436,441 research outputs found
Forbidden ordinal patterns in higher dimensional dynamics
Forbidden ordinal patterns are ordinal patterns (or `rank blocks') that
cannot appear in the orbits generated by a map taking values on a linearly
ordered space, in which case we say that the map has forbidden patterns. Once a
map has a forbidden pattern of a given length , it has forbidden
patterns of any length and their number grows superexponentially
with . Using recent results on topological permutation entropy, we study in
this paper the existence and some basic properties of forbidden ordinal
patterns for self maps on n-dimensional intervals. Our most applicable
conclusion is that expansive interval maps with finite topological entropy have
necessarily forbidden patterns, although we conjecture that this is also the
case under more general conditions. The theoretical results are nicely
illustrated for n=2 both using the naive counting estimator for forbidden
patterns and Chao's estimator for the number of classes in a population. The
robustness of forbidden ordinal patterns against observational white noise is
also illustrated.Comment: 19 pages, 6 figure
Minimal Forbidden Factors of Circular Words
Minimal forbidden factors are a useful tool for investigating properties of
words and languages. Two factorial languages are distinct if and only if they
have different (antifactorial) sets of minimal forbidden factors. There exist
algorithms for computing the minimal forbidden factors of a word, as well as of
a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an
algorithm that, given the trie recognizing a finite antifactorial language ,
computes a DFA recognizing the language whose set of minimal forbidden factors
is . In the same paper, they showed that the obtained DFA is minimal if the
input trie recognizes the minimal forbidden factors of a single word. We
generalize this result to the case of a circular word. We discuss several
combinatorial properties of the minimal forbidden factors of a circular word.
As a byproduct, we obtain a formal definition of the factor automaton of a
circular word. Finally, we investigate the case of minimal forbidden factors of
the circular Fibonacci words.Comment: To appear in Theoretical Computer Scienc
Forbidden triads and Creative Success in Jazz: The Miles Davis Factor
This article argues for the importance of forbidden triads - open triads with
high-weight edges - in predicting success in creative fields. Forbidden triads
had been treated as a residual category beyond closed and open triads, yet I
argue that these structures provide opportunities to combine socially evolved
styles in new ways. Using data on the entire history of recorded jazz from 1896
to 2010, I show that observed collaborations have tolerated the openness of
high weight triads more than expected, observed jazz sessions had more
forbidden triads than expected, and the density of forbidden triads contributed
to the success of recording sessions, measured by the number of record releases
of session material. The article also shows that the sessions of Miles Davis
had received an especially high boost from forbidden triads
The Fixed Point Property for Posets of Small Width
The fixed point property for finite posets of width 3 and 4 is studied in
terms of forbidden retracts. The ranked forbidden retracts for width 3 and 4
are determined explicitly. The ranked forbidden retracts for the width 3 case
that are linearly indecomposable are examined to see which are minimal
automorphic. Part of a problem of Niederle from 1989 is thus solved
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