An Optimal Estimate for the Anisotropic Logarithmic Potential

This paper introduces the new annulus body to establish the optimal lower bound for the anisotropic logarithmic potential as the complement to the theory of its upper bound estimate which has already been investigated. The connections with convex geometry analysis and some metric properties are also established. For the application, a polynomial dual log-mixed volume difference law is deduced from the optimal estimate.

Differential time allocation of foraging workers in the subterranean termite

Background Foraging in group living animals such as social insects, is collectively performed by individuals. However, our understanding on foraging behavior of subterranean termites is extremely limited, as the process of foraging in the field is mostly concealed. Because of this limitation, foraging behaviors of subterranean termites were indirectly investigated in the laboratory through tunnel geometry analysis and observations on tunneling behaviors. In this study, we tracked subsets of foraging workers from juvenile colonies of Coptotermes formosanus (2-yr-old) to describe general foraging behavioral sequences and to find how foraging workers allocate time between the foraging site (food acquisition or processing) and non-foraging site (food transportation). Results Once workers entered into the foraging site, they spent, on average, a significantly longer time at the foraging site than the non-foraging site. Our clustering analysis revealed two different types of foraging workers in the subterranean termite based on the duration of time they spent at the foraging site and their foraging frequency. After entering the foraging site, some workers (cluster 1) immediately initiated masticating wood fragments, which they transferred as food boluses to recipient workers at the foraging site. Conversely, the recipient workers (cluster 2) moved around after entering the foraging site and received food from donating workers. Conclusions This study provides evidence of task specialization within foraging cohorts in subterranean termites.