From: Edmund R. Kennedy <ekennedyx_at_yahoo_dot_com>

Date: Sat Jul 22 2006 - 13:59:37 CDT

Date: Sat Jul 22 2006 - 13:59:37 CDT

Hello All:

--- laird popkin <lairdp@gmail.com> wrote:

*> While a chart is great to _illustrate_ the
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*> relationships between the
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*> variables, as a math major, I'd agree with Ed that
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*> they're just an
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*> illustration, and say that it would be much better
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*> to present the required
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*> sample size given the various inputs as a formula
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*> (if possible, and it seems
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*> to me that it ought to be) because it's much easier
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*> to analyze, and thus
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*> trust, a formula than a computer program. Computer
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*> programs typically are
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*> great for validating models (e.g. monte carlo
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*> simulations) but aren't a
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*> great way to prove things in an absolute sense. And
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*> while graphs are great
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*> for showing relationships, if people actually use
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*> graphs to look up values
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*> it's slow and error prone. Imagine if people had to
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*> look up their tax rates
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*> on a chart to fill out their income taxes. :-) A
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*> formula, and perhaps
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*> pre-calculated reference tables, would be ideal.
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*>
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*> To illustrate the relationships between the
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*> variables, you don't need to
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*> graph all of the combinations. You could do a
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*> reasonable job of a basic
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*> sensitivity analysis with only four graphs (e.g.
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*> "typical values for three
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*> inputs, then chart the fourth input against the
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*> confidence level", for each
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*> of the four inputs). Most business sensitivity
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*> analysis are worked out to
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*> this level, as it's enough to answer questions like
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*> "how do my assumptions
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*> of the maximum rate of margin-shifting per machine
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*> affect the required vote
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*> count audit sample size?"
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*>
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*> To be more thorough, such as for a deeper academic
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*> analysis, you might want
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*> to show all combinations of three values per input
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*> (min, mean and max, for
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*> example). That would be 108 charts (3*3*3*4), which
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*> nobody would ever read.
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*> But you could put three lines on each chart (i.e.
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*> the lines for the
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*> min/mean/max of one of the inputs, or "family of
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*> curves" you mentioned) and
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*> that would get you down to 36 charts, which is (IMO)
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*> manageable for a
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*> detailed, academic analysis.
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*>
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*> Hmm. I don't know whether than explanation of how
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*> the charting could be done
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*> is sufficiently clear. If you can send me the
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*> confidence formula, I can
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*> quickly generate a set of the charts as I've
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*> described, so that you can see
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*> what I'm talking about. If the "formula" is a
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*> computer program, this might
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*> be tricker, depending on the program's complexity
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*> and what it's written in.
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*>
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*> - LP
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*>
*

*> On 7/22/06, Kathy Dopp <kathy.dopp@gmail.com> wrote:
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*> >
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*> > On 7/21/06,
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*> >
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*> > > Message: 3
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*> > > Date: Fri, 21 Jul 2006 11:30:35 -0700 (PDT)
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*> > > From: "Edmund R. Kennedy" <ekennedyx@yahoo.com>
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*> > > Subject: Re: [OVC-discuss] approximate solutions
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*> > >
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*> > > Hello Jerry:
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*> > >
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*> > > Actually the graphs and tables are still quite
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*> useful
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*> > > for checking and cutting down orders of
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*> magnitude
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*> > > errors.
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*> > > While it's great to get precise solutions with
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*> > > today's calculators and computers, it's much
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*> easier to
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*> > > display how things relate to the variables with
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*> a
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*> > > graphical approximation.
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*> >
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*> > Ed and Jerry,
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*> >
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*> > I love graphs, but there are four independent
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*> variables (election
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*> > margin, total #vote counts, desired probability,
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*> and the assumed
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*> > maximum rate of margin-shifting per machine) and
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*> one dependent
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*> > variable - the vote count audit sample size. We
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*> could make graphs by
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*> > holding three of the independent variables fixed
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*> and vary one of the
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*> > independent variables for each graph, but you
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*> would end up with LOTS
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*> > of graphs. The three variables with the fewest
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*> real life values for
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*> > them that would be needed, would be assumed
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*> maximum margin
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*> > shift/machine, probability and candidate margin,
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*> so taking candidate
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*> > margins from 1% to say 15% and probabilities of
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*> say 90% to 98%, there
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*> > could be 15*8 =120 charts that election officials
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*> could use to look up
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*> > how many vote counts to select for audit if they
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*> have N vote counts in
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*> > their county - assuming we give them only one
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*> option for max vote
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*> > counts.
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*> >
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*> > I think that you are suggesting that we could
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*> simply do something
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*> > like have 15 charts for the 15 margins of interest
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*> (assuming that all
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*> > races in a county are audited with the same sample
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*> size determined by
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*> > the race with the smallest margin -- I don't know
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*> enough yet to
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*> > conclude that would be the case with optical scan
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*> ballots that you
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*> > could sort to count, but I would assume that would
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*> have to be the best
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*> > approach with stupid DRE paper rolls) each with
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*> nine curves on them
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*> > for the nine probabilities they may want.
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*> >
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*> > To do a family of curves for a family of charts to
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*> make it easy to
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*> > look up values for vote count auditing would
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*> require some
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*> > decision-making re. the range of values to use to
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*> create charts and
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*> > curves for.
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*> >
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*> > I agree with you that presenting a book of charts
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*> and/or tables for
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*> > people to use to calculate vote count audit
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*> margins is a good idea
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*> > providing the "family of curves" for each desired
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*> probability or
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*> > candidate vote count margin don't overlap each
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*> other illegibly because
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*> > then say 120 charts would be needed rather than 15
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*> - but regardless,
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*> > this is a big project that a computer would need
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*> to generate.
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*> >
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*> > So we still need a program or spreadsheet that
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*> will generate the
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*> > charts for us, whether from an exact formula if we
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*> obtain one, or from
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*> > an algorithm.
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*> >
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*> > A book of tables and charts may be more likely to
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*> be used than a
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*> > spreadsheet that required trial and error or even
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*> a computer program
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*> > that let users input the four independent vars and
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*> found the exact
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*> > answer - is that what you're saying?
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*> >
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*> > Thanks.
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*> >
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*> > Kathy
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*> >
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*> > "Enlighten the people generally, and tyranny and
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*> oppressions of body
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*> > and mind will vanish like evil spirits at the dawn
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*> of day," wrote
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*> > Thomas Jefferson in 1816
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*> > _______________________________________________
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*> > OVC-discuss mailing list
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*> > OVC-discuss@listman.sonic.net
*

*> >
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*> http://lists.sonic.net/mailman/listinfo/ovc-discuss
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*> >
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*>
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*>
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*>
*

*> --
*

*> - Laird Popkin, cell: 917/453-0700
*

*> > _______________________________________________
*

*> OVC-discuss mailing list
*

*> OVC-discuss@listman.sonic.net
*

*> http://lists.sonic.net/mailman/listinfo/ovc-discuss
*

*>
*

-- 10777 Bendigo Cove San Diego, CA 92126-2510 858-578-8842 Work for the common good. My profile: <http://geocities.com/ekennedyx/> I blog now and then at: <http://ekennedyx.blogspot.com/> _______________________________________________ OVC-discuss mailing list OVC-discuss@listman.sonic.net http://lists.sonic.net/mailman/listinfo/ovc-discuss ================================================================== = The content of this message, with the exception of any external = quotations under fair use, are released to the Public Domain ==================================================================Received on Mon Jul 31 23:17:06 2006

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