Symmetry-protected higher-order exceptional points in staggered flatband rhombic lattices

Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, constructing higher-order EPs still remains as a challenge due to the strict requirement of the system symmetries. Here we demonstrate that higher-order EPs can be judiciously fabricated in PT -symmetric staggered rhombic lattices by introducing not only on-site gain/loss but also nonHermitian couplings. Zero-energy flatbands persist and symmetry-protected third-order EPs (EP3) arise in these systems owing to the non-Hermitian chiral/sublattice symmetry, but distinct phase transitions and propagation dynamics occur. Specifically, the EP3 arises at the Brillouin zone (BZ) boundary in the presence of on-site gain/loss. The single-site excitations display an exponential power increase in the PT -broken phase. Meanwhile, a nearly flatband sustains when a small lattice perturbation is applied. For the lattices with non-Hermitian couplings, however, the EP3 appears at the BZ center. Quite remarkably, our analysis unveils a dynamical delocalization-localization transition for the excitation of the dispersive bands and a quartic power increase beyond the EP3. Our scheme provides a new platform towards the investigation of the higher-order EPs, and can be further extended to the study of topological phase transitions or nonlinear processes associated with higher-order EPs.Comment: 10 pages, 10 figure

Mining Diversity on Social Media Networks

The fast development of multimedia technology and increasing availability of network bandwidth has given rise to an abundance of network data as a result of all the ever-booming social media and social websites in recent years, e.g., Flickr, Youtube, MySpace, Facebook, etc. Social network analysis has therefore become a critical problem attracting enthusiasm from both academia and industry. However, an important measure that captures a participant’s diversity in the network has been largely neglected in previous studies. Namely, diversity characterizes how diverse a given node connects with its peers. In this paper, we give a comprehensive study of this concept. We first lay out two criteria that capture the semantic meaning of diversity, and then propose a compliant definition which is simple enough to embed the idea. Based on the approach, we can measure not only a user’s sociality and interest diversity but also a social media’s user diversity. An efficient top-k diversity ranking algorithm is developed for computation on dynamic networks. Experiments on both synthetic and real social media datasets give interesting results, where individual nodes identified with high diversities are intuitive