时间：2017年10月 25日下午4:00 - 5:00
报告题目：If, only if, and iff conditions on the eigenvalues of signed Laplacians
报告摘要：In this talk we study the eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights. In the first part of the talk, a class of directed signed graphs in which one pair of nodes (either connected or not) is perturbed with negative weights is investigated. A necessary condition is introduced, under which, the real parts of the non-zero eigenvalues of the perturbed
Laplacian matrix are positive. Also, a sufficient condition is also presented that ensures the aforementioned objective for the perturbed graph. Then the case where the condition becomes necessary and sufficient is discussed. In the second part of the talk, a subset of node pairs in a directed graphs are identified such that the following statement holds: if any if an edge with infinitesimal negative weight is inserted between these pairs, the resulting Laplacian matrix will have at least one eigenvalue with negative real part.
Iman Shames博士概况：Iman Shames is currently a Senior Lecturer (Assistant Professor) at the Department of Electrical and Electronic Engineering, the University of Melbourne. Previously, he had been a McKenzie fellow at the same department from 2012 to 2014. Previously, he was an ACCESS Postdoctoral Researcher at the ACCESS Linnaeus Centre, the KTH Royal Institute of Technology, Stockholm, Sweden. He received his B.Sc. degree in Electrical Engineering from Shiraz University, Iran in 2006, and the Ph.D. degree in engineering and computer science from the Australian National University, Canberra, Australia in 2011. His current research interests include, but are not limited to, optimisation theory and numerical optimisation, mathematical systems theory, and security and privacy in cyber-physical systems.