Colaiori Francesca, Castellano Claudio, Cuskley Christine F, Loreto Vittorio, Pugliese Martina, Tria Francesca
Istituto dei Sistemi Complessi (ISC-CNR), via dei Taurini 19, I-00185 Roma, Italy and Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy.
Istituto dei Sistemi Complessi (ISC-CNR), via dei Taurini 19, I-00185 Roma, Italy and Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy and ISI Foundation, Via Alassio 11/C, Torino, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):012808. doi: 10.1103/PhysRevE.91.012808. Epub 2015 Jan 9.
Empirical evidence shows that the rate of irregular usage of English verbs exhibits discontinuity as a function of their frequency: the most frequent verbs tend to be totally irregular. We aim to qualitatively understand the origin of this feature by studying simple agent-based models of language dynamics, where each agent adopts an inflectional state for a verb and may change it upon interaction with other agents. At the same time, agents are replaced at some rate by new agents adopting the regular form. In models with only two inflectional states (regular and irregular), we observe that either all verbs regularize irrespective of their frequency, or a continuous transition occurs between a low-frequency state, where the lemma becomes fully regular, and a high-frequency one, where both forms coexist. Introducing a third (mixed) state, wherein agents may use either form, we find that a third, qualitatively different behavior may emerge, namely, a discontinuous transition in frequency. We introduce and solve analytically a very general class of three-state models that allows us to fully understand these behaviors in a unified framework. Realistic sets of interaction rules, including the well-known naming game (NG) model, result in a discontinuous transition, in agreement with recent empirical findings. We also point out that the distinction between speaker and hearer in the interaction has no effect on the collective behavior. The results for the general three-state model, although discussed in terms of language dynamics, are widely applicable.
实证证据表明，英语动词的不规则使用频率呈现出一种不连续性，它是动词频率的函数：最常用的动词往往完全不规则。我们旨在通过研究基于主体的简单语言动态模型来定性地理解这一特征的起源，在这些模型中，每个主体采用动词的一种屈折形式，并可能在与其他主体互动时改变它。同时，主体会以一定速率被采用规则形式的新主体所取代。在只有两种屈折形式（规则和不规则）的模型中，我们观察到要么所有动词都会规则化，而不论其频率如何，要么在低频状态（词元完全规则）和高频状态（两种形式共存）之间会发生连续转变。引入第三种（混合）状态，即主体可以使用任何一种形式，我们发现可能会出现第三种性质不同的行为，即频率上的不连续转变。我们引入并解析求解了一类非常通用的三态模型，这使我们能够在一个统一的框架中全面理解这些行为。包括著名的命名博弈（NG）模型在内的现实交互规则集，会导致不连续转变，这与最近的实证研究结果一致。我们还指出，交互中说话者和听者之间的区别对集体行为没有影响。一般三态模型的结果，尽管是从语言动态的角度进行讨论的，但具有广泛的适用性。
