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

The emergence of self-organization in complex systems–Preface

“…A crucial role is assumed by the statistical distribution of the inter-event times, being each event given by the bioluminescent emission. This approach lies into the general framework of complexity interpreted as fractal intermittency, also denoted as Temporal Complexity and described in papers [17] and [31]. The authors of paper [29] investigate the diffusion properties of a system of active dumbbell molecules with repulsive interactions, which is a prototype of Active Matter.…”

“…In particular, the authors investigate the interplay of memory and of the shear fluid flow on the cross-correlation functions of harmonically trapped Brownian particles, finding the important effect of memory-induced sign reversals. The authors of paper [17] discuss the effects of a Poisson point process, which is seen as a sort of additive "noise" term, on a complex signal characterized by fractal intermittency. The complex signal is represented as a telegraph signal, i.e., a dichotomous signal that can assume only two states, but with a power-law distribution of transition times.…”

“…In papers [13,14,15,16,17] the modeling approach to complexity is based on the theory of stochastic processes. All these papers, with the exception of the last one, are based on the standard or generalized Langevin equation.…”

The Challenge of Brain Complexity - A Brief Discussion about a Fractal Intermittency-based Approach

“…This is denoted as renewal condition and the sequence of transition events is a renewal point process (Cox, 1962;Paradisi and Allegrini, 2015;Paradisi et al, 2015a;Paradisi et al, 2012a;Paradisi et al, 2012b;Paradisi et al, 2009b;Akin et al, 2006;Paradisi et al, 2008;Akin et al, 2009;Bianco et al, 2007;Paradisi et al, 2009a) In this case the WTs τ n are mutually independent random variables. Conversely, in the time interval (t n ,t n+1 ) between two events, i.e., in correspondence of a self-organized state, the dynamics are strongly correlated.…”

“…This powerlaw behavior in the WT distribution is a crucial emergent property, characterizing the capacity of the complex system to trigger self-organization. This condition is denoted as fractal intermittency (Paradisi et al, 2012b;Paradisi et al, 2013;Allegrini et al, 2013;Paradisi et al, 2015b;Paradisi and Allegrini, 2015). This complex behavior is also known as Temporal Complexity (Grigolini, 2015;Beig et al, 2015;Turalska et al, 2011;Grigolini and Chialvo, 2013), a term that was introduced to underline the difference of the intermittency-based approach to complexity, focused on the study of the temporal structure of selforganization, with the more extensively investigated approach associated with the estimation of topological and spatial indicators of complexity (e.g., the degree distribution in a complex network, the avalanche size distribution) (Beggs and Plenz, 2003;Plenz and Thiagarjan, 2007;Fraiman et al, 2009;Chialvo, 2010;Grigolini and Chialvo, 2013).…”