Realizability of Polytopes as a Low Rank Matrix Completion Problem

This article gives necessary and sufficient conditions for a relation to be the containment relation between the facets and vertices of a polytope. Also given here, are a set of matrices parameterizing the linear moduli space and another set parameterizing the projective moduli space of a combinatorial polytope

Visualizing sound emission of elephant vocalizations: evidence for two rumble production types

Recent comparative data reveal that formant frequencies are cues to body size in animals, due to a close relationship between formant frequency spacing, vocal tract length and overall body size. Accordingly, intriguing morphological adaptations to elongate the vocal tract in order to lower formants occur in several species, with the size exaggeration hypothesis being proposed to justify most of these observations. While the elephant trunk is strongly implicated to account for the low formants of elephant rumbles, it is unknown whether elephants emit these vocalizations exclusively through the trunk, or whether the mouth is also involved in rumble production. In this study we used a sound visualization method (an acoustic camera) to record rumbles of five captive African elephants during spatial separation and subsequent bonding situations. Our results showed that the female elephants in our analysis produced two distinct types of rumble vocalizations based on vocal path differences: a nasally- and an orally-emitted rumble. Interestingly, nasal rumbles predominated during contact calling, whereas oral rumbles were mainly produced in bonding situations. In addition, nasal and oral rumbles varied considerably in their acoustic structure. In particular, the values of the first two formants reflected the estimated lengths of the vocal paths, corresponding to a vocal tract length of around 2 meters for nasal, and around 0.7 meters for oral rumbles. These results suggest that African elephants may be switching vocal paths to actively vary vocal tract length (with considerable variation in formants) according to context, and call for further research investigating the function of formant modulation in elephant vocalizations. Furthermore, by confirming the use of the elephant trunk in long distance rumble production, our findings provide an explanation for the extremely low formants in these calls, and may also indicate that formant lowering functions to increase call propagation distances in this species'

The potential to encode sex, age, and individual identity in the alarm calls of three species of Marmotinae

In addition to encoding referential information and information about the sender’s motivation, mammalian alarm calls may encode information about other attributes of the sender, providing the potential for recognition among kin, mates, and neighbors. Here, we examined 96 speckled ground squirrels (Spermophilus suslicus), 100 yellow ground squirrels (Spermophilus fulvus) and 85 yellow-bellied marmots (Marmota flaviventris) to determine whether their alarm calls differed between species in their ability to encode information about the caller’s sex, age, and identity. Alarm calls were elicited by approaching individually identified animals in live-traps. We assume this experimental design modeled a naturally occurring predatory event, when receivers should acquire information about attributes of a caller from a single bout of alarm calls. In each species, variation that allows identification of the caller’s identity was greater than variation allowing identification of age or sex. We discuss these results in relation to each species’ biology and sociality