In this article, the authors discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. The authors find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent...

We study the subordination to a process that is periodic in the natural time scale, and equivalent to a clock with N states. The rationale for this investigation is given by a set of many interacting clocks with N states. The natural time scale representation corresponds to the dynamics of an...

The brain is probably the most interesting example of a complex network having 1/f variability as determined through the analysis of EEG time series and magnetoencephalogram recordings. Herein we develop a theory of 1/f noise of human cognition to explain the recent experimental observations...

We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann's concept of orthodes. These are the statistical ensembles that satisfy the heat theorem, according to which the heat exchanged divided by the temperature is an exact...

We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic fluctuations with a given distribution ψ(τ) of residence...

In this paper, we propose a mathematical model for the Trojan war that, supposedly, took place around 1180 BC. Supported by archaeological findings and by Homer’s Iliad, we estimate the numbers of warriors, the struggle rate parameters, the number of individuals per hectare, and other related...

In this article, the authors study a fully connected network (cluster) of interacting two-state units as a model of cooperative decision making. Each unit in isolation generates a Poisson process with rate g. The authors show that when the number of nodes is finite, the decision-making process...

We propose a dynamical model generating the same non-Poisson renewal events as those currently found in complex systems as the blinking quantum dots and the human brain. Our results suggest that these complex systems can be interpreted as a set of synchronized neurons.

The combined use of the ‘reduced’ model theory, adiabatic elimination of the fast variables and continued fraction procedure is shown to make it possible to study chemical relaxation in the presence of radiative excitation. This requires that the reaction coordinate be assumed to be slow...

We study the effects of an external periodic perturbation on a Poisson rate process, with special attention to the perturbation-induced sojourn-time patterns. We show that these patterns correspond to turning a memory-less sequence into a sequence with memory. The memory effects are stronger the...