Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General three-state model with biased population replacement: Analytical
  solution and application to language dynamics   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.

26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th