157,031 research outputs found

    Towards efficient SimRank computation on large networks

    Get PDF
    SimRank has been a powerful model for assessing the similarity of pairs of vertices in a graph. It is based on the concept that two vertices are similar if they are referenced by similar vertices. Due to its self-referentiality, fast SimRank computation on large graphs poses significant challenges. The state-of-the-art work [17] exploits partial sums memorization for computing SimRank in O(Kmn) time on a graph with n vertices and m edges, where K is the number of iterations. Partial sums memorizing can reduce repeated calculations by caching part of similarity summations for later reuse. However, we observe that computations among different partial sums may have duplicate redundancy. Besides, for a desired accuracy ϵ, the existing SimRank model requires K = [logC ϵ] iterations [17], where C is a damping factor. Nevertheless, such a geometric rate of convergence is slow in practice if a high accuracy is desirable. In this paper, we address these gaps. (1) We propose an adaptive clustering strategy to eliminate partial sums redundancy (i.e., duplicate computations occurring in partial sums), and devise an efficient algorithm for speeding up the computation of SimRank to 0(Kdn2) time, where d is typically much smaller than the average in-degree of a graph. (2) We also present a new notion of SimRank that is based on a differential equation and can be represented as an exponential sum of transition matrices, as opposed to the geometric sum of the conventional counterpart. This leads to a further speedup in the convergence rate of SimRank iterations. (3) Using real and synthetic data, we empirically verify that our approach of partial sums sharing outperforms the best known algorithm by up to one order of magnitude, and that our revised notion of SimRank further achieves a 5X speedup on large graphs while also fairly preserving the relative order of original SimRank scores

    Fe/Ni ratio in the Ant Nebula Mz 3

    Full text link
    We have analyzed the [Fe II] and [Ni II] emission lines in the bipolar planetary nebula Mz~3. We find that the [Fe II] and [Ni II] lines arise exclusively from the central regions. Fluorescence excitation in the formation process of these lines is negligible for this low-excitation nebula. From the [Fe II]/[Ni II] ratio, we obtain a higher Fe/Ni abundance ratio with respect to the solar value. The current result provides further supporting evidence for Mz 3 as a symbiotic Mira.Comment: 2 pages, 1 figure, to be published in the Proceedings of the IAU Symposium 234: Planetary Nebulae in Our Galaxy and Beyond, eds. M.J. Barlow, R.H. Mende

    The structure and magnetism of graphone

    Full text link
    Graphone is a half-hydrogenated graphene. The structure of graphone is illustrated as trigonal adsorption of hydrogen atoms on graphene at first. However, we found the trigonal adsorption is unstable. We present an illustration in detail to explain how a trigonal adsorption geometry evolves into a rectangular adsorption geometry. We check the change of magnetism during the evolution of geometry by evaluating the spin polarization of the intermediate geometries. We prove and clarify that the rectangular adsorption of hydrogen atoms on graphene is the most stable geometry of graphone and graphone is actually antiferromagnetic.Comment: 11 pages, 4 figure

    Data Unfolding with Wiener-SVD Method

    Full text link
    Data unfolding is a common analysis technique used in HEP data analysis. Inspired by the deconvolution technique in the digital signal processing, a new unfolding technique based on the SVD technique and the well-known Wiener filter is introduced. The Wiener-SVD unfolding approach achieves the unfolding by maximizing the signal to noise ratios in the effective frequency domain given expectations of signal and noise and is free from regularization parameter. Through a couple examples, the pros and cons of the Wiener-SVD approach as well as the nature of the unfolded results are discussed.Comment: 26 pages, 12 figures, match the accepted version by JINS