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

Association between chronic viral hepatitis infection and breast cancer risk: a nationwide population-based case-control study

<p>Abstract</p> <p>Background</p> <p>In Taiwan, there is a high incidence of breast cancer and a high prevalence of viral hepatitis. In this case-control study, we used a population-based insurance dataset to evaluate whether breast cancer in women is associated with chronic viral hepatitis infection.</p> <p>Methods</p> <p>From the claims data, we identified 1,958 patients with newly diagnosed breast cancer during the period 2000-2008. A randomly selected, age-matched cohort of 7,832 subjects without cancer was selected for comparison. Multivariable logistic regression models were constructed to calculate odds ratios of breast cancer associated with viral hepatitis after adjustment for age, residential area, occupation, urbanization, and income. The age-specific (<50 years and ≥50 years) risk of breast cancer was also evaluated.</p> <p>Results</p> <p>There were no significant differences in the prevalence of hepatitis C virus (HCV) infection, hepatitis B virus (HBV), or the prevalence of combined HBC/HBV infection between breast cancer patients and control subjects (<it>p </it>= 0.48). Multivariable logistic regression analysis, however, revealed that age <50 years was associated with a 2-fold greater risk of developing breast cancer (OR = 2.03, 95% CI = 1.23-3.34).</p> <p>Conclusions</p> <p>HCV infection, but not HBV infection, appears to be associated with early onset risk of breast cancer in areas endemic for HCV and HBV. This finding needs to be replicated in further studies.</p