How can we track synchronized behavior in a stream of time-stamped tuples, such as mobile devices installing and uninstalling applications in the lockstep, to boost their ranks in the app store? We model such tuples as entries in a streaming tensor,
which augments attribute sizes in its modes over time. Synchronized behavior tends to form dense blocks (i.e. subtensors) in such a tensor, signaling anomalous behavior, or interesting communities. However, existing dense block detection methods are either based on a static tensor, or lack an efficient algorithm in a streaming setting. Therefore, we propose a fast streaming algorithm, AugSplicing, which can detect the top dense blocks by incrementally splicing the previous detection with the incoming ones in new tuples, avoiding re-runs over all the history data at every tracking time step. AugSplicing is based on a splicing condition that guides the algorithm (Section 4). Compared to the state-of-the-art methods, our method is (1) effective to detect fraudulent behavior in installing data of real-world apps and find a synchronized group of students with interesting features in campus Wi-Fi data; (2) robust with splicing theory for dense block detection; (3) streaming and faster than the existing streaming algorithm, with closely comparable accuracy.
In this work, we study the lepton-number-violating processes of $K^pm$ and $D^pm$ mesons. Two quasi-degenerate sterile neutrinos are assumed to induce such processes. Different with the case where only one sterile neutrino involves, here, the CP phas
es of the mixing parameters could give sizable contribution. This, in turn, would affect the absolute values of the mixing parameters determined by the experimental upper limits of the branching fractions. A general function which express the difference of the mixing parameters for two-generation and one-generation is presented. Special cases with specific relations of the parameters are discussed. Besides, we also thoroughly investigate the CP violation effect of such processes. It is shown that generally $mathcal A_{CP}$ is a function of the sterile neutrino mass.
