On the efficiency of estimating penetrating rank on large graphs

P-Rank (Penetrating Rank) has been suggested as a useful measure of structural similarity that takes account of both incoming and outgoing edges in ubiquitous networks. Existing work often utilizes memoization to compute P-Rank similarity in an iterative fashion, which requires cubic time in the worst case. Besides, previous methods mainly focus on the deterministic computation of P-Rank, but lack the probabilistic framework that scales well for large graphs. In this paper, we propose two efficient algorithms for computing P-Rank on large graphs. The first observation is that a large body of objects in a real graph usually share similar neighborhood structures. By merging such objects with an explicit low-rank factorization, we devise a deterministic algorithm to compute P-Rank in quadratic time. The second observation is that by converting the iterative form of P-Rank into a matrix power series form, we can leverage the random sampling approach to probabilistically compute P-Rank in linear time with provable accuracy guarantees. The empirical results on both real and synthetic datasets show that our approaches achieve high time efficiency with controlled error and outperform the baseline algorithms by at least one order of magnitude

Towards efficient SimRank computation on large networks

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

Dibaryons with two heavy quarks

The relativistic six-quark equations are constructed in the framework of the dispersion relation technique. The relativistic six-quark amplitudes of dibaryons including the light $u$, $d$ and heavy $c$, $b$ quarks are calculated. The approximate solutions of these equations using the method based on the extraction of leading singularities of the heavy hexaquark amplitudes are obtained. The poles of these amplitudes determine the masses of charmed and bottom dibaryons with the isospins I=0, 1, 2 and the spin-parities $J^P=0^+$, $1^+$, $2^+$.Comment: 10 pages, types corrected. arXiv admin note: substantial text overlap with arXiv:1105.081

Comparing two haptic interfaces for multimodal graph rendering

This paper describes the evaluation of two multimodal interfaces designed to provide visually impaired people with access to various types of graphs. The interfaces consist of audio and haptics which is rendered on commercially available force feedback devices. This study compares the usability of two force feedback devices: the SensAble PHANToM and the Logitech WingMan force feedback mouse in representing graphical data. The type of graph used in the experiment is the bar chart under two experimental conditions: single mode and multimodal. The results show that PHANToM provides better performance in the haptic only condition. However, no significant difference has been found between the two devices in the multimodal condition. This has confirmed the advantages of using multimodal approach in our research and that low-cost haptic devices can be successful. This paper introduces our evaluation approach and discusses the findings of the experiment

Using XMM-Newton to study the energy dependent variability of H 1743-322 during its 2014 outburst

Black hole transients during bright outbursts show distinct changes of their spectral and variability properties as they evolve during an outburst, that are interpreted as evidence for changes in the accretion flow and X-ray emitting regions. We obtained an anticipated XMM-Newton ToO observation of H 1743-322 during its outburst in September 2014. Based on data of eight outbursts observed in the last 10 years we expected to catch the start of the hard-to-soft state transition. The fact that neither the general shape of the observed power density spectrum nor the characteristic frequency show an energy dependence implies that the source still stays in the low-hard state at the time of our observation near outburst peak. The spectral properties agree with the source being in the low-hard state and a Swift/XRT monitoring of the outburst reveals that H 1743-322 stays in the low-hard state during the entire outburst (a. k. a. 'failed outburst'). We derive the averaged QPO waveform and obtain phase-resolved spectra. Comparing the phase-resolved spectra to the phase averaged energy spectrum reveals spectral pivoting. We compare variability on long and short time scales using covariance spectra and find that the covariance ratio does not show an increase towards lower energies as has been found in other black hole X-ray binaries. There are two possible explanations: either the absence of additional disc variability on longer time scales is related to the rather high inclination of H 1743-322 compared to other black hole X-ray binaries or it is the reason why we observe H 1743-322 during a failed outburst. More data on failed outbursts and on high-inclination sources will be needed to investigate these two possibilities further.Comment: 9 pages, 7 figures, accepted by MNRA

Gauging Correct Relative Rankings For Similarity Search

© 2015 ACM.One of the important tasks in link analysis is to quantify the similarity between two objects based on hyperlink structure. SimRank is an attractive similarity measure of this type. Existing work mainly focuses on absolute SimRank scores, and often harnesses an iterative paradigm to compute them. While these iterative scores converge to exact ones with the increasing number of iterations, it is still notoriously difficult to determine how well the relative orders of these iterative scores can be preserved for a given iteration. In this paper, we propose efficient ranking criteria that can secure correct relative orders of node-pairs with respect to SimRank scores when they are computed in an iterative fashion. Moreover, we show the superiority of our criteria in harvesting top-K SimRank scores and bucket orders from a full ranking list. Finally, viable empirical studies verify the usefulness of our techniques for SimRank top-K ranking and bucket ordering