Higher-order homophily on simplicial complexes.

Higher-order network models are becoming increasingly relevant for their ability to explicitly capture interactions between three or more entities in a complex system at once. In this paper, we study homophily, the tendency for alike individuals to form connections, as it pertains to higher-order interactions. We find that straightforward extensions of classical homophily measures to interactions of size 3 and larger are often inflated by homophily present in pairwise interactions.

Diameter Dependence of Water Filling in Lithographically Segmented Isolated Carbon Nanotubes.

Although the structure and properties of water under conditions of extreme confinement are fundamentally important for a variety of applications, they remain poorly understood, especially for dimensions less than 2 nm. This problem is confounded by the difficulty in controlling surface roughness and dimensionality in fabricated nanochannels, contributing to a dearth of experimental platforms capable of carrying out the necessary precision measurements. In this work, we utilize an experimental platform based on the interior of lithographically segmented, isolated single-walled carbon nanotubes to study water under extreme nanoscale confinement.