Noisy cooperative intermittent processes: From blinking quantum dots to human consciousness

Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency

“…Nevertheless, the renewal condition plays an important role in the theoretical modeling of these perturbed point processes, allowing to derive both analytical and numerical results. (see, e.g., [10,11,12,13,14,15]). …”

“…On the contrary, it has been proved that the EDDiS approach is able to separate different regimes of both diffusion scalings δ and H, but only for the Asymmetric Jump (AJ) and Symmetric Jump (SJ) walking rules (see Appendix Appendix A) [15,17,9]. This is a crucial property when noise affects the recorded time series.…”

“…Following this interpretation, the role of added noise in complex systems has been extensively investigated by many authors, as it can affect the observed scaling properties [55,53,15,56,57,58,59,60]. In particular, many authors have studied the effect of added noise on monofractal and multifractal signals.…”

“…Further, the presence of short-term noise can affect the calculation of long-range correlations [55,58] and of intermittency features [53,15]. Recently, the presence of added Gaussian noise, white or exponentially correlated, has been recognized to play a crucial role for the interpretation of single particle tracking of biomolecules in the cell [59].…”

“…More surprisingly, normal scaling emerge also in the Symmetric Velocity (SV) rule, which is dichotomous telegraph signal (see Appendix A), but this normal scaling is seen in the long-time range [16,15]. This is related to a non-linear superposition of effects and, for this reason, the estimation of the diffusion scaling is often not reliable for the SV rule.…”