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Memory-cognizant generalization to Simon’s random-copying neutral model

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posted on 2022-10-05, 14:06 authored by Joseph D. O'Brien, James GleesonJames Gleeson
Simon’s classical random-copying model, introduced in 1955, has garnered much attention for its ability, in spite of an apparent simplicity, to produce characteristics similar to those observed across the spectrum of complex systems. Through a discrete-time mechanism in which items are added to a sequence based upon rich-gets-richer dynamics, Simon demonstrated that the resulting size distributions of such sequences exhibit power-law tails. The simplicity of this model arises from the approach by which copying occurs uniformly over all previous elements in the sequence. Here we propose a generalization of this model which moves away from this uniform assumption, instead incorporating memory effects that allow the copying event to occur via an arbitrary age-dependent kernel. Through this approach, we first demonstrate the potential to determine further information regarding the structure of sequences from the classical model before illustrating, via analytical study and numeric simulation, the flexibility offered by the arbitrary choice of memory. Furthermore, we demonstrate how previously proposed memory-dependent models can be further studied as specific cases of the proposed framework.

Funding

Dynamics of the metabolic state in the context of a systematic approach to the study of the processes of growth and development of higher plants and fungi

Russian Foundation for Basic Research

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Development of theoretical and experimental criteria for predicting the wear resistance of austenitic steels and nanostructured coatings based on a hard alloy under conditions of erosion-corrosion wear

Russian Foundation for Basic Research

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History

Publication

Physical Review Research;3, 043057

Publisher

American Physical Society

Note

peer-reviewed

Other Funding information

SFI

Language

English

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  • MACSI - Mathematics Application Consortium for Science & Industry

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  • Mathematics & Statistics

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