Complexity as Aging Non-Poisson Renewal Processes

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.

Grantor dc:publisher

University of North Texas

Year dc:date

2007

Author dc:creator

• Bianco, Simone

Contributors dc:contributor

• Grigolini, Paolo
• Deering, William D.
• Krokhin, Arkadii
• Roberts, James A.

• complexity
• renewal theory
• modulation
• single molecule spectroscopy
• complex networks
• Complexity (Philosophy)
• Renewal theory.

Statement dc:rights

• Public
• Copyright
• Bianco, Simone
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 176906132
https://digital.library.unt.edu/ark:/67531/metadc3706/
ark: ark:/67531/metadc3706

OAI identifier oai:identifier

info:ark/67531/metadc3706