Ricci Curvature of the Internet Topology

Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's "thin triangle condition", which is tightly related to core congestion and route reliability. In this work we analyze the discrete Ricci curvature of the Internet, defined by Ollivier, Lin, etc. Ricci curvature measures whether local distances diverge or converge. It is a more local measure which allows us to understand the distribution of curvatures in the network. We show by various Internet data sets that the distribution of Ricci cuvature is spread out, suggesting the network topology to be non-homogenous. We also show that the Ricci curvature has interesting connections to both local measures such as node degree and clustering coefficient, global measures such as betweenness centrality and network connectivity, as well as auxilary attributes such as geographical distances. These observations add to the richness of geometric structures in complex network theory.Comment: 9 pages, 16 figures. To be appear on INFOCOM 201

Modeling and Analysis of Bifurcation in a Delayed Worm Propagation Model

A delayed worm propagation model with birth and death rates is formulated. The stability of the positive equilibrium is studied. Through theoretical analysis, a critical value τ0 of Hopf bifurcation is derived. The worm propagation system is locally asymptotically stable when time delay is less than τ0. However, Hopf bifurcation appears when time delay τ passes the threshold τ0, which means that the worm propagation system is unstable and out of control. Consequently, time delay should be adjusted to be less than τ0 to ensure the stability of the system stable and better prediction of the scale and speed of Internet worm spreading. Finally, numerical and simulation experiments are presented to simulate the system, which fully support our analysis

Efficient nano iron particle-labeling and noninvasive MR imaging of mouse bone marrow-derived endothelial progenitor cells

In this study, we sought to label mouse bone marrow-derived endothelial progenitor cells (EPCs) with Resovist® in vitro and to image them using 7.0 Tesla (T) magnetic resonance imaging (MRI). Mouse bone marrow-derived EPCs were cultured in endothelial basal medium with endothelial growth supplement. They were then characterized by immunocytochemistry, flow cytometry, and fluorescence quantitative polymerase chain reaction. Their functions were evaluated by measuring their uptake of 1,1-dioctadecyl-3,3,3,3-tetramethylindocarbocyanine-labeled acetylated low-density lipoprotein (Dil-Ac-LDL), binding of fluorine isothiocyanate (FITC)-labeled Ulex europaeus agglutinin (UEA), and formation of capillary-like networks. EPCs were labeled with superparamagnetic iron oxide (SPIO) and their proliferation was then assessed in a water-soluble tetrazolium (WST-8)-based cell proliferation assay. Spin echo sequence (multislice, multiecho [MSME]) and gradient echo sequence (2D-FLASH) were used to detect differences in the numbers of labeled cells by 7.0 T MRI. The results showed that the cultured cells were of “cobblestone”-like shape and positive for CD133, CD34, CD31, von Willebrand factor, kinase domain receptor, and CD45, but negative for F4/80. They could take up Dil-Ac-LDL, bind FITC-UEA, and form capillary-like networks on Matrigel in vitro. Prussian-blue staining demonstrated that the cells were efficiently labeled with SPIO. The single-cell T2* effect was more obvious in the 2D-FLASH sequence than in the MSME sequence. Further, there were almost no adverse effects on cell vitality and proliferation. In conclusion, mouse bone marrow-derived EPCs can be efficiently labeled with SPIO and imaged with 7.0-T MRI. They may thus be traced by MRI following transplantation for blood vessel disorders and cancer treatment