163,155 research outputs found
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
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
Radiative corrections to the neutron star mass inferred from QPO frequencies
The frequencies of kHz QPOs are widely interpreted as being indicative of the
values of characteristic frequencies related to orbital motion around neutron
stars, e.g., the radial epicyclic frequency. In regions directly exposed to the
radiation from the luminous neutron star these frequencies change with the
luminosity. Including radiative corrections will change the neutron star mass
value inferred from the QPO frequencies. Radiative forces may also be behind
the puzzling phenomenon of parallel tracks.Comment: 6 pages including 1 figur
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 , and heavy , 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 ,
, .Comment: 10 pages, types corrected. arXiv admin note: substantial text overlap
with arXiv:1105.081
Heavy dibaryons
The relativistic six-quark equations are found in the framework of the
dispersion relation technique. The approximate solutions of these equations
using the method based on the extraction of leading singularities of the heavy
hexaquark amplitudes are obtained. The relativistic six-quark amplitudes of
dibaryons including the light quarks , and heavy quarks , are
calculated. The poles of these amplitudes determine the masses of charmed and
bottom dibaryons with the isospins 1/2, 3/2, 5/2.Comment: 16 page
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
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