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Biography

Dr.  Yilun  Shang
Northumbria University,  UK

Title: Skew characteristics polynomial of operations on oriented graphs and their applications in graph neural networks

Abstract:

Let G be an oriented graph with n vertices and m arcs having underlying graph G. The skew matrix of G is a (–1, 0, 1)-skew-symmetric matrix. The skew eigenvalues of G are the eigenvalues of the skew matrix, and its characteristic polynomial is the skew characteristic polynomial of G. The sum of the absolute values of the skew eigenvalues is the skew energy of G. In this talk, we talk about the skew characteristic polynomial and skew eigenvalues of the joined union of oriented graphs and some of its variations. We show that the skew eigenvalues of the joined union of oriented graphs and some variations of oriented graphs are the union of the skew eigenvalues of the component-oriented graphs except for some eigenvalues, which are given by an auxiliary matrix associated with the joined union. We present concrete examples and explore the links between the polynomials of such operations on oriented graphs and graph neural networks with a focus on combinatorial optimization and natural language processing. 

Biography:

Yilun Shang is currently an Associate Professor (Reader) and the Program Leader for MSC in Artificial Intelligence at Northumbria University. He received his PhD degree in Mathematics from Shanghai Jiao Tong University in 2010. His main research interests include graph theory, network theory, probability, nonlinear system, and distributed algorithm. He is a recipient of the Dimitrie Pompeiu Prize in 2016 and the 2019, 2020 Outstanding Associate Editor Award of IEEE Access. He is an invited reviewer for Mathematical Reviews.

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