The Inversion of the Real Kinematic Properties of Coronal Mass Ejections by Forward Modeling

The kinematic properties of coronal mass ejections (CMEs) suffer from the projection effects, and it is expected that the real velocity should be larger and the real angular width should be smaller than the apparent values. Several attempts have been tried to correct the projection effects, which however led to a too large average velocity probably due to the biased choice of the CME events. In order to estimate the overall influence of the projection effects on the kinematic properties of the CMEs, we perform a forward modeling of the real distributions of the CME properties, such as the velocity, the angular width, and the latitude, by requiring their projected distributions to best match the observations. Such a matching is conducted by Monte Carlo simulations. According to the derived real distributions, it is found that (1) the average real velocity of all non-full-halo CMEs is about 514 km s$^{-1}$, and the average real angular width is about 33$^\circ$, in contrast to the corresponding apparent values of 418 km s$^{-1}$ and 42.7$^\circ$ in observations; (2) For the CMEs with the angular width in the range of $20^\circ- 120^\circ$, the average real velocity is 510 km s$^{-1}$ and the average real angular width is 43.4$^\circ$, in contrast to the corresponding apparent values of 392 km s$^{-1}$ and 52$^\circ$ in observations.Comment: 8 pages, 4 figures, to be published in Res. Astron. Astrophys. (RAA

Minimizing Seed Set Selection with Probabilistic Coverage Guarantee in a Social Network

A topic propagating in a social network reaches its tipping point if the number of users discussing it in the network exceeds a critical threshold such that a wide cascade on the topic is likely to occur. In this paper, we consider the task of selecting initial seed users of a topic with minimum size so that with a guaranteed probability the number of users discussing the topic would reach a given threshold. We formulate the task as an optimization problem called seed minimization with probabilistic coverage guarantee (SM-PCG). This problem departs from the previous studies on social influence maximization or seed minimization because it considers influence coverage with probabilistic guarantees instead of guarantees on expected influence coverage. We show that the problem is not submodular, and thus is harder than previously studied problems based on submodular function optimization. We provide an approximation algorithm and show that it approximates the optimal solution with both a multiplicative ratio and an additive error. The multiplicative ratio is tight while the additive error would be small if influence coverage distributions of certain seed sets are well concentrated. For one-way bipartite graphs we analytically prove the concentration condition and obtain an approximation algorithm with an $O(\log n)$ multiplicative ratio and an $O(\sqrt{n})$ additive error, where $n$ is the total number of nodes in the social graph. Moreover, we empirically verify the concentration condition in real-world networks and experimentally demonstrate the effectiveness of our proposed algorithm comparing to commonly adopted benchmark algorithms.Comment: Conference version will appear in KDD 201