Description: This article discusses a dynamical model for DNA sequences. Abstract: We address the problem of 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 δ-function 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 that 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 determined by the joint action of the deterministic and the random process, the correlation effects of the "deterministic dynamics" are canceled on the short-range scale, but show up in the long-range one. We denote their prescription to generate statistical sequences as the copying mistake map (CMM). We carry out their analysis of several DNA sequences and their CMM realizations with a variety of techniques and the authors ...

Description: This article discusses fractional Brownian motion as a nonstationary process. Abstract: The long-range correlations in DNA sequences are currently interpreted as an example of stationary fractional Brownian motion (FBM). First the authors show that the dynamics of a dichotomous stationary process with long-range correlations such as that used to model DNA sequences should correspond to Lévy statistics and not to FBM. To explain why, in spite of this, the statistical analysis of the data seems to be compatible with FBM, the authors notice that an initial Gaussian condition, generated by a process foreign to the mechanism establishing the long-range correlations and consequently implying a departure from the stationary condition is maintained approximately unchanged for very long times. This is so because due to the nature itself of the long-range correlation process, it takes virtually an infinite time for the system to reach the genuine stationary state. Then the authors discuss a possible generator of initial Gaussian conditions, based on a folding mechanism of the nucleic acid in the cell nucleus. The model adopted is compatible with the known biological and physical constraints, namely, it is shown to be consistent with the information of current biological literature on folding as well ...

Description: This article discusses a dynamical approach to Lévy processes.Abstract: We derive the diffusion process generated by a correlated dichotomous fluctuating variable y starting from a Liouville-like equation by means of a projection procedure. This approach makes it possible to derive all statistical properties of the diffusion process from the correlation function of the dichotomous fluctuating variable Φy(t). Of special interest is that the distribution of the times of sojourn in the two states of the fluctuating process is proportional to d²Φy(t)/dt². Furthermore, in the special case where Φy(t) has an inverse power law, with the index β ranging from 0 to 1, thus making it nonintegrable, the authors show analytically that the statistics of the diffusing variable approximate in the long-time limit the α-stable Lévy distributions. The departure of the diffusion process of dynamical origin from the ideal condition of the Lévy statistics is established by means of a simple analytical expression. We note, first of all, that the characteristic function of a genuine Lévy process should be an exponential in time. We evaluate the correction to this exponential and show it to be expressed by a harmonic time oscillation modulated by the correlation function Φy(t). Since the characteristic function ...

Description: This article discusses simultaneous measurement of the average ion-induced electron emission yield and the mean charge for isotachic ions in carbon foils. Knowledge of the incident ion's atomic number (Z₁) dependence of ion-induced electron emission yields can be the basis for a general understanding of ion-atom interaction phenomena and, in particular, for the design of Z₁-sensitive detectors that could be useful, for example, in the separation of isobars in accelerator mass spectrometry. The Z₁ dependence of ion-induced electron emission yields, y, has been investigating using heavy ions C³⁺, O³⁺, F³⁺, Na³⁺, Al³⁺, Si³⁺, P³⁺, S³⁺, Cl³⁺, K³⁺, Ti³⁺, Cr³⁺, Mn⁴⁺, Fe⁴⁺, Co⁴⁺, Ni⁴⁺, Cu⁴⁺, Ga⁴⁺, As⁵⁺, Br⁵⁺, Ru⁷⁺, Ag⁷⁺, Sn⁷⁺, and I⁸⁺ of identical velocity (v = 2v₀, where v₀ is the Bohr velocity) normally incident on 50 μg/cm² sputter-cleaned carbon foils. Measured yields as a function of Z₁ reveal an oscillatory behavior with pronounced maxima and minima. Contrary to previously reported yields that assumed to monotonically increasing empirical mean charge state for the exiting ion, the present work indicates the Z₁ oscillations in the experimentally measured yields, a fact masked in previous work. The strong Z₁ oscillations can only be observed by simultaneous measurement of the yield and the ...

Description: This article discusses the linear response of Hamiltonian chaotic systems as a function of the number of degrees of freedom. Abstract: Using numerical simulations we show that the response to weak perturbations of a variable of Hamiltonian chaotic systems depend on the number of degrees of freedom: When this is small (≈2) the response is not linear, in agreement with the well known objections to the Kubo linear response theory, while, for a larger number of degrees of freedom, the response becomes linear. This is due to the fact that increasing the number of degrees of freedom the shape of the distribution function, projected onto the subspace of the variable of interest, becomes fairly "regular."