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Memory-cognizant generalization to Simon’s random-copying neutral model
Date
2021
Abstract
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.
Supervisor
Description
peer-reviewed
Publisher
American Physical Society
Citation
Physical Review Research;3, 043057
Files
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OBrien_2021_Memory.pdf
Adobe PDF, 1.05 MB
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Funding code
Funding Information
Science Foundation Ireland (SFI)