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Model for Long-range Correlations in DNA Sequences

Description: We address the problem of the DNA sequences developing a "dynamical" method based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic, with long-range correlations, and the other random and delta correlated. The generator of the deterministic evolution is a nonlinear map, belonging to a class of maps recently tailored to mimic the processes of weak chaos responsible for the birth of anomalous diffusion. It is assumed that the deterministic process corresponds to unknown biological rules which determine the DNA path, whereas the noise mimics the influence of an infinite-dimensional environment on the biological process under study. We prove that the resulting diffusion process, if the effect of the random process is neglected, is an a-stable Levy process with 1 < a < 2. We also show that, if the diffusion process is determined by the joint action of the deterministic and the random process, the correlation effects of the "deterministic dynamics" are cancelled on the short-range scale, but show up in the long-range one. We denote our prescription to generate statistical sequences as the Copying Mistake Map (CMM). We carry out our analysis of several DNA sequences, and of their CMM realizations, with a variety of techniques, and we especially focus on a method of regression to equilibrium, which we call the Onsager Analysis. With these techniques we establish the statistical equivalence of the real DNA sequences with their CMM realizations. We show that long-range correlations are present in exons as well as in introns, but are difficult to detect, since the exon "dynamics" is shown to be determined by theentaglement of three distinct and independent CMM's. Finally we study the validity of the stationary assumption in DNA sequences and we discuss a biological model for the ...
Date: December 1996
Creator: Allegrini, Paolo
Partner: UNT Libraries

Dynamical approach to Lévy processes

Description: This article discusses a dynamical approach to Lévy processes, which makes it possible to derive all statistical properties of the diffusion process from the correlation function of the dichotomous fluctuating variable Φy(t).
Date: November 1996
Creator: Allegrini, Paolo; Grigolini, Paolo & West, Bruce J.
Partner: UNT College of Arts and Sciences

Dynamical model for DNA sequences

Description: This article discusses a dynamical model for DNA sequences based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic with long-range correlations and the other random and δ-function correlated.
Date: November 1995
Creator: Allegrini, Paolo; Barbi, M.; Grigolini, Paolo & West, Bruce J.
Partner: UNT College of Arts and Sciences

Renewal aging and linear response

Description: Paper discussing the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion.
Date: February 6, 2008
Creator: Allegrini, Paolo; Ascolani, Gianluca; Bologna, Mauro & Grigolini, Paolo
Partner: UNT College of Arts and Sciences