2006/08/20 by Radhakrishnan Nagarajan, Nagarajan, Radhakrishnan
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fractal and DNA sequence analysis #Neural Networks and Applications #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.nlin/0608049
12 Pages, 2 Figures
openalex publication_date 2006/08/20 · arxiv created 2007/09/07 · arxiv updated 2011/11/10 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Lempel-Ziv complexity (LZ) [1] and its variants have been used widely to identify non-random patterns in biomedical signals obtained across distinct physiological states. Non-random signatures of the complexity measure can occur under nonlinear deterministic as well as non-deterministic settings. Surrogate data testing have also been encouraged in the past in conjunction with complexity estimates to make a finer distinction between various classes of processes. In this brief letter, we make two important observations (1) Non-Gaussian noise at the dynamical level can elude existing surrogate algorithms namely: Phase-randomized surrogates (FT) amplitude-adjusted Fourier transform (AAFT) and iterated amplitude adjusted Fourier transform (IAAFT). Thus any inference nonlinear determinism as an explanation for the non-randomness is incomplete (2) Decrease in complexity can be observed even across two linear processes with identical auto-correlation functions. The results are illustrated with a second-order auto-regressive process with Gaussian and non-Gaussian innovations. AR (2) processes have been used widely to model several physiological phenomena, hence their choice. The results presented encourage cautious interpretation of non-random signatures in experimental signals using complexity measures.