Toward A "Universal Sequence Indicator" (USI)?
Jon Awbrey
jawbrey at oakland.edu
Sat Jul 7 16:10:32 CEST 2001
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Neil & SeqFan Group,
I introduced the theme of a 'Universal Sequence Indicator' (USI)
to the Topic Map Mail List as a potential subject for web-based
development. Here is their archive site if anybody here wishes
to follow or to participate in the discussion:
http://www.infoloom.com/pipermail/topicmapmail/
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| I Know Off The Wall ...
| Off The Wall Isa Friend Of Mine ...
Murray & the Wallflowers, [didn't they warm for the Stimes one time? ...]
The graphical structures that I chrismed "riffs" and "rotes"
arose in my work of the late 70's and early 80's while I was
thinking of questions like: What would be the limiting case
of a molecular tagging strategy? What if the molecules that
we already have were designed to be the tagends of something
else that formed the base of this very sort of recursive bit?"
And so on ...
I have recently returned, due to a sequence of coincidences
that I am still trying to assimilate, to revisit this work --
I am between the flu and fleeing on holiday right now, but
I will get a series of reports together for TopicMapMail &
other (imp)ertinent lists in due time.
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Murray Altheim wrote:
>
> This is going to sound perhaps a bit off the wall, but for the work
> I'm doing with the Bootstrap Institute (bootstrap.org), I'm likely to
> be publishing a new markup language. While XTM can support a topic map
> view of a set of nodes as a "document," more traditional documents are
> merely sequences of nodes, sometimes portions of which (headers, footers,
> legal notices, etc.) are repeated. I've whipped up a prototype Sequence Map
> Markup Language (SMML) which is capable of representing such sequences of node
> identifiers. It's pretty simple, really.
>
> Do you guys think there might be any application for this amongst the
> integer people? (I'll likely not get back to this thread until Friday
> or Saturday, BTW). What types of features do you think would be needed?
>
> Thanks!
>
> Jon Awbrey wrote:
> >
> > ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
> >
> > Paul Prueitt wrote:
> > >
> > > The transformation of the web site on integer sequences to a topic map "index"
> > > would face a couple of issues. First of all sequences are mutually related by
> > > being "another sequences" but also by other kinds of relationships, some known
> > > and some unknown. A major piece of number theory will have already gone into
> > > delineating the relationships between sequences.
> > >
> > > I would imagine that the average number of pair wise relationships might be 5 - 10.
> > > (Actually this number of relationships could go very high.)
> > >
> > > Would anyone see a problem with this issue?
> > >
> > > ***
> > >
> > > Also I have a question:
> > >
> > > Bernard said:
> > >
> > > 4. "Author" should be another topic type, linked to sequences through
> > > "authoring" associations. (One question which is open in defining
> > > such association types is the incidence of each role type:
> > > one author or one sequence by association?)
> > >
> > > Would you explain what you mean here by incidence of each role type ...
> > > in this context?
> > >
> > > Perhaps this is the same question, but how might scope be used
> > > in a retrival or navigation task?
> > >
> > > _______________________________________________
> > > topicmapmail mailing list
> > > topicmapmail at infoloom.com
> > > http://www.infoloom.com/mailman/listinfo/topicmapmail
> >
> > ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
> >
> > Paul,
> >
> > FYSMI ("funny you should mention it"), I just sent
> > a note off to the SeqFan List about this very topic,
> > which is short enough to copy here:
> >
> > ¤~~~~~~~~~¤~~~~~~~~~¤~ARCHIVE~¤~~~~~~~~~¤~~~~~~~~~¤
> >
> > Subj: Universal Sequence Index (USI)?
> > Date: Sat, 30 Jun 2001 12:34:01 -0400
> > From: Jon Awbrey <jawbrey at oakland.edu>
> > To: Sequence Fanatics <seqfan at ext.jussieu.fr>
> >
> > [ Nota Bene. I had meant to write "Universal Sequence Indicator"
> > | but a long-entrained motor habit took possession of my fingers.
> > ]
> >
> > SeqFans,
> >
> > Several recent notes have given me flashbacks to this old theme,
> > which I just realized how to express in more contemporary terms.
> > For some reason Marc's note makes me think of Conway's Fractran.
> >
> > EIS is a resource that I will call "Lot_X", or "L_X" for short,
> > X being an index value to be named later. I am tempted to let
> > X equal something between 1 and 7^2, but I do not know yet how
> > much of an initial segment might be needed for other resources.
> >
> > I do not have a complete idea here, but here are a couple
> > of fragmentary ideas that may form the ingredients of one:
> >
> > Ingredient 1.
> >
> > If L_X^(L_A061396) = L_X^(L_A061396^1) is my initial sequence,
> > then the expression "L_X^(L_A061396^n)" might serve to denote
> > A061396's n-th element, although I don't want to fix this too
> > rigidly right yet as other ways of doing this may work better.
> >
> > Ingredient 2.
> >
> > Now, riffs are constituted in such a way as to yield a code value v(f)
> > for each finite partial function f : M -> M, where M = 1, 2, 3, 4, ...
> > Is there a good way of using this natural scheme to specify a sequence
> > in terms of references to other sequences, assuming that we can design
> > all the details of de/referencing to work out as elegantly as possible?
> > Exercise for the reader. I'll think about it a bit and get back to you.
> >
> > Jon Awbrey
> >
> > ¤~~~~~~~~~¤~~~~~~~~~¤~EVIHCRA~¤~~~~~~~~~¤~~~~~~~~~¤
> >
> > Data about "riffs" (rooted index-functional forests")
> > and cousin "rotes" (rooted odd trees with only exponent symmetries")
> > can be found at the following locations:
> >
> > http://www.research.att.com/~njas/sequences/a061396.txt
> > http://www.research.att.com/~njas/sequences/a061396a.txt
> > http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A061396
> > http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A062504
> > http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A062860
> > http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A062537
> >
> > I think that if one thinks about it one would realize, as I know that at least one did,
> > that this problem is much more generic vis-à-vis storing and finding hyperdata than it
> > may initially appear.
> >
> > Jon Awbrey
> >
> > P.S. I am copying this note to Sloane and the SeqFan List, using BCC,
> > not to be secretive or anything, but just to avoid bothering the
> > busy beavers more than need B.
> > J.A.
> >
> > ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
> >
> > topicmapmail mailing list
> > topicmapmail at infoloom.com
> > http://www.infoloom.com/mailman/listinfo/topicmapmail
>
> --
>
> Murray
>
> ...........................................................................
> Murray Altheim <mailto:murray.altheim@sun.com>
> XML Technology Center
> Sun Microsystems, Inc., MS MPK17-102, 1601 Willow Rd., Menlo Park, CA 94025
>
> In the evening
> The rice leaves in the garden
> Rustle in the autumn wind
> That blows through my reed hut. -- Minamoto no Tsunenobu
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