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Advisor(s)
Abstract(s)
It has been shown that in reality at least two general scenarios of data structuring are possible:
(a) a self-similar (SS) scenario when the measured data form an SS structure and
(b) a quasi-periodic (QP) scenario when the repeated (strongly correlated) data form random
sequences that are almost periodic with respect to each other. In the second case it becomes
possible to describe their behavior and express a part of their randomness quantitatively in
terms of the deterministic amplitude–frequency response belonging to the generalized Prony
spectrum. This possibility allows us to re-examine the conventional concept of measurements
and opens a new way for the description of a wide set of different data. In particular, it
concerns different complex systems when the ‘best-fit’ model pretending to be the description
of the data measured is absent but the barest necessity of description of these data in terms of
the reduced number of quantitative parameters exists. The possibilities of the proposed
approach and detection algorithm of the QP processes were demonstrated on actual data:
spectroscopic data recorded for pure water and acoustic data for a test hole. The suggested
methodology allows revising the accepted classification of different incommensurable and
self-affine spatial structures and finding accurate interpretation of the generalized Prony
spectroscopy that includes the Fourier spectroscopy as a partial case.
Description
Keywords
Complex systems Random data processing Quasi-periodic process The generalized Prony spectrum
Citation
Publisher
IOP Science - Royal Swedish Academy of Sciences