Memory-cognizant generalization to Simon's random-copying neutral model
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.043057 |
| _version_ | 1797210901655322624 |
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| author | Joseph D. O'Brien James P. Gleeson |
| author_facet | Joseph D. O'Brien James P. Gleeson |
| author_sort | Joseph D. O'Brien |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:17:58Z |
| format | Article |
| id | doaj.art-05939af2afa04a1286d689e2abded8e4 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:17:58Z |
| publishDate | 2021-10-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-05939af2afa04a1286d689e2abded8e42024-04-12T17:14:59ZengAmerican Physical SocietyPhysical Review Research2643-15642021-10-013404305710.1103/PhysRevResearch.3.043057Memory-cognizant generalization to Simon's random-copying neutral modelJoseph D. O'BrienJames P. GleesonSimon'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.http://doi.org/10.1103/PhysRevResearch.3.043057 |
| spellingShingle | Joseph D. O'Brien James P. Gleeson Memory-cognizant generalization to Simon's random-copying neutral model Physical Review Research |
| title | Memory-cognizant generalization to Simon's random-copying neutral model |
| title_full | Memory-cognizant generalization to Simon's random-copying neutral model |
| title_fullStr | Memory-cognizant generalization to Simon's random-copying neutral model |
| title_full_unstemmed | Memory-cognizant generalization to Simon's random-copying neutral model |
| title_short | Memory-cognizant generalization to Simon's random-copying neutral model |
| title_sort | memory cognizant generalization to simon s random copying neutral model |
| url | http://doi.org/10.1103/PhysRevResearch.3.043057 |
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