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Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. However, much less work has been done on signal classification, where the data consists of many functions (referred to as signals) defined on the vertices of a single graph. These tasks require networks designed differently from those designed for traditional GNN tasks. Indeed, traditional GNNs rely on localized low-pass filters, and signals of interest may have intricate multi-frequency behavior and exhibit long range interactions. This motivates us to introduce the BLIS-Net (Bi-Lipschitz Scattering Net), a novel GNN that builds on the previously introduced geometric scattering transform. Our network is able to capture both local and global signal structure and is able to capture both low-frequency and high-frequency information. We make several crucial changes to the original geometric scattering architecture which we prove increase the ability of our network to capture information about the input signal and show that BLIS-Net achieves superior performance on both synthetic and real-world data sets based on traffic flow and fMRI data. 

Abstract The Hawaiian Ridge has long been a focus site for studying lithospheric flexure due to intraplate volcano loading, but crucial load and flexure details remain unclear. We address this problem using wide‐angle seismic refraction and reflection data acquired along a ∼535‐km‐long profile that intersects the ridge between the islands of Maui and Hawai'i and crosses 80–95 Myr‐old lithosphere. A tomographic image constructed using travel time data of several seismic phases reveals broad flexure of Pacific oceanic crust extending up to ∼200–250 km either side of the Hawaiian Ridge, and vertically up to ∼6–7 km. TheP‐wave velocity structure, verified by gravity modeling, reveals that the west flank of Hawaii is comprised of extrusive lavas overlain by volcanoclastic sediments and a carbonate platform. In contrast, the Hāna Ridge, southeast of Maui, contains a high‐velocity core consistent with mafic or ultramafic intrusive rocks. Magmatic underplating along the seismic line is not evident. Reflectors at the top and bottom of the pre‐existing oceanic crust suggest a ∼4.5–6 km crustal thickness. Simple three‐dimensional flexure modeling with an elastic plate thickness,T_e, of 26.7 km shows that the depths to the reflectors beneath the western flank of Hawai'i can be explained by volcano loading in which Maui and the older islands in the ridge contribute ∼43% to the flexure and the island of Hawai'i ∼51%. Previous studies, however, revealed a higherT_ebeneath the eastern flank of Hawai'i suggesting that isostatic compensation may not yet be complete at the youngest end of the ridge. 

Mechanosensory corpuscles detect transient touch and vibration in the skin of vertebrates, enabling precise sensation of the physical environment. The corpuscle contains a mechanoreceptor afferent surrounded by lamellar cells (LCs), but corpuscular ultrastructure and the role of LCs in touch detection are unknown. We report the three-dimensional architecture of the avian Meissner (Grandry) corpuscle acquired using enhanced focused ion beam scanning electron microscopy and machine learning-based segmentation. The corpuscle comprises a stack of LCs interdigitated with terminal endings from two afferents. Simultaneous electrophysiological recordings from both cell types revealed that mechanosensitive LCs use calcium influx to trigger action potentials in the afferent and thus serve as physiological touch sensors in the skin. The elaborate architecture and bicellular sensory mechanism in the corpuscles, which comprises the afferents and LCs, create the capacity for nuanced encoding of the submodalities of touch.