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Continuous time limits of the utterance selection model.
1School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom.
Physical Review. E
|March 17, 2017
Summary
This study explores alternative continuous time limits for the utterance selection model (USM) in language change. Researchers found that network size influences convention emergence, with larger networks potentially hindering it.
Area of Science:
- Complex systems
- Computational linguistics
- Statistical physics
Background:
- The original utterance selection model (USM) has limitations in its continuous time limit, restricting its parameter range.
- A Fokker-Planck continuous time limit was previously derived, but it is only valid under specific parameter constraints.
Purpose of the Study:
- To derive alternative continuous time limits for the utterance selection model (USM) that are valid for a wider range of parameters.
- To investigate the impact of relaxing constraints on model parameters and explore new approximations.
- To analyze the dynamics of language change in different network structures.
Main Methods:
- Derivation of a weak-noise stochastic differential equation as a continuous time limit of the USM.
- Application of a normal approximation to the multinomial approximation.
- Development of a coarse-graining procedure using a stochastic heterogeneous mean field approximation.
- Analysis of regular and star-shaped networks to study finite-size effects and node degree influence.
Main Results:
- A new continuous time limit for the USM was derived, incorporating weak noise that was previously neglected.
- A finite-size effect was identified: increasing network size can shift the system from convention emergence to no convention emergence.
- Node degree was shown to act as a timescale, with significant variations in heterogeneous networks potentially causing noisier dynamics for highly connected nodes.
Conclusions:
- The derived weak-noise stochastic differential equation provides a more robust framework for studying language change dynamics.
- Network size and heterogeneity significantly impact the emergence and stability of conventions.
- The findings offer insights into the complex interplay between network structure, dynamics, and the evolution of language.
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