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Partner: UNT College of Arts and Sciences
Department: Center for Nonlinear Science
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### Power spectra for both interrupted and perennial aging processes

Date: November 10, 2008
Creator: Lukovic, Mirko & Grigolini, Paolo
Description: Article on power spectra for both interrupted and perennial aging processes.
Contributing Partner: UNT College of Arts and Sciences

### Fast-computational approach to the evaluation of slow-motion EPR spectra in terms of a generalized Langevin equation

Date: October 1983
Creator: Giordano, Marco; Grigolini, Paolo; Leporini, Dino & Marin, P.
Description: Article discussing a fast-computational approach to the evaluation of slow-motion EPR spectra in terms of a generalized Langevin equation. Abstract: A Mori-type generalized Langevin equation is shown to be the only theoretical tool necessary for setting up a fast-computational method of evaluation EPR spectra. The advantages of this algorithm, concerning memory storage and time consumption, are clearly illustrated by explicitly evaluating the line shape of a nitroxide spin probe both in an isotropic liquid solution and in a liquid-crystal mesophase. This method makes theoretical EPR spectra of an orientating potential renders the EPR spectrum much more sensitive to the details of molecular dynamics, thereby making this a potentially powerful tool for monitoring rotational dynamics in liquid mesophases.
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### Neural Dynamics: Criticality, Cooperation, Avalanches and Entrainment between Complex Networks

Date: May 22, 2012
Creator: Grigolini, Paolo; Zare, Marzieh; Svenkeson, Adam & West, Bruce J.
Description: Book chapter discussing neural dynamics and the criticality, cooperation, avalanches and entrainment between complex networks.
Contributing Partner: UNT College of Arts and Sciences

### Renewal aging and linear response

Date: February 6, 2008
Creator: Allegrini, Paolo; Ascolani, Gianluca; Bologna, Mauro & Grigolini, Paolo
Description: Paper discussing renewal aging and linear response. Abstract: We study the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion. We use the phenomenological approach to the linear response adopted in earlier work of other groups, and we find that aging may have the effect of annihilating any sign of coherent response to harmonic perturbation. We also derive the linear response using dynamic arguments and we find a coherent response, although with an intensity dying out very slowly. In the case of a step-like perturbation the dynamic arguments yield in the long-time limit a steady signal whose intensity may be significantly smaller than the phenomenological approach prediction.
Contributing Partner: UNT College of Arts and Sciences

### Real event detection and the treatment of congestive heart failure: an efficient technique to help cardiologists to make crucial decisions

Date: September 2002
Creator: Allegrini, Paolo; Balocchi, Rita; Chillemi, Santi; Grigolini, Paolo; Hamilton, P.; Maestri, Roberto et al.
Description: Paper discussing the treatment of congestive heart failure. Abstract: Using a method of entropic analysis of time series we establish the correlation between heartbeat long-range memory and mortality risk in patients with congestive heart failure.
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.
Contributing Partner: UNT College of Arts and Sciences

### Breakdown of the Onsager Principle as a Sign of Aging

Date: July 19, 2011
Creator: Allegrini, Paolo; Aquino, Gerardo; Grigolini, Paolo; Palatella, Luigi & Rosa, Angelo
Description: Article discussing the breakdown of the Onsager principle as a sign of aging. Abstract: We discuss the problem of the equivalence between Continuous Time Random Walk (CTRW) and Generalized Master Equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site or extended time. The sojourn times have a distribution ψ (t) that is assumed to be an inverse power law with the power index μ. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case when ψ (t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is non-stationary, thereby implying aging, while the Onsager principle, is valid only in the case of fully aged systems. The case of Poissonian distribution of sojourn times is the only one with no aging associated to it, and consequently with no need to establish special initial conditions to fulfill the Onsager principle. We consider the case of a dichotomous fluctuation, and we prove that ...
Contributing Partner: UNT College of Arts and Sciences

### Cognitive Scale-Free Networks as a Model for Intermittency in Human Natural Language

Date: 2003
Creator: Allegrini, Paolo; Grigolini, Paolo & Palatella, Luigi
Description: Paper discussing cognitive scale-free networks as a model for intermittency in human natural language. Abstract: We model certain features of human language complexity by means of advanced concepts borrowed from statistical mechanics. Using a time series approach, the diffusion entropy method (DE), we compute the complexity of an Italian corpus of newspapers and magazines. We find that the anomalous scaling index is compatible with a simple dynamical model, a random walk on a complex scale-free network, which is linguistically related to Saussurre's paradigms. The model yields the famous Zipf's law in terms of the generalized central limit theorem.
Contributing Partner: UNT College of Arts and Sciences

### From Knowledge, Knowability and the Search for Objective Randomness to a New Vision of Complexity

Date: February 2, 2008
Creator: Allegrini, Paolo; Giuntoli, Martina; Grigolini, Paolo & West, Bruce J.
Description: Paper discussing knowledge, knowability, and the search for objective randomness to a new vision of complexity. Abstract: Herein we consider various concepts of entropy as measure of the complexity of phenomena and in so doing encounter a fundamental problem in physics that affects how we understand the nature of reality. In essence the difficulty has to do with our understanding of randomness, irreversibility and unpredictability using physical theory, and these in turn undermine our certainty regarding what we can and what we cannot know about complex phenomena in general. The sources of complexity examined herein appear to be channels for the amplification of naturally occurring randomness in the physical world. Our analysis suggests that when the conditions for the renormalization group apply, this spontaneous randomness, which is not a reflection of our limited knowledge, but a genuine property of nature, does not realize the conventional thermodynamic state, and a new condition, intermediate between the dynamic and the thermodynamic state, emerges. We argue that with this vision of complexity, life, which with ordinary statistical mechanics seems to be foreign to physics, becomes a natural consequence of dynamical processes.
Contributing Partner: UNT College of Arts and Sciences

### Intermittency and scale-free networks: a dynamical model for human language complexity

Date: 2004
Creator: Allegrini, Paolo; Grigolini, Paolo & Palatella, Luigi
Description: Article discussing intermittency, scale-free networks, and a dynamical model for human language complexity. Abstract: In this paper we try to model certain features of human language complexity by means of advanced concepts borrowed from statistical mechanics. We use a time series approach, the diffusion entropy method (DE), to compute the complexity of an Italian corpus of newspapers and magazines. We find that the anomalous scaling index is compatible with a simple dynamical model, a random walk on a complex scale-free network, which is linguistically related to Saussurre's paradigms. The network complexity is independently measured on the same corpus, looking at the co-occurrence of nouns and verbs. This connection of cognitive complexity with long-range time correlations also provides an explanation for the famous Zipf's law in terms of the generalized central limit theorem.
Contributing Partner: UNT College of Arts and Sciences
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