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

Will systems biology offer new holistic paradigms to life sciences?

A biological system, like any complex system, blends stochastic and deterministic features, displaying properties of both. In a certain sense, this blend is exactly what we perceive as the “essence of complexity” given we tend to consider as non-complex both an ideal gas (fully stochastic and understandable at the statistical level in the thermodynamic limit of a huge number of particles) and a frictionless pendulum (fully deterministic relative to its motion). In this commentary we make the statement that systems biology will have a relevant impact on nowadays biology if (and only if) will be able to capture the essential character of this blend that in our opinion is the generation of globally ordered collective modes supported by locally stochastic atomisms