The evolution of a citation network topology: The development of the journal Scientometrics

By mapping the electronic database containing all papers in Scientometrics for a 26-year period (1978-2004), we uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The citation network of the journal displays the characteristic features of a “small-world” network of local dense clusters of highly specialized literature. These clusters, however, are efficiently connected into a large single component by a small number of “hub” papers that allow short-distance connection among increasingly large numbers of papers. The patterns of evolution of the network toward this “small-world” are also explored

Non-ergodic Convergence Analysis of Heavy-Ball Algorithms

In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions. For objective functions satisfying a relaxed strongly convex condition, the linear convergence is established under weaker assumptions on the step size and inertial parameter than made in the existing literature. We extend our results to multi-block version of the algorithm with both the cyclic and stochastic update rules. In addition, our results can also be extended to decentralized optimization, where the ergodic analysis is not applicable

Site-specific selection reveals selective constraints and functionality of tumor somatic mtDNA mutations.

BACKGROUND: Previous studies have indicated that tumor mitochondrial DNA (mtDNA) mutations are primarily shaped by relaxed negative selection, which is contradictory to the critical roles of mtDNA mutations in tumorigenesis. Therefore, we hypothesized that site-specific selection may influence tumor mtDNA mutations. METHODS: To test our hypothesis, we developed the largest collection of tumor mtDNA mutations to date and evaluated how natural selection shaped mtDNA mutation patterns. RESULTS: Our data demonstrated that both positive and negative selections acted on specific positions or functional units of tumor mtDNAs, although the landscape of these mutations was consistent with the relaxation of negative selection. In particular, mutation rate (mutation number in a region/region bp length) in complex V and tRNA coding regions, especially in ATP8 within complex V and in loop and variable regions within tRNA, were significantly lower than those in other regions. While the mutation rate of most codons and amino acids were consistent with the expectation under neutrality, several codons and amino acids had significantly different rates. Moreover, the mutations under selection were enriched for changes that are predicted to be deleterious, further supporting the evolutionary constraints on these regions. CONCLUSION: These results indicate the existence of site-specific selection and imply the important role of the mtDNA mutations at some specific sites in tumor development