Recurrence Quantification Analysis and Principal Components in the Detection of Short Complex Signals

Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence quantification analysis with principal components analysis to allow for a probabilistic evaluation for the presence of deterministic signals in relatively short data lengths.Comment: 10 pages, 3 figures; Elsevier preprint, elsart style; programs used for analysis available for download at http://homepages.luc.edu/~cwebbe

Fractal Fluctuations and Quantum-Like Chaos in the Brain by Analysis of Variability of Brain Waves: A New Method Based on a Fractal Variance Function and Random Matrix Theory

We developed a new method for analysis of fundamental brain waves as recorded by EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given

Electronic Journal of Theoretical Physics Non Linear Assessment of Musical Consonance

Abstract: The position of intervals and the degree of musical consonance can be objectively explained by temporal series formed by mixing two pure sounds covering an octave. This result is achieved by means of Recurrence Quantification Analysis (RQA) without considering neither overtones nor physiological hypotheses. The obtained prediction of a consonance can be considered a novel solution to Galileo’s conjecture on the nature of consonance. It constitutes an objective link between musical performance and listeners ’ hearing activity

Recurrence quantification analysis as a tool for the characterization of molecular dynamics simulations

A molecular dynamics simulation of a Lennard-Jones fluid, and a trajectory of the B1 immunoglobulin G-binding domain of streptococcal protein G (B1-IgG) simulated in water are analyzed by recurrence quantification, which is noteworthy for its independence from stationarity constraints, as well as its ability to detect transients, and both linear and nonlinear state changes. The results demonstrate the sensitivity of the technique for the discrimination of phase sensitive dynamics. Physical interpretation of the recurrence measures is also discussed.Comment: 7 pages, 8 figures, revtex; revised for review for Phys. Rev. E (clarifications and expansion of discussion)-- addition of the 8 postscript figures previously omitted, but unchanged from version