语言竞争与汉明距离
Competition of Languages and their Hamming Distance
摘要：
我们考虑的传播和竞争的语言是由一个人口的个人。个体可以在其一生中改变其母语，将其语言传给后代，并最终死亡。这些语言用位串来描述，它们之间的差异用汉明距离来表示。语言的进化是由突变和适应率决定的。特别是，我们考虑的情况下，由另一个语言的替代是由他们的相互汉明距离。作为一个功能的突变率，我们发现一个急剧过渡的情况下，一个占主导地位的语言和分裂成许多语言集群。这种转变也反映在两种语言之间的汉明距离上，这两种语言的使用者人数最多和第二多。我们还考虑的情况下，人口是本地化的一个正方形格子和个人的相互作用被限制在一定的几何域。在这里，汉明距离又一次对语言的最终命运起着至关重要的作用。
英文摘要：
We consider the spreading and competition of languages that are spoken by a population of individuals. The individuals can change their mother tongue during their lifespan, pass on their language to their offspring and finally die. The languages are described by bitstrings, their mutual difference is expressed in terms of their Hamming distance. Language evolution is determined by mutation and adaptation rates. In particular we consider the case where the replacement of a language by another one is determined by their mutual Hamming distance. As a function of the mutation rate we find a sharp transition between a scenario with one dominant language and fragmentation into many language clusters. The transition is also reflected in the Hamming distance between the two languages with the largest and second to largest number of speakers. We also consider the case where the population is localized on a square lattice and the interaction of individuals is restricted to a certain geometrical domain. Here it is again the Hamming distance that plays an essential role in the final fate of a language of either surviving or being extinct.
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