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From: Osher Doctorow on 20 Jun 2010 19:54
From Osher Doctorow

As readers can see from the last few posts, Probable Causation/
Influence (PI) is closely related to Paperfolding, Fibonacci topics of
all types, Palindromes and/or Reversals, and so on.

Jean-Paul Allouche (CNRS, LRI, U.-Paris-Sud), Michael Baake (U.
Greifswald Germany), Julien Cassaigne (CNDS, IML), and David Damanik
(CalTech USA), in "Palindrome Complexity," arXiv: math/0106121 v1
[math.CO] 14 Jan 2001, 24 pages, relate these to each other or one
another and to quasicrystals and Fibonacci words directly or
indirectly.

I already pointed out recently that "Palindromes" as keyword has 19
papers in arXiv, and "Paperfolding (sequences)" has 3 papers in arXiv,
Rudin-Shapiro sequences has 2 papers in arXiv (covered in Allouche et
al 2001), Fibonacci Word has 1 paper in arXiv (2010), while
"Sturmian" (also covered in Allouche et al 2001) has 37 papers in
arXiv between 1993 and 2010 including 5 in 2010 and 3 in 2009.
"Sturmian Word", "Sturmian Strings," "Sturmian Sequences", "Sturmian
numbers", "Sturmian factors" are covered directly or indirectly in
Allouche at al 2001 also.

See also Wikipedia's "Fibonacci Word" online, which gives a famous
example of a (standard) Sturmian word which is the Fibonacci Word
whose various properties are related to the Fibonacci Numbers which in
turn are related to PI from earlier posts in this thread, and in turn
to the Golden Ratio.

Osher Doctorow
From: Osher Doctorow on 20 Jun 2010 20:06
From Osher Doctorow

To a one-dimensional quasicrystal, one can associated a discrete
family of one-dimensional Schrodinger operators whose spectral
properties determine the "conductivity" properties of the structure -
roughly, if the spectrum is absolutely continuous, then it behaves
like a conductor, while for a pure point spectrum it behaves like an
insulator, and in between the singular continuous spectrum has various
complicated properties, explained in part by Allouche (2001) et al.

Osher Doctorow
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