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A recently proposed unified scaling law for interoccurrence times of earthquakes is analyzed, both theoretically and with data from Southern California. We decompose the corresponding probability density into local-instantaneous distributions, which scale with the rate of earthquake occurrence. The fluctuations of the rate, characterizing the(More)
Popular music is a key cultural expression that has captured listeners' attention for ages. Many of the structural regularities underlying musical discourse are yet to be discovered and, accordingly, their historical evolution remains formally unknown. Here we unveil a number of patterns and metrics characterizing the generic usage of primary musical facets(More)
Spatiotemporal properties of seismicity are investigated for a worldwide (WW) catalog and for southern California in the stationary case (SC), showing a nearly universal scaling behavior. Distributions of distances between consecutive earthquakes (jumps) are magnitude independent and show two power-law regimes, separated by jump values about 200 (WW) and 15(More)
1 Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages [1, 2, 3] and competition amongst them [3, 4]. In terms of language usage, one of the most influential results is Zipf's law of word frequencies [5]. Zipf's law appears to be universal, and may not even be unique to human language [6].(More)
Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that we explore a method for fitting power laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it(More)
Zipf's law is a fundamental paradigm in the statistics of written and spoken natural language as well as in other communication systems. We raise the question of the elementary units for which Zipf's law should hold in the most natural way, studying its validity for plain word forms and for the corresponding lemma forms. We analyze several long literary(More)
Context. Recent results have revised upwards the total X-ray background (XRB) intensity below ∼10 keV, therefore an accurate determination of the source counts is needed. There are also contradicting results on the clustering of X-ray selected sources. Aims. We have studied the X-ray source counts in four energy bands soft (0.5-2 keV), hard (2-10 keV), XID(More)
The detection of very similar patterns in a time series, commonly called motifs, has received continuous and increasing attention from diverse scientific communities. In particular, recent approaches for discovering similar motifs of different lengths have been proposed. In this work, we show that such variable-length similarity-based motifs cannot be(More)
Many sound-related applications use Mel-Frequency Cepstral Coefficients (MFCC) to describe audio timbral content. Most of the research efforts dealing with MFCCs have been focused on the study of different classification and clustering algorithms, the use of complementary audio descriptors, or the effect of different distance measures. The goal of this(More)