Interpretable Rotation-Equivariant Quaternion Neural Networks for 3D Point Cloud Processing.

This study proposes a set of generic rules to revise existing neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs), in order to make feature representations of neural networks to be rotation-equivariant and permutation-invariant. Rotation equivariance of features means that the feature computed on a rotated input point cloud is the same as applying the same rotation transformation to the feature computed on the original input point cloud. We find that the rotation-equivariance of features is naturally satisfied, if a neural network uses quaternion features. Interestingly, we prove that such a network revision also makes gradients of features in the REQNN to be rotation-equivariant w.r.t. inputs, and the training of the REQNN to be rotation-invariant w.r.t. inputs. Besides, permutation-invariance examines whether the intermediate-layer features are invariant, when we reorder input points. We also evaluate the stability of knowledge representations of REQNNs, and the robustness of REQNNs to adversarial rotation attacks. Experiments have shown that REQNNs outperform traditional neural networks in both terms of classification accuracy and robustness on rotated testing samples.

A Review of the Role of Extracellular Polymeric Substances (EPS) in Wastewater Treatment Systems.

A review of the characterization and functions of extracellular polymeric substances (EPS) of microbial aggregates in biological wastewater treatment systems is presented in this paper. EPS represent the complex high-molecular-weight mixture of polymers excreted by microorganisms generated from cell lysis as well as adsorbed inorganic and organic matter from wastewater. EPS exhibit a three-dimensional, gel-like, highly hydrated matrix that facilitates microbial attachment, embedding, and immobilization. EPS play multiple roles in containments removal, and the main components of EPS crucially influence the properties of microbial aggregates, such as adsorption ability, stability, and formation capacity. Moreover, EPS are important to sludge bioflocculation, settleability, and dewatering properties and could be used as carbon and energy sources in wastewater treatment. However, due to the complex structure of EPS, related knowledge is incomplete, and further research is necessary to understand fully the precise roles in biological treatment processes.