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We introduce SignNet and BasisNet---new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if v is an eigenvector then so is -v; and (ii) more general basis symmetries, which occur in higher dimensional eigenspaces with infinitely many choices of basis eigenvectors. We prove that under certain conditions our networks are universal, i.e., they can approximate any continuous function of eigenvectors with the desired invariances. When used with Laplacian eigenvectors, our networks are provably more expressive than existing spectral methods on graphs; for instance, they subsume all spectral graph convolutions, certain spectral graph invariants, and previously proposed graph positional encodings as special cases. Experiments show that our networks significantly outperform existing baselines on molecular graph regression, learning expressive graph representations, and learning neural fields on triangle meshes. Our code is available at https://github.com/cptq/SignNet-BasisNet. 

Abstract High-pressure electrical resistivity measurements reveal that the mechanical deformation of ultra-hard WB 2 during compression induces superconductivity above 50 GPa with a maximum superconducting critical temperature, T c of 17 K at 91 GPa. Upon further compression up to 187 GPa, the T c gradually decreases. Theoretical calculations show that electron-phonon mediated superconductivity originates from the formation of metastable stacking faults and twin boundaries that exhibit a local structure resembling MgB 2 (hP3, space group 191, prototype AlB 2 ). Synchrotron x-ray diffraction measurements up to 145 GPa show that the ambient pressure hP12 structure (space group 194, prototype WB 2 ) continues to persist to this pressure, consistent with the formation of the planar defects above 50 GPa. The abrupt appearance of superconductivity under pressure does not coincide with a structural transition but instead with the formation and percolation of mechanically-induced stacking faults and twin boundaries. The results identify an alternate route for designing superconducting materials. 

High-pressure electrical resistivity measurements reveal that the mechanical deformation of ultra-hard WB2 during compression induces superconductivity above 50 GPa with a maximum super-conducting critical temperature, Tc of 17 K at 91 GPa. Upon further compression up to 187 GPa, the Tc gradually decreases. Theoretical calculations show that electron-phonon mediated super-conductivity originates from the formation of metastable stacking faults and twin boundaries that exhibit a local structure resembling MgB2 (hP3, space group 191, prototype AlB2). Synchrotron x-ray diffraction measurements up to 145 GPa show that the ambient pressure hP12 structure (space group 194, prototype WB2) continues to persist to this pressure, consistent with the formation of the planar defects above 50 GPa. The abrupt appearance of superconductivity under pressure does not coincide with a structural transition but instead with the formation and percolation of mechanically-induced stacking faults and twin boundaries. The results identify an alternate route for designing superconducting materials. 

Social media has become a powerful and efficient platform for information diffusion. The increasing pervasiveness of social media use, however, has brought about the problems of fraudulent accounts that are intended to diffuse misinformation or malicious contents. Twitter recently released comprehensive archives of fraudulent tweets that are possibly connected to a propaganda effort of Internet Research Agency (IRA) on the 2016 U.S. presidential election. To understand information diffusion in fraudulent networks, we analyze structural properties of the IRA retweet network, and develop deep neural network models to detect fraudulent tweets. The structure analysis reveals key characteristics of the fraudulent network. The experiment results demonstrate the superior performance of the deep learning technique to a traditional classification method in detecting fraudulent tweets. The findings have potential implications for curbing online misinformation. 

Despite the tremendous role of online consumer reviews (OCRs) in facilitating consumer purchase decision making, the potential inconsistency between product ratings and review content could cause the uncertainty and confusions of prospect consumers toward a product. This research is aimed to investigate such inconsistency so as to better assist potential consumers with making purchase decisions. First, this study extracted a reviewer’s sentiments from review text via sentiment analysis. Then, it examined the correlation and inconsistency between product ratings and review sentiments via Pearson correlation coefficients (PCC) and box plots. Next, we compared such inconsistency patterns between fake and authentic reviews. Based on an analysis of 24,539 Yelp reviews, we find that although the ratings and sentiments are highly correlated, the inconsistency between the two is more salient in fake reviews than in authentic reviews. The comparison also reveals different inconsistency patterns between the two types of reviews.