## 4 Results
### Timings and Coordination  
Coordination and timings are important and challenging aspects to study for nasal vowels. The use of GAMMs and FLMMs makes it possible, for the first time, to consider data from several EP speakers, advancing on previous single-speaker approaches.  
Since we aimed to analyze timing and coordination of the lower lip with the velar aperture and compare patterns across vowels, we have recorded vowels produced after a bilabial consonant. Resulting from these analyses of FLMMs, Figure 6 shows the variation in time of the lip and velar aperture for the different oral/nasal pairs.  
Overall, temporal evolution of velar apertures during vowel production is as expected for both consonantal contexts. For contexts where the vowel is preceded by an oral consonant (i.e., \([\mathrm{p}]\)), the velum starts closed, opens during the nasal vowel, and closes again. When the preceding consonant is instead nasal (i.e., \([\mathrm{m}]\)), the velum starts open and gradually closes during the oral vowel, or continues closing after the nasal vowel. In the oral context (i.e., after \([\mathrm{p}]\)), the velum gestures seem to open simultaneously or shortly after the vowel start (33) and to close during the coda consonant \([\mathrm{t}]\). For \([\bar{\mathrm{e}}]\), and \([\bar{\mathrm{i}}]\), the curves seem compatible with the possibility of lip closure minima after the vowel, occurring slightly before velar closure. However, without further processing--which is outside the scope of the work presented here--it is not possible to make further conclusions.  
For vowel \([\bar{\mathrm{e}}]\), in both contexts, the lip aperture's maximum occurs earlier than for the oral vowel. The smaller aperture is consistent with the more closed vowel quality of the nasal congener. Vowels \([\bar{\mathrm{e}}]\) and \([\bar{\mathrm{i}}]\) seem to show a similar (albeit less pronounced) pattern. For the nasals in \([\mathrm{p}]\) context, the onset of velar opening (at around 0.3 of duration) seems to happen slightly after lip occlusion release (occurring around 0.2 of duration).  
In summary, the FLMMs depict data that is in agreement with the expected general behavior of the lips and velum. The resulting models show only a small variability, apart from a more noticeable error interval observed for \([\mathrm{\SIUnitSymbolFace{S}}]\), \([\mathrm{\SIUnitSymbolFace{S}}]\), and \([\bar{\mathrm{u}}]\), hinting at a good representative pattern of the modeled behavior considering the data for the 11 speakers.  
Figure 5: FLMMs showing the aperture function of the vocal tract for three time points. Each row presents the aperture function for 20%, 50%, and 80%, along the vowel. Each of the presented plots shows, in red, the curve for the oral and, in blue, the curve for the nasal. The curves for the oral bilabial context \([\mathrm{p}]\) showed similar patterns, and are thus not presented. The vertical axis represents the aperture, measured in millimeters (i.e., a higher value means a greater vocal tract opening).  
Figure 6: FLMMs of lip and velar aperture over time for the different vowels and contexts, obtained from articulatory data from 11 speakers. Curves for the oral vowels in red, and for the nasals in blue.