Nonlinear analysis of correlations in Alu repeat sequences in DNA

Abstract

We report on a nonlinear analysis of deterministic structures in Alu repeats, one of the richest repetitive DNA sequences in the human genome. Alu repeats contain the recognition sites for the restriction endonuclease AluI, which is what gives them their name. Using the nonlinear prediction method developed in chaos theory, we find that all Alu repeats have novel deterministic structures and show strong nonlinear correlations that are absent from exon and intron sequences. Furthermore, the deterministic structures of Alus of younger subfamilies show panlike shapes. As young Alus can be seen as mutation free copies from the "master genes," it may be suggested that the deterministic structures of the older subfamilies are results of an evolution from a "panlike" structure to a more diffuse correlation pattern due to mutation.

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor

“…Thus far, various forecasting methods based on the orbital instability of nearest neighboring points in the phase space have been used to distinguish deterministic chaos from randomness and noisy periodicity. 22,23,34,[41][42][43][44][45] Two of the authors have recently reported that the nonlinear determinism in complex flame dynamics induced by buoyancy=swirl coupling can be successfully quantified by nonlinear forecasting method, 34 but the possibility that the short-term prediction of the combustion dynamics can be achieved has not been discussed from a practical viewpoint. In addition to the applicability of the nonlinear forecasting method for identifying deterministic chaos, the results obtained in this work demonstrate that the nonlinear forecasting method has sufficient potential use for predicting the pressure fluctuations of the combustion instability in a lean premixed gas-turbine combustor and that it is worthwhile from a practical viewpoint.…”

Nonlinear modelling approach to human promoter sequences

“…An alternative solution to distinguish the deterministic structures is presented in Xiao et al (2003). The ratio g ¼ EðM; k; dÞ=E uncorrelated is used and according to the calculations with fewer sample sequences the criterion is set to be gpg c ¼ 0:85.…”

“…In two stimulating papers (Barral et al, 2000;Xiao et al, 2003), the nonlinear modelling (NM) technique is used to find the deterministic structures in non-coding regions and in Alu repeats. The NM method is initially designed to distinguish between chaos and noise in time series (Farmer and Sidorowich, 1987;Sugihara and May, 1990;Rubin, 1992;Garcia et al, 1996).…”

Short-term prediction of dynamical behavior of flame front instability induced by radiative heat loss

“…In the field of nonlinear physics, nonlinear forecasting based on orbital instability in the phase space or neural network theory has been shown to ensure good performance in the short-term prediction of deterministic chaos. 15,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] This can be considered to be an inverse approach in the sense that the underlying dynamics is expressed by a predictive model constructed from the observed temporal behavior. The importance of the inverse approach has previously been discussed by some of the authors.…”