11454 7 61427 3 168913 document 61427 Understanding scaling through history-dependent processes with collapsing sample space.pdf application/pdf 0a5e3654eea8fd0462432c0d108a11f7 MD5 1212968 2016-06-09 12:37:03 https://pure.iiasa.ac.at/id/eprint/11454/1/Understanding%20scaling%20through%20history-dependent%20processes%20with%20collapsing%20sample%20space.pdf 11454 1 1 application/pdf text en public cc_by_nc

Understanding scaling through history-dependent processes with collapsing sample space.pdf

published 61452 2 168948 document 61452 lightbox.jpg image/png e894b462469f06ea70c11f48d481419c MD5 74696 2016-06-09 12:47:07 https://pure.iiasa.ac.at/id/eprint/11454/2/lightbox.jpg 11454 2 2 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/61427 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/61427 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/61427 archive 351 disk0/00/01/14/54 2016-01-15 08:53:18 2021-08-27 17:39:54 2016-01-15 08:53:18 article show Corominas-Murtra B. Hanel R. Thurner S. 1918 pub iis_sys prog_asa network diffusion; path dependence; random walks; scaling laws, Zipf's law History-dependent processes are ubiquitous in natural and social systems. Many such stochastic proceses, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample space, or their set of possible outcomes, reduces as they age. We demonstrate that these sample-space-reducing (SSR) processs necessarily lead to Zipf's law in the rank distributions of their outcomes. We show that by adding noise to SSR processes the corresponding rank distributions remain exact power laws, p(x)~x^-Lambda, where the exponent directly corresponds to the mixng ratio of the SSR process and noise. This allows us to give a precise meaning to the scaling exponent in terms of the degree to which a given process reduces its distributions ranging from alpha = 2 to Infinity. We discuss several applications showing how SSR processes can be used to understand Zipf's law in word frequencies, and how they are related to diffusion processes in directed networks, or aging processes such as in fragmentation processes. SSR processes provide a new alternative to understand the origin of scaling in complex systems without the recourse to multiplicative, preferential, or self-organized critical processes. 2015-04 published National Academy of Sciences 10.1073/pnas.1420946112 XJ-15-108 PNAS; 112(17):5348-5353 (April 2015) [doi:10.1073/pnas.1420946112] 307 public Proceedings of the National Academy of Sciences 112 17 5348-5353 TRUE 1091-6490 FALSE info:eu-repo/semantics/article