We propose two methods for the unsupervised detection of communities in undirected multiplex networks. These networks consist of multiple layers that record different relationships between the same entities or incorporate data from different sources. Both methods are formulated as gradient flows of suitable energy functionals: the first (MPBTV) builds on the minimization of a balanced total...
We introduce past-aware game-theoretic centrality, a class of centrality measures that captures the collaborative contribution of nodes in a network, accounting for both uncertain and certain collaborators. A general framework for computing standard game-theoretic centrality is extended to the past-aware case. As an application, we develop a new heuristic for different versions of the...
I will present two recent works, coauthored with Mei-Heng Yueh, in which we propose Riemannian optimization algorithms for computing spherical and toroidal area-preserving mappings of genus-zero and genus-one closed surfaces, respectively. The proposed framework is based on retraction-based Riemannian optimization, which provides an effective way to handle the geometric constraints of the...
We investigate the propagation of initial value perturbations along the solution of a linear ordinary differential equation $y'(t) = Ay(t)$. This propagation is analyzed using the relative error rather than the absolute error. Our focus is on the long-term behavior of this relative error, which differs significantly from that of the absolute error. Understanding the long-term behavior provides...
