Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page

A unified approach to sparse signal processing

A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i

An evaluation of the broadband direction finding capabilities of array signal processing techniques

The objective of this study was to determine and compare the direction finding capabilities of high resolution spectral analysis techniques applied to the signals from an antenna array. The maintenance of acceptable resolution over a broad operating frequency range was of particular concern. The comparison was accomplished by computer simulation of the performance of a linear array of eleven isotropic elements, spaced 15 cm apart, over the frequency range from 100 MHz to 1.0 GHz;The two-signal resolution of three linear prediction based algorithms was compared. The variation in performance with signal-to-noise ratio, frequency, and center angle of arrival was also evaluated;An algorithm due to Tufts and Kumaresan which reduces the effects of noise by replacing the noisy signal correlation matrix by a smoothed, least-squares fit to it gave the best performance at the cost of the highest computational complexity. A special case of this method which is easy to compute exhibited blind angles, where performance was severely degraded in spite of wide spacing of the sources;The ratio of the physical length of the array to the length of the modulation envelope set up by the interference of the two incoming signals was found to be a constant at the point of resolution. This led to an expression for the two-signal resolution as a function of look angle, array length, frequency, and this algorithm dependent constant

A pre-filtering maximum likelihood approach to multiple source direction estimation.

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