BlogPost #030

Abstract: Two competing types of node interactions often play an important part in shaping system behaviour, e.g., activatory or inhibitory functions in biological systems. Hence, signed networks, where each connection can be either positive or negative, have become popular models over recent years. In this talk, we first introduce a classification of signed networks into balanced, antibalanced or strictly unbalanced ones, and then characterise each type of signed networks in terms of the spectral properties of the signed weighted adjacency matrix. In particular, we show that the spectral radius of the matrix with signs is smaller than that without if and only if the signed network is strictly unbalanced. We then apply the results to understand important dynamics on signed networks – random walks. Specifically, we show that biconsensus can be obtained asymptotically when the graph is structurally balanced, while global consensus can be achieved when the graph is strictly unbalanced. Finally, we numerically verify these properties through experiments on both synthetic and real networks. The results can also contribute to a better understanding of the related problems, e.g., the influence maximisation.

Abstract: It is hard to imagine what will happen on a job until you actually start it. But what if it is far from what you have expected? It may be that your supervisor wants to meet more than once a day, or the opposite that you have almost no meeting with your supervisor(s) over a year. It may be that you are involved in too many projects to manage, or the opposite that you are an outlier, surrounded by people doing so different and independent research that it is difficult to even start a single project together. In this part of the talk, I plan to discuss broadly how I manage the challenges in my postdoctoral research, both mentally such as managing my expectations, and practically, such as taking a visiting scholar role at universities nearby.