aam9n@uvaee.ee.virginia.EDU (Ali Minai) (10/06/89)
I have a question which might or might not make sense. Still, since
it is of great interest to me, I shall be grateful if people share
their views, suggestions and references on this topic with me. Of
course, I shall be particularly grateful if someone pointed out the
absurdity of the whole issue.
The question is this:
Given deterministic data {(X,Y)} where X is in a finite interval of
n-d real space and Y is in a finite interval of m-d real space,
what *structural* measures (if any) have people suggested for
the "complexity" of the data?
This immediately raises several other issues:
1) What possible notions of "complexity" might one admit in this regard?
2) What might be the *order* of this complexity? Should it, for example,
be defined over the set of all points, all pairs, all triplets etc.?
3) Given that the data is not uniformly distributed over the domain (i.e.
it is "lumpy"), what assumptions must be made regarding the blank areas?
Should these be statistical? (probably yes).
4) How can such a "complexity" measure be made scale-invariant?
etc.
Also, what about such complexity measures for continuous functions?
I mean measures defined structurally, not according to the type
of the function (e.g. degree for polynomials).
My gut feeling is that some sort of information-based measure is
appropriate, but whatever is used must be efficiently computable.
Have other people tried to deal with this problem? Since I am sure
they have, where can I find the material? What would be the appropriate
area of mathematics to look for such references? I am currently searching
approximation theory, statistical modelling, maximum-entropy theory,
measure theory, information theory, complexity theory (both system
and computational) and non-linear dynamics literature. Obviously, I
will miss more than I will find, hence this request. A particularly
helpful thing would be names of journals which regularly carry material
relevant to this issue. Also, is the International Journal of General
Systems still published? If not, what did it turn into? Or rather, who
carries articles about "the theory of things", "the calculus of
indications" etc? I am extremely interested.
Thank you.
Ali Minai
Dept. of Electrical Engg.
Thornton Hall,
University of Virginia,
Charlottesville, VA 22903.
aam9n@uvaee.ee.virginia.edupa1159@sdcc13.ucsd.EDU (Matt Kennel) (10/07/89)
In article <517@uvaee.ee.virginia.EDU> aam9n@uvaee.ee.virginia.EDU (Ali Minai) writes: > > >The question is this: > >Given deterministic data {(X,Y)} where X is in a finite interval of >n-d real space and Y is in a finite interval of m-d real space, >what *structural* measures (if any) have people suggested for >the "complexity" of the data? > I don't know what other people have suggested, but I'll spout out a suggestion of my own: crib ideas from the nonlinear dynamics people. For a rough-and-ready measure of the complexity of the input space, why not use fractal dimension? And for the output space, what about the sum of the positive Lyapunov exponents of the nonlinear mapping? >4) How can such a "complexity" measure be made scale-invariant? That's exactly what the fractal dimension does? > >etc. > >Also, what about such complexity measures for continuous functions? >I mean measures defined structurally, not according to the type >of the function (e.g. degree for polynomials). I don't understand what you mean by "defined structurally." >Ali Minai >aam9n@uvaee.ee.virginia.edu Matt Kennel UCSD physics pa1159@sdcc13.ucsd.edu
cybsys@bingvaxu.cc.binghamton.edu (CYBSYS-L Moderator) (10/10/89)
[ Cross-posted from CYBSYS-L@BINGVMB ] Really-From: heirich%cs@ucsd.edu (Alan Heirich) I am also interested in the question of complexity measures raised by Ali Minai. I think it is an important issue for anyone concerned with self organizing systems -- i.e. how can you measure the extent to which a system is organized? Some candidates I've thought of are Shannon entropy, Kolmogorov entropy, "integrality" (a measure defined by I-don't-remember-who, discussed by Brooks in the recent book "Information, entropy and evolution", which I assume readers of this list are familiar with, or should be). I would like to hear about other possibilties. ------------------------- Alan Heirich Comp. Sci. & Eng., Cognitive Science C-014 University of California, San Diego 92093 heirich@cs.ucsd.edu aheirich@ucsd.bitnet
cjoslyn@bingvaxu.cc.binghamton.edu (Cliff Joslyn) (10/17/89)
I'd like to thank the contributors (I agree more with the latter). This
discussion was originally cross-posted to alt.cyb-sys, and this
conversation continues on subjects of key interest to systems scientists
and cyberneticians.
I am taking the liberty of cross-posting these two notes again to
alt.cyb-sys and also to my mailing list, CYBSYS-L@BINGVMB.BITNET. I'd
like to invite anyone interested here to joing us there. Blurb follows.
============================================================================
ANNOUNCING FORMATION OF A MAILING LIST FOR SYSTEMS AND CYBERNETICS
An electronic mailing list dedicated to Systems Science and Cybernetics
is currently in operation on the SUNY-Binghamton computer system. The
list is commited to discussing a general understanding of the evolution
of complex, multi-level systems like organisms, minds, and societies as
informational entities containing possibly circular processes. Specific
subjects include Complex Systems Theory, Self-Organizing Systems Theory,
Dynamic Systems Theory, Artificial Intelligence, Network Theory,
Semiotics, fractal geometry, Fuzzy Set Theory, Recursive Theory, computer
simulation, Information Theory, and more.
The purposes of the list include: 1) facilitating discussion among those
working in or just interested in the general fields of Systems and
Cybernetics; 2) providing a means of communicating to the general
research community about the work that Systems Scientists and
Cyberneticians do; 3) housing a repository of electronic files for
general distribution concerning Systems and Cybernetics; and 4) providing
a central, public directory of working Systems Scientists and
Cyberneticians. The mailing list can store or transmit notes and
messages, technical papers, references, calls for papers, computer
programs, and pictures and diagrams.
The list is coordinated by members of the Systems Science department of
the Watson School at SUNY-Binghamton, and is affiliated with the
International Society for the Systems Sciences (ISSS) and the American
Society for Cybernetics (ASC). The list is open to everyone, and we
currently have two hundred members from America, Canada, and Europe. Our
subscribers are from both academia and industry, and while many are
active researchers, others are just "listening in". We share in an
exciting, ongoing, multi-way conversation about many aspects of Systems
and Cybernetics. Different levels and kinds of knowledge and experience
are represented.
We invite all to join the discussion. To subscribe, you need a computer
account with access to one of the international networks (e.g. BITNET,
USENET, ARPANET, INTERNET, CSNET). Send a file containing only the line:
'SUB CYBSYS-L Your Full Name' to the list server at the address
LISTSERV@BINGVMB.BITNET.
Once subscribed, please post a message to the list itself at the address
CYBSYS-L@BINGVMB.BITNET. In the message, include your name, affiliation,
and a brief description of your work and/or interest in the fields of
Systems and Cybernetics.
List moderator: CYBSYS@BINGVAXU.CC.BINGHAMTON.EDU
Author: Cliff Joslyn, CJOSLYN@BINGVAXU.CC.BINGHAMTON.EDU
--
O---------------------------------------------------------------------->
| Cliff Joslyn, Cybernetician at Large
| Systems Science, SUNY Binghamton, cjoslyn@bingvaxu.cc.binghamton.edu
V All the world is biscuit shaped. . .