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It is well known that the azimuth deviations of the auxiliary sources severely degrade the performance of classical subspace-based calibration methods that assume the direction-of-arrivals of calibration sources are perfectly measured. Therefore, aiming at the effects of source location deviations, the estimation variance of the multiplicative modeling errors for the subspace-based calibration method is first derived by applying matrix eigen-perturbation theory and first-order perturbation analysis approach. The theoretical analysis is undertaken under the assumption that the azimuth deviations are small enough for the first-order perturbation analysis to be valid. In addition, to mitigate the effects of the location errors, a structured total least squares optimization model is established using first-order Taylor series expansion method. Then, the corresponding numerical algorithm is presented to provide a robust estimate for multiplicative modeling errors. The exact Cramér-Rao bound expressions for the unknowns are also deduced in the presence of the azimuth deviations. Simulation results confirm the effectiveness of the theoretical analysis and demonstrate the desirable behavior of the robust calibration algorithm in comparison with the subspace-based calibration methods. [ABSTRACT FROM AUTHOR]

Communities are virtually ubiquitous in real-world networks, and the statistic of modularity index Q is the classical measurement for community detection algorithms. However, the relationship between the modularity property and network multilever micro-scale structures is still not clear. In this paper, we study community detection results both in artificial and real-life complex networks by constructing different order null networks, and the results uncover that how micro-structures (such as degree distribution, assortativity and clustering coefficient) affect community properties. Meanwhile, we also propose two novel null networks (increasing or decreasing community structures) to verify the robustness of different community detection algorithms. Our results indicate that the modularity index Q is not a suitable statistic to measure the weak community property which is widely available in empirical networks. Our findings can not only be used to test the robustness of different community detection methods, but also be helpful to uncover the correlation of network structures between microcosmic and mesoscopic scales. [ABSTRACT FROM AUTHOR]