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   We study data-driven representations for three- dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants, which learn from the local metric tensor via the Laplacian operator. Despite offering excellent sample complexity and built-in invariances, intrinsic geometry alone is invariant to isometric deformations, making it unsuitable for many applications. To overcome this limitation, we propose several upgrades to GNNs to leverage extrinsic differential geometry properties of three-dimensional surfaces, increasing its modeling power. In particular, we propose to exploit the Dirac operator, whose spectrum detects principal curva- ture directions — this is in stark contrast with the classical Laplace operator, which directly measures mean curvature. We coin the resulting models Surface Networks (SN). We prove that these models define shape representations that are stable to deformation and to discretization, and we demonstrate the efficiency and versatility of SNs on two challenging tasks: temporal prediction of mesh deformations under non-linear dynamics and generative models using a variational autoencoder framework with encoders/decoders given by SNs. 

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   It has been observed that real-world social networks often exhibit stratification along economic or other lines, with consequences for class mobility and access to opportunities. With the rise in human interaction data and extensive use of online social networks, the structure of social networks (representing connections between individuals) can be used for measuring stratification. However, although stratification has been studied extensively in the social sciences, there is no single, generally applicable metric for measuring the level of stratification in a network. In this work, we first propose the novel Stratification Assortativity (StA) metric, which measures the extent to which a network is stratified into different tiers. Then, we use the StA metric to perform an in-depth analysis of the stratification of five co-authorship networks. We examine the evolution of these networks over 50 years and show that these fields demonstrate an increasing level of stratification over time, and, correspondingly, the trajectory of a researcher’s career is increasingly correlated with her entry point into the network. 

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5. Reconstructing Sparse Multiplex Networks with Application to Covert Networks

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   Yu, Jin-Zhu; Wu, Mincheng; Bichler, Gisela; Aros-Vera, Felipe; Gao, Jianxi (January 2023, Entropy)

   Network structure provides critical information for understanding the dynamic behavior of complex systems. However, the complete structure of real-world networks is often unavailable, thus it is crucially important to develop approaches to infer a more complete structure of networks. In this paper, we integrate the configuration model for generating random networks into an Expectation–Maximization–Aggregation (EMA) framework to reconstruct the complete structure of multiplex networks. We validate the proposed EMA framework against the Expectation–Maximization (EM) framework and random model on several real-world multiplex networks, including both covert and overt ones. It is found that the EMA framework generally achieves the best predictive accuracy compared to the EM framework and the random model. As the number of layers increases, the performance improvement of EMA over EM decreases. The inferred multiplex networks can be leveraged to inform the decision-making on monitoring covert networks as well as allocating limited resources for collecting additional information to improve reconstruction accuracy. For law enforcement agencies, the inferred complete network structure can be used to develop more effective strategies for covert network interdiction. 

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