Ting Li

Ting Li, Bin Wang

In this paper, energy-preserving methods are formulated and studied for solving charged-particle dynamics. We first formulate the scheme of energy-preserving methods and analyze its basic properties including algebraic order and symmetry. Then it is shown that these novel methods can exactly preserve the energy of charged-particle dynamics. Moreover, the long time momentum conservation is studied along such energy-preserving methods. A numerical experiment is carried out to illustrate the notable superiority of the new methods in comparison with the popular Boris method in the literature.

Bing-Yi Jing, Ting Li, Zhongyuan Lyu et al.

We study the problem of community detection in multi-layer networks, where pairs of nodes can be related in multiple modalities. We introduce a general framework, i.e., mixture multi-layer stochastic block model (MMSBM), which includes many earlier models as special cases. We propose a tensor-based algorithm (TWIST) to reveal both global/local memberships of nodes, and memberships of layers. We show that the TWIST procedure can accurately detect the communities with small misclassification error as the number of nodes and/or the number of layers increases. Numerical studies confirm our theoretical findings. To our best knowledge, this is the first systematic study on the mixture multi-layer networks using tensor decomposition. The method is applied to two real datasets: worldwide trading networks and malaria parasite genes networks, yielding new and interesting findings.