In this task, you will be presented with a context from an academic paper and a question separated with a
. You have to answer the question based on the context.
Q: Three clear domains can be noticed in the behavior of $\langle cc
angle $ versus $\wp $, at $t_f$, as shown in Fig. FIGREF15 (blue squares). Phase I: $\langle cc
angle $ increases smoothly for $\wp < 0.4$, indicating that for this domain there is a small correlation between word neighborhoods. Full vocabularies are attained also for $\wp < 0.4$; Phase II: a drastic transition appears at the critical domain $\wp ^* \in (0.4,0.6)$, in which $\langle cc
angle $ shifts abruptly towards 1. An abrupt change in $V(t_f)$ versus $\wp $ is also found (Fig. FIGREF16) for $\wp ^*$; Phase III: single-word languages dominate for $\wp > 0.6$. The maximum value of $\langle cc
angle $ indicate that word neighborhoods are completely correlated.
Question: What are three possible phases for language formation?
A:
Phase I: $\langle cc
angle $ increases smoothly for $\wp < 0.4$, indicating that for this domain there is a small correlation between word neighborhoods. Full vocabularies are attained also for $\wp < 0.4$ Phase II: a drastic transition appears at the critical domain $\wp ^* \in (0.4,0.6)$, in which $\langle cc
angle $ shifts abruptly towards 1. An abrupt change in $V(t_f)$ versus $\wp $ is also found (Fig. FIGREF16) for $\wp ^*$ Phase III: single-word languages dominate for $\wp > 0.6$. The maximum value of $\langle cc
angle $ indicate that word neighborhoods are completely correlated