Circle bundles over 4-manifolds

Every 1-connected topological 4-manifold M admits a $S^{1}$-covering by #_{r-1}S^{2}\times S^{3}, where $r=$rankH^{2}(M;\QTR{Bbb}{Z}).Comment: 6 pages to appear in Archiv der Mat

Network synchronizability analysis: the theory of subgraphs and complementary graphs

In this paper, subgraphs and complementary graphs are used to analyze the network synchronizability. Some sharp and attainable bounds are provided for the eigenratio of the network structural matrix, which characterizes the network synchronizability, especially when the network's corresponding graph has cycles, chains, bipartite graphs or product graphs as its subgraphs.Comment: 13 pages, 7 figure

DNA nanotechnology-enabled chiral plasmonics: from static to dynamic

In this Account, we discuss a variety of static and dynamic chiral plasmonic nanostructures enabled by DNA nanotechnology. In the category of static plasmonic systems, we first show chiral plasmonic nanostructures based on spherical AuNPs, including plasmonic helices, toroids, and tetramers. To enhance the CD responses, anisotropic gold nanorods with larger extinction coefficients are utilized to create chiral plasmonic crosses and helical superstructures. Next, we highlight the inevitable evolution from static to dynamic plasmonic systems along with the fast development of this interdisciplinary field. Several dynamic plasmonic systems are reviewed according to their working mechanisms.Comment: 7 figure