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- Nicola Scafetta, Paolo Grigolini
- Physical review. E, Statistical, nonlinear, and…
- 2002

The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where ordinary statistical properties hold true even if strange kinetics are involved. We illustrate a method of statistical… (More)

This is an introduction to the special issue titled “Collective behavior and evolutionary games” that is in the making at Chaos, Solitons & Fractals. The term collective behavior covers many different phenomena in nature and society. From bird flocks and fish swarms to social movements and herding effects [1–5], it is the lack of a central planner that… (More)

We argue that a process of social interest is a balance of order and randomness, thereby producing a departure from a stationary diffusion process. The strength of this effect vanishes if the order to randomness intensity ratio vanishes, and this property allows us to reveal, although in an indirect way, the existence of a finite order to randomness… (More)

- Malgorzata Turalska, Mirko Lukovic, Bruce J West, Paolo Grigolini
- Physical review. E, Statistical, nonlinear, and…
- 2009

We 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 . We show that when the number of nodes is finite, the decision-making process becomes intermittent. The decision-time distribution density is characterized by inverse power-law… (More)

We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where the waiting time distribution is an inverse power law with index μ. We focus our attention on μ < 3, and we evaluate the… (More)

- Gerardo Aquino, Mauro Bologna, Bruce J West, Paolo Grigolini
- Physical review. E, Statistical, nonlinear, and…
- 2011

We study the transport of information between two complex systems with similar properties. Both systems generate non-Poisson renewal fluctuations with a power-law spectrum 1/f(3-μ), the case μ=2 corresponding to ideal 1/f noise. We denote by μ(S) and μ(P) the power-law indexes of the system of interest S and the perturbing system P, respectively. By… (More)

- P. Grigolini, A. Rocco, B. J. West
- 1999

We generalize the method of Van Hove @Physica ~Amsterdam! 21, 517 ~1955!# so as to deal with the case of nonordinary statistical mechanics, that being phenomena with no time-scale separation. We show that in the case of ordinary statistical mechanics, even if the adoption of the Van Hove method imposes randomness upon Hamiltonian dynamics, the resulting… (More)

- Simone Bianco, Massimiliano Ignaccolo, Mark S Rider, Mary J Ross, Phil Winsor, Paolo Grigolini
- Physical review. E, Statistical, nonlinear, and…
- 2007

In this paper we show that both music composition and brain function, as revealed by the electroencephalogram (EEG) analysis, are renewal non-Poisson processes living in the nonergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of… (More)

- M Ignaccolo, M Latka, W Jernajczyk, P Grigolini, B J West
- Physical review. E, Statistical, nonlinear, and…
- 2010

In recent studies a number of research groups have determined that human electroencephalograms (EEG) have scaling properties. In particular, a crossover between two regions with different scaling exponents has been reported. Herein we study the time evolution of diffusion entropy to elucidate the scaling of EEG time series. For a cohort of 20 awake healthy… (More)

- Bruce J West, Paolo Grigolini
- Medical hypotheses
- 2010

It is hypothesized that the special way information is exchanged between living networks, the Living Matter Way (LMW), is determined by the Principle of Complexity Matching, which asserts that the relative complexity of two complex networks determines the transfer of information between them. The LMW explains the neurophysiology of habituation and why… (More)