Complexity as Aging Non-Poisson Renewal Processes

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The search for a satisfactory model for complexity, meant as an intermediate condition between total order and total disorder, is still subject of debate in the scientific community. In this dissertation the emergence of non-Poisson renewal processes in several complex systems is investigated. After reviewing the basics of renewal theory, another popular approach to complexity, called modulation, is introduced. I show how these two different approaches, given a suitable choice of the parameter involved, can generate the same macroscopic outcome, namely an inverse power law distribution density of events occurrence. To solve this ambiguity, a numerical instrument, based on the ... continued below

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Bianco, Simone May 2007.

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This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 262 times . More information about this dissertation can be viewed below.

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  • Bianco, Simone

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Description

The search for a satisfactory model for complexity, meant as an intermediate condition between total order and total disorder, is still subject of debate in the scientific community. In this dissertation the emergence of non-Poisson renewal processes in several complex systems is investigated. After reviewing the basics of renewal theory, another popular approach to complexity, called modulation, is introduced. I show how these two different approaches, given a suitable choice of the parameter involved, can generate the same macroscopic outcome, namely an inverse power law distribution density of events occurrence. To solve this ambiguity, a numerical instrument, based on the theoretical analysis of the aging properties of renewal systems, is introduced. The application of this method, called renewal aging experiment, allows us to distinguish if a time series has been generated by a renewal or a modulation process. This method of analysis is then applied to several physical systems, from blinking quantum dots, to the human brain activity, to seismic fluctuations. Theoretical conclusions about the underlying nature of the considered complex systems are drawn.

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  • May 2007

Added to The UNT Digital Library

  • Sept. 28, 2007, 9:50 p.m.

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  • Jan. 17, 2008, 3:12 p.m.

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Bianco, Simone. Complexity as Aging Non-Poisson Renewal Processes, dissertation, May 2007; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc3706/: accessed August 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .