Quantification and Comparison of Degree Distributions in Complex Networks

The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to compare the degree distribution of two given networks and extract the amount of similarity between the two distributions. In this paper, we propose a novel method for quantification of the degree distributions in complex networks. Based on this quantification method,a new distance function is also proposed for degree distributions, which captures the differences in the overall structure of the two given distributions. The proposed method is able to effectively compare networks even with different scales, and outperforms the state of the art methods considerably, with respect to the accuracy of the distance function

A perturbation theory for the Anderson model of magnetic impurities in simple metals

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Feature Extraction from Degree Distribution for Comparison and Analysis of Complex Networks

The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree distribution is a necessary step. Moreover, many applications need a similarity function for comparison of complex networks based on their degree distributions. Such a similarity measure has many applications including classification and clustering of network instances, evaluation of network sampling methods, anomaly detection, and study of epidemic dynamics. The existing methods are unable to effectively capture the similarity of degree distributions, particularly when the corresponding networks have different sizes. Based on our observations about the structure of the degree distributions in networks over time, we propose a feature extraction and a similarity function for the degree distributions in complex networks. We propose to calculate the feature values based on the mean and standard deviation of the node degrees in order to decrease the effect of the network size on the extracted features. The proposed method is evaluated using different artificial and real network datasets, and it outperforms the state of the art methods with respect to the accuracy of the distance function and the effectiveness of the extracted features.Comment: arXiv admin note: substantial text overlap with arXiv:1307.362

Transport in the metallic regime of Mn doped III-V Semiconductors

The standard model of Mn doping in GaAs is subjected to a coherent potential approximation (CPA) treatment. Transport coefficients are evaluated within the linear response Kubo formalism. Both normal (NHE) and anomalous contributions (AHE) to the Hall effect are examined. We use a simple model density of states to describe the undoped valence band. The CPA bandstructure evolves into a spin split band caused by the $p-d$ exchange scattering with Mn dopants. This gives rise to a strong magnetoresistance, which decreases sharply with temperature. The temperature ($T$) dependence of the resistance is due to spin disorder scattering (increasing with $T$), CPA bandstructure renormalization and charged impurity scattering (decreasing with $T$). The calculated transport coefficients are discussed in relation to experiment, with a view of assessing the overall trends and deciding whether the model describes the right physics. This does indeed appear to be case, bearing in mind that the hopping limit needs to be treated separately, as it cannot be described within the band CPA.Comment: submitted to Phys. Rev.

A bibliography on formal methods for system specification, design and validation

Literature on the specification, design, verification, testing, and evaluation of avionics systems was surveyed, providing 655 citations. Journal papers, conference papers, and technical reports are included. Manual and computer-based methods were employed. Keywords used in the online search are listed