Hierarchical temporal structure in music, speech and animal vocalizations: jazz is like a conversation, humpbacks sing like hermit thrushes

Humans talk, sing and play music. Some species of birds and whales sing long and complex songs. All these behaviours and sounds exhibit hierarchical structure—syllables and notes are positioned within words and musical phrases, words and motives in sentences and musical phrases, and so on. We developed a new method to measure and compare hierarchical temporal structures in speech, song and music. The method identifies temporal events as peaks in the sound amplitude envelope, and quantifies event clustering across a range of timescales using Allan factor (AF) variance. AF variances were analysed and compared for over 200 different recordings from more than 16 different categories of signals, including recordings of speech in different contexts and languages, musical compositions and performances from different genres. Non-human vocalizations from two bird species and two types of marine mammals were also analysed for comparison. The resulting patterns of AF variance across timescales were distinct to each of four natural categories of complex sound: speech, popular music, classical music and complex animal vocalizations. Comparisons within and across categories indicated that nested clustering in longer timescales was more prominent when prosodic variation was greater, and when sounds came from interactions among individuals, including interactions between speakers, musicians, and even killer whales. Nested clustering also was more prominent for music compared with speech, and reflected beat structure for popular music and self-similarity across timescales for classical music. In summary, hierarchical temporal structures reflect the behavioural and social processes underlying complex vocalizations and musical performances.

Time clustering of wave storms in the Mediterranean Sea

In this contribution we identify storm time clustering in the Mediterranean Sea through a comprehensive analysis of the Allan factor. This parameter is evaluated from a long time series of wave height provided by oceanographic buoy measurements and hindcast reanalysis of the whole basin, spanning the period 1979–2014 and characterized by a horizontal resolution of about 0.1° in longitude and latitude and a temporal sampling of 1 h Mentaschi et al. (2015). The nature of the processes highlighted by the AF and the spatial distribution of the parameter are both investigated. Results reveal that the Allan factor follows different curves at two distinct timescales. The range of timescales between 12 h to 50 days is characterized by a departure from the Poisson distribution. For timescales above 50 days, a cyclic Poisson process is identified. The spatial distribution of the Allan factor reveals that the clustering at smaller timescales is present to the north-west of the Mediterranean, while seasonality is observed across the whole basin. This analysis is believed to be important for assessing the local increased flood and coastal erosion risks due to storm clustering.

Time-clustering of wave storms in the Mediterranean Sea

In this contribution we identify storm time-clustering in the Mediterranean Sea through the analysis of the spatial distribution of the Allan Factor. This parameter is evaluated from long time series of wave height provided by means of oceanographic buoy measurements and hindcast re-analysis spanning in the period 1979–2014 and characterized by a horizontal resolution of about 0.1 degree in longitude and latitude and a temporal sampling of one hour (Mentaschi et a., 2015). Results reveal clustering mainly for two distinct ranges of time scales. The first range of time scales (12 hrs to 50 days) is associated to sequences of storms generated by the persistence of the same meteorological system. The second range, associated to timescales beteween 50 and 100 days, reveals seasonal fluctuations. Transitional regimes are present at some locations in the basin. The spatial distribution of the Allan Factor reveals that the clustering at smaller time scales is present in the North-West of the Mediterranean, while clustering at larger scales is observed in the whole basin. This analysis is believed to be important to assess the local increased flood and coastal erosion risks due to storm clustering.

Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model

Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, derived from the time series using the EEMD, to a detailed analysis to draw information content of the time series. Also, we investigate the influence of random noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behaviour. Here, we extend the Fano factor and Allan factor analysis to the time series of state-to-state transition frequencies of a Markov chain. Our results support not only the usefulness of the intrinsic mode functions in understanding the time series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.

Insight into earthquake sequencing: analysis and interpretation of time-series constructed from the directed graph of the Markov chain model

Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time-series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time-series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, the orthogonal basis set derived from the time-series using the EEMD, to a detailed analysis to draw information-content of the time-series. Also, we investigate the influence of random-noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behavior. Here, we extend the Fano factor and Allan factor analysis to the time-series of state-to state transition frequencies of a Markov chain. Our results support not only the usefulness the intrinsic mode functions in understanding the time-series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.

Temporal clustering of the seismicity of the Absheron-Prebalkhan region in the Caspian Sea area

The historical and instrumental catalog of the Absheron-Prebalkhan region in the Caspian Sea area was analyzed in order to reveal the existence of temporal clustering in the time dynamics of the seismicity. The timespan of the catalog is from 1842 to 2012 and the magnitude of the events ranges from 2.5 to 6.8. The Gutenberg-Richter analysis indicates 4.0 as the completeness magnitude of the catalog. The temporal clustering analysis was performed over the sequence of events with magnitude M ≥ 4 by using the methods of the Allan Factor and the coefficient of variation. Both the methods have revealed the presence of time-clusterized structures in the time dynamics of large events in the Absheron-Prebalkhan region. Such findings, which suggest a non-Poissonian behavior of the seismicity of the investigated area, could contribute to a deeper knowledge of the time dynamics of the seismicity and to a better assessment of the relative seismic hazard.

Investigation of the temporal fluctuations of the 1960–2010 seismicity of Caucasus

The time-clustering behaviour of the seismicity of the Caucasus spanning from 1960 to 2010 was investigated. The analysis was performed on the whole and aftershock-depleted catalogues by means of the method of Allan Factor, which permits the identification and quantification of time-clustering in point processes. The whole sequence is featured by two scaling regimes with the scaling exponent at intermediate timescales lower than that at high timescales, and a crossover that could be probably linked with aftershock time activiation. The aftershock-depleted sequence is characterized by higher time-clustering degree and the presence of a periodicity probably correlated with the cyclic earth surface load variations on regional and local scales, e.g. with snow melting in Caucasian mountains and large Enguri dam operations. The obtained results were corroborated by the application of two surrogate methods: the random shuffling and the generation of Poissonian sequences.