Research

You can also find my articles on my Google Scholar profile.

Publications

Higher-order Connection Laplacians for Directed Simplicial Complexes

Gong, X, Higham, D.J. and Zygalakis, K, and Bianconi, G.

Published in Journal of Physics: Complexity, 2023 journal arXiv

Higher-order networks encode the many-body interactions existing in complex systems, such as the brain, protein complexes, and social interactions. Simplicial complexes are higher-order networks that allow a comprehensive investigation of the interplay between topology and dynamics. However, simplicial complexes have the limitation that they only capture undirected higher-order interactions while in real-world scenarios, often there is a need to introduce the direction of simplices, extending the popular notion of direction of edges. On graphs and networks the Magnetic Laplacian, a special case of connection Laplacian, is becoming a popular operator to address edge directionality. Here we tackle the challenge of handling directionality in simplicial complexes by formulating higher-order connection Laplacians taking into account the configurations induced by the simplices’ directions. Specifically, we define all the connection Laplacians of directed simplicial complexes of dimension two and we discuss the induced higher-order diffusion dynamics by considering instructive synthetic examples of simplicial complexes. The proposed higher-order diffusion processes can be adopted in real scenarios when we want to consider higher-order diffusion displaying non-trivial frustration effects due to conflicting directionalities of the incident simplices.

Recommended citation: Gong, X, Higham, D.J., Zygalakis, K. and Bianconi, G. Higher-order connection Laplacians for directed simplicial complexes. Journal of Physics: Complexity 5.1 (2024): 015022.

Generative hypergraph models and spectral embedding

Published in Scientic Report, 2023 journal arXiv

We consider the problem of embedding a hypergraph into low-dimensional Euclidean space so that most interactions are short-range. We focus on two spectral embedding algorithms customized to hypergraphs which recover linear and periodic structures respectively. We show that the two spectral hypergraph embedding algorithms are associated with a new class of generative hypergraph models. We demonstrate the hypergraph embedding and follow-on tasks – including structure quantification, clustering and hyperedge prediction – on synthetic and real-world hypergraphs. We also compare several triadic edge prediction methods on high school contact data where our algorithm improves upon benchmark methods when the amount of training data is limited.

Recommended citation: Gong, X, Higham, D.J. and Zygalakis, K. Generative hypergraph models and spectral embedding. Scientific Report 13, 540 (2023). https://doi.org/10.1038/s41598-023-27565-9

Directed network Laplacians and random graph models

Royal Society open science, 2021 journal arXiv

We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph model. We focus on two existing spectral approaches that build and analyse Laplacian-style matrices via the minimization of frustration and trophic incoherence. We show that reordering nodes using the two algorithms, or mapping them onto a specified lattice, is associated with new classes of directed random graph models. Using this random graph setting, we are able to compare the two algorithms on a given network and quantify which structure is more likely to be present. We illustrate the approach on synthetic and real networks, and discuss practical implementation issues.

Recommended citation: Gong, X, Higham, D.J. and Zygalakis, K, 2021. Directed network Laplacians and random graph models. Royal Society open science , 8(10), p.211144. https://doi.org/10.1098/rsos.211144

Large-area synthesis of monolayer and few-layer MoSe2 films on SiO2 substrates

Published in Nano Letters, 2009 journal

We present successful synthesis of large area atomically thin MoSe2 films by selenization of MoO3 in a vapor transport chemical vapor deposition (CVD) system. Experiments reveal the high quality of as-grown MoSe2 in optics, and highlight the potential applications of the sample in nanoelectronics.

Recommended citation: Lu X, Utama MI, Lin J, Gong X, Zhang J, Zhao Y, Pantelides ST, Wang J, Dong Z, Liu Z, Zhou W. Large-area synthesis of monolayer and few-layer MoSe2 films on SiO2 substrates. Nano Letters . 2014 May 14;14(5):2419-25. https://doi.org/10.1021/nl5000906