From Osher Doctorow
Take a look at Wikipedia's "Higher spin alternating sign matrix,"
which has both rows and columns summing not to 1 as usual but to
integer r (the spin). They have applications in statistical mechanics
and physics including representing symmetry groups in ice crystal
formation.
There are 31 arXiv papers on "alternating-sign matrices", and 37
papers on "alternating matrix", and on the authors, James Propp of U.
Wisconsin Madison USA (previously MIT), had his 2002 paper (submitted
or revise in 2006?) supported by both the National Science Foundations
and the National Security Agency USA. This is "The many faces of
alternating-sign matrices," arXiv: math.CO/0208125 v1 15 Aug 2002, 22
pages.
Causal alternating signs in Probable Influence/Causation (PI) arise in
various ways, one of the most curious being the following way.
Consider:
1) A1 --> (A2 --> (A3 --> ...
which can be infinite or terminating. Now replace each set/event Ai,
i = 1, 2, ..., by a Probable Influence Pi:
2) P1 --> (P2 --> (P3 --> ...
This translates as:
3) 1 - (P1 - (P2 - (P3 - (P4 - ...
which the reader can show equals:
4) 1 - P1 + P2 - P3 + P4 - ...
Thus, alternating series whether finite or infinite, can represent
Causal relationships among the terms, and conversely a search for
Causal relationships can well be directed toward such series.
Osher Doctorow
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