Browsing by Author "Zhu, Yu"
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Item Graphene-carbon nanotube hybrid materials and use as electrodes(2016-09-27) Tour, James M.; Zhu, Yu; Li, Lei; Yan, Zheng; Lin, Jian; Rice University; United States Patent and Trademark OfficeProvided are methods of making graphene-carbon nanotube hybrid materials. Such methods generally include: (1) associating a graphene film with a substrate; (2) applying a catalyst and a carbon source to the graphene film; and (3) growing carbon nanotubes on the graphene film. The grown carbon nanotubes become covalently linked to the graphene film through carbon-carbon bonds that are located at one or more junctions between the carbon nanotubes and the graphene film. In addition, the grown carbon nanotubes are in ohmic contact with the graphene film through the carbon-carbon bonds at the one or more junctions. The one or more junctions may include seven-membered carbon rings. Also provided are the formed graphene-carbon nanotube hybrid materials.Item Hypergraph cuts with edge-dependent vertex weights(Springer Nature, 2022) Zhu, Yu; Segarra, SantiagoWe develop a framework for incorporating edge-dependent vertex weights (EDVWs) into the hypergraph minimum s-t cut problem. These weights are able to reflect different importance of vertices within a hyperedge, thus leading to better characterized cut properties. More precisely, we introduce a new class of hyperedge splitting functions that we call EDVWs-based, where the penalty of splitting a hyperedge depends only on the sum of EDVWs associated with the vertices on each side of the split. Moreover, we provide a way to construct submodular EDVWs-based splitting functions and prove that a hypergraph equipped with such splitting functions can be reduced to a graph sharing the same cut properties. In this case, the hypergraph minimum s-t cut problem can be solved using well-developed solutions to the graph minimum s-t cut problem. In addition, we show that an existing sparsification technique can be easily extended to our case and makes the reduced graph smaller and sparser, thus further accelerating the algorithms applied to the reduced graph. Numerical experiments using real-world data demonstrate the effectiveness of our proposed EDVWs-based splitting functions in comparison with the all-or-nothing splitting function and cardinality-based splitting functions commonly adopted in existing work.Item Hypergraphs with edge-dependent vertex weights: p-Laplacians and spectral clustering(Frontiers, 2023) Zhu, Yu; Segarra, SantiagoWe study p-Laplacians and spectral clustering for a recently proposed hypergraph model that incorporates edge-dependent vertex weights (EDVW). These weights can reflect different importance of vertices within a hyperedge, thus conferring the hypergraph model higher expressivity and flexibility. By constructing submodular EDVW-based splitting functions, we convert hypergraphs with EDVW into submodular hypergraphs for which the spectral theory is better developed. In this way, existing concepts and theorems such as p-Laplacians and Cheeger inequalities proposed under the submodular hypergraph setting can be directly extended to hypergraphs with EDVW. For submodular hypergraphs with EDVW-based splitting functions, we propose an efficient algorithm to compute the eigenvector associated with the second smallest eigenvalue of the hypergraph 1-Laplacian. We then utilize this eigenvector to cluster the vertices, achieving higher clustering accuracy than traditional spectral clustering based on the 2-Laplacian. More broadly, the proposed algorithm works for all submodular hypergraphs that are graph reducible. Numerical experiments using real-world data demonstrate the effectiveness of combining spectral clustering based on the 1-Laplacian and EDVW.Item Joint embedding of biological networks for cross-species functional alignment(Oxford University Press, 2023) Li, Lechuan; Dannenfelser, Ruth; Zhu, Yu; Hejduk, Nathaniel; Segarra, Santiago; Yao, VickyModel organisms are widely used to better understand the molecular causes of human disease. While sequence similarity greatly aids this cross-species transfer, sequence similarity does not imply functional similarity, and thus, several current approaches incorporate protein–protein interactions to help map findings between species. Existing transfer methods either formulate the alignment problem as a matching problem which pits network features against known orthology, or more recently, as a joint embedding problem.We propose a novel state-of-the-art joint embedding solution: Embeddings to Network Alignment (ETNA). ETNA generates individual network embeddings based on network topological structure and then uses a Natural Language Processing-inspired cross-training approach to align the two embeddings using sequence-based orthologs. The final embedding preserves both within and between species gene functional relationships, and we demonstrate that it captures both pairwise and group functional relevance. In addition, ETNA’s embeddings can be used to transfer genetic interactions across species and identify phenotypic alignments, laying the groundwork for potential opportunities for drug repurposing and translational studies.https://github.com/ylaboratory/ETNAItem Learning on Inhomogeneous Hypergraphs(2023-04-17) Zhu, Yu; Segarra, SantiagoAlthough graphs are widely used in a myriad of machine learning tasks, they are limited to representing pairwise interactions. By contrast, in many real-world applications the entities engage in higher-order relations. Such relations can be modeled by hypergraphs, where the notion of an edge is generalized to a hyperedge that can connect more than two vertices. Traditional hypergraph models treat all the vertices in a hyperedge equally while in practice these vertices might contribute differently to the hyperedge. To deal with such cases, edge-dependent vertex weights (EDVWs) are introduced into hypergraphs which are able to reflect different importance of vertices within the same hyperedge. In this thesis, I study several fundamental problems considering the hypergraph model with EDVWs. First, I develop valid Laplacian matrices for this hypergraph model through random walks defined on vertices and hyperedges and incorporating EDVWs, based on which I propose spectral partitioning algorithms for co-clustering vertices and hyperedges. Second, I develop a framework for incorporating EDVWs into hypergraph cut problems via introducing a new class of hyperedge splitting functions which are both submodular and dependent on EDVWs. I also generalize existing reduction as well as sparsification techniques to our setting. Finally, I define p-Laplacians for this hypergraph model and focus on the p=1 case. I propose an efficient algorithm to compute the eigenvector associated with the second smallest eigenvalue of the 1-Laplacian and then use this eigenvector to cluster vertices in order to achieve better performance than traditional spectral clustering based on the 2-Laplacian.Item Signal processing on higher-order networks: Livin’ on the edge... and beyond(Elsevier, 2021) Schaub, Michael T.; Zhu, Yu; Seby, Jean-Baptiste; Roddenberry, T. Mitchell; Segarra, SantiagoIn this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on simplicial complexes and hypergraphs, two common higher-order network abstractions that can incorporate polyadic relationships. We provide brief introductions to simplicial complexes and hypergraphs, with a special emphasis on the concepts needed for the processing of signals supported on these structures. Specifically, we discuss Fourier analysis, signal denoising, signal interpolation, node embeddings, and nonlinear processing through neural networks, using these two higher-order network models. In the context of simplicial complexes, we specifically focus on signal processing using the Hodge Laplacian matrix, a multi-relational operator that leverages the special structure of simplicial complexes and generalizes desirable properties of the Laplacian matrix in graph signal processing. For hypergraphs, we present both matrix and tensor representations, and discuss the trade-offs in adopting one or the other. We also highlight limitations and potential research avenues, both to inform practitioners and to motivate the contribution of new researchers to the area.