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Anisotropic planar polaritons - hybrid electromagnetic modes mediated by phonons, plasmons, or excitons - in biaxial two-dimensional (2D) van der Waals crystals have attracted significant attention due to their fundamental physics and potential nanophotonic applications. In this Perspective, we review the properties of planar hyperbolic polaritons and the variety of methods that can be used to experimentally tune them. We argue that such natural, planar hyperbolic media should be fairly common in biaxial and uniaxial 2D and 1D van der Waals crystals, and identify the untapped opportunities they could enable for functional (i.e. ferromagnetic, ferroelectric, and piezoelectric) polaritons. Lastly, we provide our perspectives on the technological applications of such planar hyperbolic polaritons.

 

Label Propagation Algorithm (LPA) and Graph Convolutional Neural Networks (GCN) are both message passing algorithms on graphs. Both solve the task of node classification, but LPA propagates node label information across the edges of the graph, while GCN propagates and transforms node feature information. However, while conceptually similar, theoretical relationship between LPA and GCN has not yet been systematically investigated. Moreover, it is unclear how LPA and GCN can be combined under a unified framework to improve the performance. Here we study the relationship between LPA and GCN in terms of feature/label influence , in which we characterize how much the initial feature/label of one node influences the final feature/label of another node in GCN/LPA. Based on our theoretical analysis, we propose an end-to-end model that combines GCN and LPA. In our unified model, edge weights are learnable, and the LPA serves as regularization to assist the GCN in learning proper edge weights that lead to improved performance. Our model can also be seen as learning the weights of edges based on node labels, which is more direct and efficient than existing feature-based attention models or topology-based diffusion models. In a number of experiments for semi-supervised node classification and knowledge-graph-aware recommendation, our model shows superiority over state-of-the-art baselines. 

Learning representations of sets of nodes in a graph is crucial for applications ranging from node-role discovery to link prediction and molecule classification. Graph Neural Networks (GNNs) have achieved great success in graph representation learning. However, expressive power of GNNs is limited by the 1-Weisfeiler-Lehman (WL) test and thus GNNs generate identical representations for graph substructures that may in fact be very different. More powerful GNNs, proposed recently by mimicking higher-order-WL tests, only focus on representing entire graphs and they are computationally inefficient as they cannot utilize sparsity of the underlying graph. Here we propose and mathematically analyze a general class of structure related features, termed Distance Encoding (DE). DE assists GNNs in representing any set of nodes, while providing strictly more expressive power than the 1-WL test. DE captures the distance between the node set whose representation is to be learned and each node in the graph. To capture the distance DE can apply various graph-distance measures such as shortest path distance or generalized PageRank scores. We propose two ways for GNNs to use DEs (1) as extra node features, and (2) as controllers of message aggregation in GNNs. Both approaches can utilize the sparse structure of the underlying graph, which leads to computational efficiency and scalability. We also prove that DE can distinguish node sets embedded in almost all regular graphs where traditional GNNs always fail. We evaluate DE on three tasks over six real networks: structural role prediction, link prediction, and triangle prediction. Results show that our models outperform GNNs without DE by up-to 15% in accuracy and AUROC. Furthermore, our models also significantly outperform other state-of-the-art methods especially designed for the above tasks. 

The subtle variation of metallic bonding, induced by external influence, plays an essential role in determining physical, mechanical, and chemical properties of metals. However, it is extremely difficult to describe this variation because of the delocalization nature of metallic bonding. Here, we utilize the reduced density gradient and topological analysis of electron density to capture the local metallic bonding variations (LMBV) caused by lattice distortion and carrier injection in many face-centered cubic (fcc) metals. We find that the LMBV determines the traits of fcc metals such as strength, malleability, and ductility. Moreover, the fcc metals can become more flexible/stronger with the electron/hole injection, providing an important guidance to tune metals for desired mechanical properties.