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Abstract In order to better understand manifold neural networks (MNNs), we introduce Manifold Filter-Combine Networks (MFCNs). Our filter-combine framework parallels the popular aggregate-combine paradigm for graph neural networks (GNNs) and naturally suggests many interesting families of MNNs which can be interpreted as manifold analogues of various popular GNNs. We propose a method for implementing MFCNs on high-dimensional point clouds that relies on approximating an underlying manifold by a sparse graph. We then prove that our method is consistent in the sense that it converges to a continuum limit as the number of data points tends to infinity, and we numerically demonstrate its effectiveness on real-world and synthetic data sets. 

This paper examines a return to the thick space of the masonry wall. The wall is where a building embraces its context and where humanity can physically experience this nexus. Contemporary technologies applied to masonry construction offer a return to both tactile solidity and the space of interaction between a building and its users. Precedents from Catalan vernacular to Herzog & de Meuron will be contrasted to offer a way of thinking through the spatial potential created through the modularity and specificity of blocks. 

Staphylococcus aureus is the leading cause of skin infections in the U.S., and its rapid evolution and resistance to antibiotics create a barrier to effective treatment. In this study, we engineered a composite membrane with bacterial cellulose and carbon nanotubes (BC-CNT) as an electroactive dressing to rapidly eradicate vancomycin-intermediate S. aureus. Nonpathogenic Komagataeibacter sucrofermentans produced the BC membrane at an air-liquid interface. Then, carboxyl-functionalized multi-walled CNTs were integrated into decellularized BC to create stable and electrically conductive BC-CNT dressings. The electric potential and ionic flux across BC-CNT were modeled and standardized via chronoamperometry for experimental validation. We found that treatment with electroactive BC-CNT increases S. aureus sensitivity to vancomycin and prevents macro-scale biofilm formation. The bactericidal efficacy of the composite membrane is consistent with electrochemical stress caused by voltage mediated with BC-CNT. After a single hour of combinatorial electrical and drug treatment, biofilm-forming capacity was inhibited by nearly 92 %. These results advance applications of electrochemistry in medicine and create a new direction to overcome S. aureus infections on skin and soft tissues.