele@isis.cgd.ucar.edu (Alfred Steele)
Subject: Re: Grobner basis reference
Organization: Climate and Global Dynamics Division/NCAR, Boulder, CO
Date: Mon, 7 Sep 1992 19:21:55 GMT

In article <9225121.16847@mulga.cs.mu.OZ.AU> ross@ecr.mu.oz.au (Ross McAree) writes:
|>Could someone please supply me with a good reference for
|>so called Grobner basis calculations. 
|>
|>Ross.
|>


Message 3/4  From Allan Adler                          Sep 5 '92 at 2:44 am -240


Date: Sat, 5 Sep 92 02:44:45 -0400


Groebner bases are explained in a lot of places. E.g.

(1) ALGEBRAIC COMPUTING WITH REDUCE by M.MacCallum and F.Wright
(2) probably in the tex file that accompanies the REDUCE Groebner basis
    package. You can get it free from reduce-netlib@rand.org by sending
    the message:
    send groebner.tex from documents
    send reduce.sty from documents
(3) Buchberger, "Groebner bases: an algorithmic method in polynomial ideal
    theory." In: Progress, directions and open problems in multidimensional
    sysytems theory, edited by N.K.Bose, pp.184-232 (1985) Reidel, Dordrecht
(4) J.H.Davenport, Y.Siret and E.TOurnier (1988) COmputer algebra: systems
    and algorithms for algebraic computation, Academic PRess, London
(5) David Bayer's thesis
(6) Maybe the Macaulay manual, but I'm not sure.
From: koiran@ens-lyon.fr (Pascal Koiran)
Newsgroups: sci.math
Subject: Re: decidability and dynamical systems
Date: 10 Sep 92 18:56:00 GMT
Reply-To: koiran@ens-lyon.fr
Organization: Ecole Normale Superieure de Lyon

The solution proposed by Arthur Rubin in sci.math.research is perfectly correct.
However, I'd like to have a less degenerate exemple. One might perhaps add 
a condition like 

"all the variables x_1,...,x_n must occur in each P_i"

or a similar but weaker condition like 

"The set of variables {1,...,n} cannot be partitioned in two subsets I1 and I2 
such that the two subsystems (x_i)_{i in I1} and (x_i)_{i in I2} evolve 
independently from each other".

The motivation behind my question is to find a dynamical property 
differentiating piecewise-linear functions from polynomial, rational, 
or analytic function on [0,1]^n. Any suggestion on this is welcome. 
For n=2, there exist non degenerate piecewise-linear functions with infinitely many k-cycles for every k, hence my question.

Pascal.
From: kosowsky@hall.harvard.edu (Jeffrey J. Kosowsky)
Newsgroups: sci.math
Subject: Re: Apology for Chess inaccuracy!
Date: 14 Sep 92 16:36:09 GMT
Organization: Harvard Robotics Lab, Harvard University

In article <BuHouB.BCF@cmptrc.lonestar.org> carter@cmptrc.lonestar.org (Carter Bennett) writes:
>	There are certainly more than two distributions of 8 rooks where no
>   two can attack one another.  Richard sent a couple of messages, the first
>   containing only the figure below.
>   @ - - - - - - -
>   - @ - - - - - -    My (inaccurate) assumption was that the rooks would
>   - - @ - - - - -  have to be lined up on one of the two diagonals.  As
>   - - - @ - - - -  shown here, this is not true.  Had I though this through
>   - - - - @ - - -  correctly, I should have realized that I could consider
>   - - - - - @ - -  one diagonal and allow all permutations of rows (or all
>   - - - - - - - @  permutations of columns, if you prefer, but not both).
>   - - - - - - @ - 
>	The upshot of this is that there are 8! distributions of 8 rooks that
>   meet the criteria that no two can attack each other; not 2, as I said
>   earlier.  >-X

Note that thes 8! "rook distributions" correspond to the group of 8x8
permutation matrices, or equivalently, the symmetric group of 8
letters.

Jeff Kosowsky
From: neilfp@astro.ocis.temple.edu (Neil F. Palumbo)
Newsgroups: sci.math
Subject: XAY+XB+CY+D=0, HELP
Date: 10 Sep 92 14:03:46 GMT
Organization: Temple University
X-Newsreader: Tin 1.1 PL5

I am trying to solve the matrix equation XAY+XB+CY+D=0 analytically for the
unknown matrices {X,Y}. Anyone have any ideas, comments, suggestions...?
Newsgroups: sci.math
From: kurt@eskimo.celestial.com (Kurt Cockrum)
Subject: Penrose tiling
Followup-To: comp.graphics
Keywords: non-periodic tiling, penrose tiling
Organization: >>> Eskimo North (206)-FOR-EVER <<<
Date: Thu, 10 Sep 1992 01:54:19 GMT

Does anybody have papers or info on Penrose tiling?
That's a non-periodic method of tiling the plane invented by Roger Penrose in
the mid-`70's.  Does anybody have a program that will generate penrose
tilings or detect when it is impossible to continue the current growth
pattern of a tiling and backtrack appropriately?  If there's enough interest,
I'll compile a bibliography and post it.
-- 
kurt@grogatch.celestial.com (Kurt Cockrum)
 "People who sign their own .sig are just net.personality wanna-bees." --
 K. Cockrum
Newsgroups: sci.math,rec.puzzles,comp.theory
From: plu@math.psu.edu (Todo Simpson)
Subject: Re: more on .999... = 10.0
Organization: Department of Mathematics, Pennsylvania State University
Date: Mon, 7 Sep 1992 20:27:27 GMT

In article <18dmplINNe0o@matt.ksu.ksu.edu> kodiak@matt.ksu.ksu.edu (Bryan D. Nehl) writes:

   Sorry for having taken so long to follow up on this subject.

   Proof that 10.0 = 9.9999...
   using algebra:

	   x =  9.999...
     10x = 99.999...
   10x-x = 99.999... - 9.999...
      9x = 90.0
       x = 10

	   10.0 = x = 9.999...

   .........................

   someone emails me using the above algebraic method that 
   ....999 is equal to -1.

Indeed, ....999 _is_ equal to -1.  We use the 5-adic valuation to
define a metric on the set of integers: d(m,n) is 5^{-ord_5(m-n)},
where ord_5(N) designates the largest integer k such that 5^k divides
N.  Thus m and n are close if m-n is divisible by a high power of 5.
Now consider the sequence 9, 99, 999, etc; the nth term is 10^n - 1,
and we have d(10^n - 1, -1) = 5^{-n}.  Therefore for any epsilon > 0,
we can find N such that from the Nth term on, the sequence is within
epsilon of -1.  Thus the limit of the sequence, which we shall denote
....999, is -1.

And now a new problem.... Say x = 1/2 + 1/4 + 1/8 + . . .
                    Then (1/2)x =       1/4 + 1/8 + . . .
                      So (1/2)x = 1/2
                          And x = 1.

But what if x = 1/2 + 2/4 +  3/8 +  4/16 + . . . ?
         Or x = 1/2 + 4/4 +  9/8 + 16/16 + . . . ?
         Or x = 1/2 + 8/4 + 27/8 + 64/16 + . . . (see the pattern)?

Try it...!

--
Todd Andrew Simpson           ``That would bother me like two per cent
Card-Carrying Elitist           of nothing at all.''  - Philip Marlowe
Newsgroups: sci.math
From: dak@tabaqui.informatik.rwth-aachen.de (David Kastrup)
Subject: Re: O(n)
Organization: Rechnerbetrieb Informatik  /  RWTH Aachen
Date: 12 Sep 92 18:52:05 GMT

nabritta@teaching.cs.adelaide.edu.au (Nigel) writes:

>Ok, this may seem a bit of a lame question to post in this group, but
>can someone out there please give me a bit of an explaination about the
>big 'o' function. I cant seem to understand what its for or the
>principle behind it. Replies by email would be appreciated.
O(n) means
always smaller in absolute value than a fixed constant times n.
This constant can be arbitrarily large, but must not depend on n.
From: be231642@longs.LANCE.ColoState.EDU (Bret Egan)
Newsgroups: sci.math
Subject: What about 3.4 dimension?
Date: 10 Sep 92 19:48:27 GMT
Reply-To: be231642@longs.LANCE.ColoState.EDU (Bret Egan)
Organization: Engineering College, Colorado State University

Is there any literature about the possibilites of dimensions of real numbers?

R^1.2 or R^pi

Bret
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: measures of the `size' of infinite sets
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Wed, 9 Sep 92 06:27:01 GMT

In article <1992Sep9.042345.7472@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:

>Well, there are various ways of keeping track of the "size" of infinite
>sets, depending on the context.  One branch of math that specializes 
								      ^in

>this is called measure theory.  The simplest example of that is the fact
>that a line segment which is twice as long as another has twice the
>"measure," even though by Cantor's definition they have the same number
>of points.  But for your problem the best answer involves not measure
>but "density".  Given a set of integers, we calculate its density as
>follows.  Figure out how many integers in your set lie between -n and n
>- say that m do.  Take the ratio n/2m ... this just tells us what
>fraction of the integers between -n and n lie in your set.  Now take the
>limit as n goes to infinity!  If the limit exists and equals d (some
>number between 0 and 1), we say your set has density d.

Okay, I got that one messed up all right.  Take the ratio m/(2n+1),
since there are 2n+1 integers between -n and n, counting the endpoints.
Newsgroups: sci.math
From: jmarlan@titan.nmt.edu (Jon Marlan)
Subject: Re: Chess Problem
Organization: New Mexico Tech
Date: Mon, 14 Sep 1992 17:49:27 GMT


In article <BuJvx3.34@acsu.buffalo.edu> kriman@acsu.buffalo.edu (Alfred M. Kriman) writes:
>
>It's not so simple.  The number of safe squares depends not only on the
>number of bishops previously placed (safely), but also on their locations.
>B(2) as given is correct only if the first bishop is placed at a corner.

Oops.  I obviously didn't give this one enough thought.  

Jon

--
Jon Marlan
jmarlan@titan.nmt.edu
From: jbaez@riesz.mit.edu (John C. Baez)
Newsgroups: sci.math
Subject: Re: ZFC etc. (was Re: Report on Philosophies of Physicists)
Date: 15 Sep 92 22:00:20 GMT
Organization: MIT Department of Mathematics, Cambridge, MA

Torkel Franzen writes:
In article <1992Sep15.165635.12446@galois.mit.edu> jbaez@riesz.mit.edu 
(John C. Baez) writes:

>   >The propositional calculus might be inconsistent and we have somehow
failed
 >  >to notice this so far; 

 >  This is an observation of the same kind as "perhaps the fundamental
>theorem of arithmetic is not really true", or "perhaps Euclid's
>algorithm sometimes gives the wrong answer", and so on. Not very
>exciting stuff.

I'm sorry not to have excited Torkel, but as the original questioner
was wondering whether the evidence for the consistency of ZFC was
only empirical, I thought this was worth noting, since some people
seem to think it is *impossible* that the propositional calculus
is inconsistent.
Newsgroups: sci.math
From: hgraber@lynx.cat.syr.edu (Harry Graber)
Subject: measures of the `size' of infinite sets
Organization: Syracuse University
Date: Tue, 8 Sep 92 13:46:24 EDT

     I am familiar with the method devised by Cantor for comparing the card-
inality of two infinite sets.  Suppose I divide all the positive integers into
two sets, one consisting of all numbers that are multiples of 29, and the other
containing all the rest (I have no special reason for choosing the number 29,
except that it is >2).  There is no doubt but that a one-to-one correspon-
dence can be established between these sets, so they are commensurable. Accord-
ing to Cantor, then, both sets are the same size.

     An associate of mine here tells me that there are other measures that
have been devised for the size of an infinite set.  Some of these measures
give a different result, and agree with our `intuitive' position that the set
of multiples of 29 is in some definite sense smaller than the set of numbers
that are not multiples of 29.  However, this is an area neither of us has
specialized in.  I never knew that these other measures even existed, and he
had heard of them but is not able to tell me what any of them is.  Will you
kind and sagacious folks out there please send some enlightenment my way?

--H. Graber
From: gvw@epcc.ed.ac.uk (Greg Wilson)
Newsgroups: sci.math
Subject: Origin of Matrices??
Date: 6 Sep 92 16:14:49 GMT
Organization: Edinburgh Parallel Computing Centre

I am trying to find out how matrices (and linear algebra) came to be ---
who was the first mathematician to use matrix notation, how quickly did
it spread, etc.

Please reply directly, as I am not a regular reader of this newsgroup.

Thanks,

 ========================================================================
  Gregory V. Wilson                    ||  For in much wisdom is much
  Technical Coordinator                ||  grief; and he that increaseth
  Edinburgh Parallel Computing Centre  ||  knowledge, increaseth sorrow.
  gvw@epcc.edinburgh.ac.uk             ||               - Ecclesiastes
 ========================================================================
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Perfect numbers requested.
Date: 10 Sep 92 01:52:01 GMT
Organization: U of Cambridge, England

You will find your search helped by the following two facts:

FACT 1. An even number is perfect if and only if it is of the form
             p-1   p
            2    (2 - 1)
        where the number in () is prime. These so-called "Mersenne primes"
        have been the subject of much investigation; it isn't even known
        whether there are infinitely many of them. About thirty have been
        found, and you should be able to find a list (which may be slightly
        out of date, but that probably doesn't matter for your purposes)
        in any decent textbook on number theory.

FACT 2. No odd perfect numbers are known, though there is no known proof
        that there are none. It has been proved that any odd perfect number
        must be very, very large indeed.
-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math
From: dzk@cs.brown.edu (Danny Keren)
Subject: Re: What is a spline?
Organization: Brown University Department of Computer Science
Date: Wed, 16 Sep 1992 01:05:30 GMT

<16863BC9B.N020BA@tamvm1.tamu.edu> N020BA@tamvm1.tamu.edu writes:
#
#     What is a spline? Reply either by E-mail or to the net. Thank you very
#much!

There are many kinds of splines. Usually, it means a function that is
piecewise polynomial (meaning its a different polynomial over different
patches of the region its defined above) which is twice differentiable
(which means the different polynomials "glue" nicely over the boundaries
of the patches). There are, however, "thin plate splines" which are
used for interpolation in Computer Vision and other areas, which
don't have any simple analytic form.

This is really a huge topic. A good reference is "A practical guide
to splines", by De-Boor, but no single book can possibly cover
everything.


-Danny Keren.


Newsgroups: sci.math
From: rjk@world.std.com (robert j kolker)
Subject: Re: What kind of algebra is this?
Organization: The World Public Access UNIX, Brookline, MA
Date: Wed, 9 Sep 1992 21:20:55 GMT

Boolean Algebra + is disjunction and * is conjunction. A both are
idempotent operators.

Robert J. Kolker (aka Conan the Librarian)