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Partner: UNT College of Arts and Sciences
Department: Center for Nonlinear Science
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### Cooperation-induced topological complexity: a promising road to fault tolerance and Hebbian learning

Date: March 16, 2012
Creator: Turalska, Malgorzata; Geneston, Elvis L.; West, Bruce J.; Allegrini, Paolo & Grigolini, Paolo
Description: This article discusses cooperation-induced topological complexity and the emergence of intelligence.
Contributing Partner: UNT College of Arts and Sciences

### Correlation Function and Generalized Master Equation of Arbitrary Age

Date: June 10, 2005
Creator: Allegrini, Paolo; Aquino, Gerardo; Grigolini, Paolo; Palatella, Luigi; Rosa, Angelo & West, Bruce J.
Description: This article discusses correlation function and generalized master equation of arbitrary age using non-Poisson, Markovian, and Liouville methods.
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### Criticality and Transmission of Information in a Swarm of Cooperative Units

Date: August 12, 2011
Creator: Vanni, Fabio; Lukovic, Mirko & Grigolini, Paolo
Description: This article discusses criticality and transmission of information in a swarm of cooperative units. Abstract: We show that the intelligence of a swarm of cooperative units (birds) emerges at criticality, as an effect of the joint action of frequent organizational collapses and of spatial correlation as extended as the flock size. The organizational collapses make the birds become independent of one another, thereby allowing the flock to follow the direction of the lookout birds. Long-range correlation violates the principle of locality, making the lookout birds transmit information on either danger or resources with a time delay determined by the time distance between two consecutive collapses.
Contributing Partner: UNT College of Arts and Sciences

### Decoherence, wave function collapses and non-ordinary statistical mechanics

Date: August 2003
Creator: Bologna, Mauro; Grigolini, Paolo; Pala, Marco G. & Palatella, Luigi
Description: Article discussing decoherence, wave function collapses, and non-ordinary statistical mechanics. Abstract: We consider a toy model of pointer interacting with a 1/2-spin system, whose $\sigma_{x}$ variable is \emph{measured} by the environment, according to the prescription of decoherence theory. If the environment measuring the variable $\sigma_{x}$ yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, relaxation regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law relaxation.
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### Detection of invisible and crucial events: from seismic fluctuations to the war against terrorism

Date: October 28, 2003
Creator: Allegrini, Paolo; Fronzoni, Leone; Grigolini, Paolo; Latora, Vito; Mega, Mirko S.; Palatella, Luigi et al.
Description: Paper discussing the detection of invisible and crucial events. Abstract: We argue that the recent discovery of the non-Poissonian statistics of the seismic main-shocks is a special case of a more general approach to the detection of the distribution of the time increments between one crucial but invisible event and the next. We make the conjecture that the proposed approach can be applied to the analysis of terrorist network with significant benefits for the Intelligence Community.
Contributing Partner: UNT College of Arts and Sciences

### Diffusion Entropy and Waiting Time Statistics of Hard-X-Ray Solar Flares

Date: March 25, 2002
Creator: Grigolini, Paolo; Leddon, Deborah & Scafetta, Nicola
Description: This article discusses diffusion entropy and waiting time statistics of hard-x-ray solar flares.
Contributing Partner: UNT College of Arts and Sciences

### Dynamic Approach to the Thermodynamics of Superdiffusion

Date: April 26, 1999
Creator: Buiatti, Marco, 1972-; Grigolini, Paolo & Montagnini, Anna
Description: This article discusses dynamic approach to the thermodynamics of superdiffusion. Abstract: We address the problem of relating thermodynamics to mechanics in the case of microscopic dynamics without a finite time scale. The solution is obtained by expressing the Tsallis entropic index q as a function of the Lévy index α, and using dynamic rather than probabilistic arguments.
Contributing Partner: UNT College of Arts and Sciences

### Dynamical approach to Lévy processes

Date: November 1996
Creator: Allegrini, Paolo; Grigolini, Paolo & West, Bruce J.
Description: This article discusses a dynamical approach to Lévy processes, which makes it possible to derive all statistical properties of the diffusion process from the correlation function of the dichotomous fluctuating variable Φy(t).
Contributing Partner: UNT College of Arts and Sciences

### Dynamical model for DNA sequences

Date: November 1995
Creator: Allegrini, Paolo; Barbi, M.; Grigolini, Paolo & West, Bruce J.
Description: This article discusses a dynamical model for DNA sequences 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.
Contributing Partner: UNT College of Arts and Sciences

### Dynamical Origin of Memory and Renewal

Date: August 8, 2006
Creator: Cakir, Rasit; Grigolini, Paolo & Krokhin, Arkadii A.
Description: This article discusses a dynamical origin of memory and renewal. Abstract: We show that the dynamic approach to fractional Brownian motion (FBM) establishes a link between a non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a nonvanishing memory of their past time evolution. It is well known that the recrossings of the origin by an ordinary one-dimensional diffusion trajectory generates a Lévy (and thus renewal) process of index θ=1/2. We prove with theoretical and numerical arguments that this is the special case of a more general condition, insofar as the recrossings produced by the dynamic FBM generates a Lévy process with 0<θ<1. This result is extended to produce a satisfactory model for the fluorescent signal of blinking quantum dots.
Contributing Partner: UNT College of Arts and Sciences