29 May 2013 Entropy estimation and Fibonacci numbers
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We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. Notably, the number of distinct metric values for a set of sequences of length m is equal to Fm+3 − 1, where Fm is a Fibonacci number.
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Evgeniy A. Timofeev, Evgeniy A. Timofeev, Alexei Kaltchenko, Alexei Kaltchenko, } "Entropy estimation and Fibonacci numbers", Proc. SPIE 8750, Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering XI, 875016 (29 May 2013); doi: 10.1117/12.2016140; https://doi.org/10.1117/12.2016140

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