Four- and three-state rock-paper-scissors games with long-range selection
Bibliographic record
Abstract
Considering the effect of a long-range selection, we investigate the crossover to extinction of species and the oscillation behaviors in the four- and three-state models of the rock-paper-scissors (RPS) game extensively on a two-dimensional lattice. It is found that the selection in a long-range leads to the destruction of species coexistence in the four-state RPS game model but it cannot induce the extinction of species nearly and even promotes the coexistence of three species when a long-range migration occurs in the three-state RPS game model. Through the simulations of spatiotemporal patterns, it is found that there are two different mechanisms to result in the extinction of species in two models. In the four-state model, a phase separation occurs and there are some vortices where three species coexist and dominate each other cyclically. Through a long-range selection, the vortices are eliminated to cause the destruction of species coexistence. In the three-state model, the spreading of species takes a key role in the crossover to extinction. When one of the species spreads rapidly, a giant cluster forms and the system becomes unstable and sensitive to the stochastic noise and the destruction of the species coexistence takes place. As the selection range is not too large, it can inhibit the formation of the giant cluster and then promotes the coexistence probability in the three-state model.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".