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Transfer learning on graphs drawn from varied distributions (domains) is in great demand across many applications. Emerging methods attempt to learn domain-invariant representations using graph neural networks (GNNs), yet the empirical performances vary and the theoretical foundation is limited. This paper aims at designing theory-grounded algorithms for graph domain adaptation (GDA). (i) As the first attempt, we derive a model-based GDA bound closely related to two GNN spectral properties: spectral smoothness (SS) and maximum frequency response (MFR). This is achieved by cross-pollinating between the OT-based (optimal transport) DA and graph filter theories. (ii) Inspired by the theoretical results, we propose algorithms regularizing spectral properties of SS and MFR to improve GNN transferability. We further extend the GDA theory into the more challenging scenario of conditional shift, where spectral regularization still applies. (iii) More importantly, our analyses of the theory reveal which regularization would improve performance of what transfer learning scenario, (iv) with numerical agreement with extensive real-world experiments: SS and MFR regularizations bring more benefits to the scenarios of node transfer and link transfer, respectively. In a nutshell, our study paves the way toward explicitly constructing and training GNNs that can capture more transferable representations across graph domains. Codes are released at https://github.com/Shen-Lab/GDA-SpecReg. 

Diffusion State Distance (DSD) is a data-dependent metric that compares data points using a data-driven diffusion process and provides a powerful tool for learning the underlying structure of high-dimensional data. While finding the exact nearest neighbors in the DSD metric is computationally expensive, in this paper, we propose a new random-walk based algorithm that empirically finds approximate k-nearest neighbors accurately in an efficient manner. Numerical results for real-world protein-protein interaction networks are presented to illustrate the efficiency and robustness of the proposed algorithm. The set of approximate k-nearest neighbors performs well when used to predict proteins’ functional labels. 

Approaches to in silico prediction of protein structures have been revolutionized by AlphaFold2, while those to predict interfaces between proteins are relatively underdeveloped, owing to the overly complicated yet relatively limited data of protein–protein complexes. In short, proteins are 1D sequences of amino acids folding into 3D structures, and interact to form assemblies to function. We believe that such intricate scenarios are better modeled with additional indicative information that reflects their multi-modality nature and multi-scale functionality. To improve binary prediction of inter-protein residue-residue contacts, we propose to augment input features with multi-modal representations and to synergize the objective with auxiliary predictive tasks. (i) We first progressively add three protein modalities into models: protein sequences, sequences with evolutionary information, and structure-aware intra-protein residue contact maps. We observe that utilizing all data modalities delivers the best prediction precision. Analysis reveals that evolutionary and structural information benefit predictions on the difficult and rigid protein complexes, respectively, assessed by the resemblance to native residue contacts in bound complex structures. (ii) We next introduce three auxiliary tasks via self-supervised pre-training (binary prediction of protein-protein interaction (PPI)) and multi-task learning (prediction of inter-protein residue–residue distances and angles). Although PPI prediction is reported to benefit from predicting intercontacts (as causal interpretations), it is not found vice versa in our study. Similarly, the finer-grained distance and angle predictions did not appear to uniformly improve contact prediction either. This again reflects the high complexity of protein–protein complex data, for which designing and incorporating synergistic auxiliary tasks remains challenging. 

Boron carbide is super-strong and has many important engineering applications such as body armor and cutting tools. However, the extended applications of boron carbide have been limited by its low fracture toughness arising from anomalous brittle failure when subjected to hypervelocity impact or under high pressure. This abnormal brittle failure is directly related to the formation of a tiny amorphous shear band of 2–3 nm in width and several hundred nm in length. In this Perspective, we discuss mitigating the amorphous shear bands in boron carbide from various strategies including microalloying, grain boundary engineering, stoichiometry control, and the addition of a second phase. Combined with recent theoretical and experimental studies, we discuss strategies that can be applied in synthesizing and producing boron carbide-based materials with improved ductility by suppressing the formation of the amorphous shear band.