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The time dynamics of the instrumental seismicity recorded in the area of the Lai Chau reservoir (Vietnam) between 2015 and 2021 were analyzed in this study. The Gutenberg–Richter analysis of the frequency–magnitude distribution has revealed that the seismic catalog is complete for events with magnitudes larger or equal to 0.6. The fractal method of the Allan Factor applied to the series of the occurrence times suggests that the seismic series is characterized by time-clustering behavior with rather large degrees of clustering, as indicated by the value of the fractal exponent α ≈ 0.55 . The time-clustering of the time distribution of the earthquakes is also confirmed by a global coefficient of variation value of 1.9 for the interevent times. The application of the correlogram-based periodogram, which is a robust method used to estimate the power spectrum of short series, has revealed three main cycles with a significance level of p < 0.01 (of 10 months, 1 year, and 2 years) in the monthly variation of the mean water level of the reservoir, and two main periodicities with a significance level of p < 0.01 (at 6 months and 2 years) in the monthly number of earthquakes. By decomposing the monthly earthquake counts into intrinsic mode functions (IMFs) using the empirical decomposition method (EMD), we identified two IMFs characterized by cycles of 10 months and 2 years, significant at the 1% level, and one cycle of 1 year, significant at the 5% level. The cycles identified in these two IMFs are consistent with those detected in the water level, showing that, in a rigorously statistical manner, the seismic process occurring in the Lai Chau area might be triggered by the loading–unloading operational cycles of the reservoir. [ABSTRACT FROM AUTHOR]

This study focuses on complexity matching and lexical matching to investigate speech convergence in the conversations of bilingual Persian-English speakers in three language conditions namely Persian, English, and mixed in the context of lingua receptiva as an attempt to investigate such matching mechanisms between a Latin-based language and a non-Latin-based language. Complexity matching investigates convergence in terms of the hierarchical temporal structure of human speech while lexical matching explores convergence in terms of the frequency occurrence of the matched lemmas. For this purpose, 14 master’s students from the Shahid Chamran University of Ahvaz majoring in English language conversed with one another in dyadic groups in three language conditions each of which had its own topic namely movies, music, and books. In complexity matching, Allan Factor analysis in terms of multiscale clustering of onset events was considered. In lexical matching, the focus was on the distribution of all lemmas and matched lemmas and the possible correlation between the two. The results revealed a gradual increase in Allan Factor log-log plots in relation to the longer timescales that correspond with discourse patterns for complexity matching. For lexical matching, the positive correlation between all lemmas and matched lemmas (rs = .607) suggested that as participants talked to each other more, they unconsciously tried to match their psychological perceptions with each other more. This suggests that speech convergence is vigorous in both bilingual and monolingual interactions.

The main purpose of this paper was to, for the first time, analyse the spatiotemporal features of the background seismicity of Northern Algeria and its vicinity, as identified by different declustering methods (specifically: the Gardner and Knopoff, Gruenthal, Uhrhammer, Reasenberg, Nearest Neighbour, and Stochastic Declustering methods). Each declustering method identifies a different declustered catalogue, namely a different subset of the earthquake catalogue that represents the background seismicity, which is usually expected to be a realisation of a homogeneous Poisson process over time, though not necessarily in space. In this study, a statistical analysis was performed to assess whether the background seismicity identified by each declustering method has the spatiotemporal properties typical of such a Poisson process. The main statistical tools of the analysis were the coefficient of variation, the Allan factor, the Markov-modulated Poisson process (also named switched Poisson process with multiple states), the Morisita index, and the L–function. The results obtained for Northern Algeria showed that, in all cases, temporal correlation and spatial clustering were reduced, but not totally eliminated in the declustered catalogues, especially at long time scales. We found that the Stochastic Declustering and Gruenthal methods were the most successful methods in reducing time correlation. For each declustered catalogue, the switched Poisson process with multiple states outperformed the uniform Poisson model, and it was selected as the best model to describe the background seismicity in time. Moreover, for all declustered catalogues, the spatially inhomogeneous Poisson process did not fit properly the spatial distribution of earthquake epicentres. Hence, the assumption of stationary and homogeneous Poisson process, widely used in seismic hazard assessment, was not met by the investigated catalogue, independently from the adopted declustering method. Accounting for the spatiotemporal features of the background seismicity identified in this study is, therefore, a key element towards effective seismic hazard assessment and earthquake forecasting in Algeria and the surrounding area. [ABSTRACT FROM AUTHOR]

In this study, the 10-min average wind speed series recorded at 132 stations distributed rather homogeneously over the territory of Switzerland were investigated, focusing on the challenging problem of the analysis and modelling of wind extreme events. Wind extremes are defined as a sequence of consecutive values above a percentile-based threshold of wind speed distribution. Considering temporal point process of wind extremes marked by their duration, the main findings of this study are that: 1) the average probability density function of the extreme duration does not depend on the percentile-based threshold and decreases with the increase of the extreme duration; 2) wind extremes are globally time-clustered, although they tend to behave as a Poisson process with the increase of the minimum extreme duration; 3) locally, wind extremes tend to be clustered for any percentile-based threshold for stations located above about 2000 m a.s.l.; 4) by using the Allan factor, it was revealed that wind extremes tend to be clustered even at lower timescales, especially for the higher stations. • Wind speed series recorded at 132 stations in Switzerland are investigated. • Wind extremes, defined on the base of run theory, represent a marked point process. • The average distribution of duration of wind extremes does not depend on the threshold. • Wind extremes are globally clustered, but locally are clustered for stations 2000 m a.s.l. • The Allan Factor reveals wind extremes clusters at lower timescales for higher stations. [ABSTRACT FROM AUTHOR]

In earthquake seismology, an independent earthquake can produce a set of clusters having fore- and/or aftershocks. The main purpose of seismicity declustering is to refine a given earthquake catalog in order to retain independent events. The goal of retention of independent events by only declustering is a crucial benchmark for most of the mainshock-based analysis in seismology. In the present article, we used a re-updated unified earthquake catalog of Turkey and obtained several declustered catalogs applying different declustering methods. To compare the performance of applied declustering methods, each declustered catalog was then examined by simulation envelopes and Monte Carlo tests using some summary statistics for temporal and spatial point patterns. We found that the declustering method of Zhuang et al. (2002) based on the Epidemic Type Aftershock Sequence (ETAS) model, original version, and particularly Grünthal's variant of the Gardner and Knopoff (1974) method seemed to be most successful in finding and removing clusters in space and time for the earthquake catalog of Turkey examined. [ABSTRACT FROM AUTHOR]

Highlights • The coefficient of variations and the Allan Factor revealed time-clustering. • The interevent times are persistent. • The magnitudes are weakly persistent or random. • The daily counts of the aftershock-depleted seismicity reveal quasi-monthly and bi-weekly periodicities. • Quasi-annual and quasi-semestral periodicities strengthen the link with Earth's tides. Abstract We studied the whole and aftershock-depleted shallow (depth ≤ 30 km) Taiwanese seismicity from 1990 to 2017 by using several independent methods. The coefficient of variations and the Allan Factor have revealed that time-clustering characterizes not only the time distribution of the whole seismic catalogue, but also that of the aftershock-depleted one, although this displays time-clustering at larger timescales. In particular the Allan Factor shows that at small timescales the seismic process of the whole as well as the aftershock-depleted one can be well described by a Poisson process. The detrended fluctuation analysis clearly evidence persistence in the interevent times and weak persistence or randomness in the magnitudes. The singular spectrum analysis of the daily counts in the aftershock-depleted catalogue reveals the existence of quasi-monthly and bi-weekly periodicities. Furthermore, quasi-annual and quasi-semestral periodicities have been identified that strengthen the link between seismic activity in Taiwan and Earth's tides. [ABSTRACT FROM AUTHOR]

Abstract This manuscript analyzes the temporal properties of sequences of car accidents in Lebanon from 2015 to 2018, using data from the Lebanese Road Accident Platform (LRAP). The Allan Factor that is a well suited methodology for investigating the time-clustering in point processes, revealed that the car accidents occurred over the whole Lebanese territory are characterized by a significant scaling behavior for timescales larger than about 2 weeks, with a clear cyclic component at 1 day. The analysis performed on car accident sequences in some specific areas of Lebanon revealed the presence of cycles varying from 1 day to 2 weeks as a function of the distance from Beirut, the capital city of Lebanon. Highlights • Temporal properties of car accidents in selected Lebanese cities were analyzed. • One-day cycles characterize the whole Lebanese dataset. • Significant scaling behavior characterize the whole Lebanese and Greater Beirut dataset. • Cycles of increasing period feature cities with increasing distance from Beirut. [ABSTRACT FROM AUTHOR]

In this paper, we propose to compare different declustering methods on the basis of the time-correlation and the space-clustering of the residual earthquake catalog after the declustering techniques have been applied. To this aim, we applied two point process clustering measures, the Allan Factor and the Morisita Index, for the identification and quantification of temporal correlation and spatial clustering in point processes, respectively. We used our joint space-time approach to study the earthquake space-time point processes of southern California and Switzerland with surrounding area, declustered by using the method of Gardner and Knopoff (with Grünthal and Uhmhammer window) and that of Reasenberg (with different setting parameters). Our results show that the residual declustered catalog is still characterized by time-correlated structures at long timescales; however, the cutoff timescale that is the lowest timescale above which the time-correlation is visible is higher with the Reasenberg method while is smaller with the Gardner and Knopoff method with Grünthal window. The space-clustering analysis performed by means of the Morisita Index suggests that the declustering technique effectively reduces the spatial clustering of the seismicity of Switzerland, but does not change the spatial properties of the residual seismic catalogue of the southern California. [ABSTRACT FROM AUTHOR]

The pairing of dynamical systems theory and complexity science brings novel concepts and methods to the study of infant motor development. Accordingly, this longitudinal case study presents a new approach to characterizing the dynamics of infant limb and vocalization behaviors. A single infant's vocalizations and limb movements were recorded from 51-days to 305-days of age. On each recording day, accelerometers were placed on all four of the infant's limbs and an audio recorder was worn on the child's chest. Using nonlinear time series analysis methods, such as recurrence quantification analysis and Allan factor, we quantified changes in the stability and multiscale properties of the infant's behaviors across age as well as how these dynamics relate across modalities and effectors. We observed that particular changes in these dynamics preceded or coincided with the onset of various developmental milestones. For example, the largest changes in vocalization dynamics preceded the onset of canonical babbling. The results show that nonlinear analyses can help to understand the functional co-development of different aspects of infant behavior. [ABSTRACT FROM AUTHOR]

Abstract: It has been found that many systems are characterized by scaling behavior. Time-scaling scale-invariant approaches are used to analyze the temporal distribution of urban fire sequences recorded in the city of Wuhan (China) in present paper. The results of the coefficient of variation show that there is a clustering distribution in the occurrence sequence of urban fire in Wuhan. And with the study of Fano factor and Allan factor for the urban fire sequences in Wuhan, it is found that the urban fire sequences have obviously time-scaling behaviors. These reveal that the point process of urban fires is a fractal process with a high degree of time-clusterization of the events. The results will be helpful to estimate urban fire risk. [Copyright &y& Elsevier]

Several statistical tests are available for testing the Poisson hypothesis and/or the equidispersion of a point process. The capability to discriminate between the Poissonian behaviour and more complex processes is fundamental in many areas of research including earthquake analysis, hydrology, ecology, biology, signal analysis and sociology. This study investigates the relationship between two indices often used for detecting departures from equidispersion, namely, the index of dispersion (ID) and the Allan factor (AF). Since an approximation of the sampling distribution of AF for Poisson data has been recently proposed in the literature, we perform a detailed analysis of its properties and its relationship with the asymptotic sampling distribution of ID. Moreover, the statistical power of the AF for testing the Poisson hypothesis is assessed by using an extensive Monte Carlo simulation, and the performances of AF and ID are compared. We propose a simplified version of the AF sampling distribution that does not depend on the rate of occurrence keeping the maximum errors of extreme percentiles always smaller than 2-3 %. The power study highlights that ID systematically outperforms AF for discriminating between equidispersed and under/over dispersed data. Both indices show the same lack of power for distinguishing between data drawn from equidispersed non-Poissonian distribution functions. Therefore, even though AF is a useful statistical tool for detecting the possible fractal behaviour of point processes, ID should be preferred when the analysis aims at assessing equidispersion. The lack of power for a small sample size confirms the difficulty of identifying the true nature of the occurrence process of rare events. [ABSTRACT FROM AUTHOR]

Abstract: The Allan factor (AF) is a statistic widely used to assess if the rate of occurrences of an event tends to cluster and show persistence in a range of space and/or time scales. For a homogeneous Poisson process, the relationship between AF and the space/time is expected to be constant, thus denoting the lack of clustering and persistence in the occurrence process. However, in time series analysis, conclusions about the persistence of the underlying process have been usually drawn by visual inspection of the diagrams of AF estimates versus scale, without applying any formal statistical test. This study investigates the sampling distribution function of the AF estimator when the underlying process is homogeneous Poissonian. Monte Carlo simulations show that the distribution of the AF estimator is described by a gamma distribution whose mean and variance can be deduced by the delta method. Therefore, the derived analytical distribution of the AF estimator can be used to build a formal statistical test to evaluate the significance of the AF fluctuation against the Poissonian hypothesis across a range of space/time scales. As an example, we apply the AF-based test to analyse the time series of the number of rainfall observations exceeding fixed high thresholds in order to study the properties of the rate of occurrence of the extreme values over a wide range of time scales. [Copyright &y& Elsevier]

The temporal fluctuations of the 1880–1994 seismicity recorded in Pannonian Basin were investigated by means of the Fano Factor and Allan Factor methods, which allows us to estimate the power spectrum for point processes. Up to our knowledge, this is the first scaling analysis performed on earthquake series spanning for almost one century. Our findings point out a presence of two temporal regimes in the analyzed seismicity, which is characterized by quasi-Poissonian behavior for low to intermediate timescales for up to about 1/2 years, and by scaling behavior for higher timescales with scaling exponent around 0.3–0.4, indicating a rather high time-clustering of the events. Furthermore the Allan Factor shows the presence of a periodicity at about 2.23 years for events with magnitude larger or equal to 3.5. [ABSTRACT FROM AUTHOR]

Temporal dynamical analysis in fire sequences recorded from 1992 to 2005 in a fire-vulnerable area of Patagonia (Argentina) was performed by using the Allan Factor statistics. Three typologies of fires were investigated: forest, steppe and urban. The obtained results show the presence of annual periodicities, superimposed to a time-scaling behaviour, which characterize the point processes of fires as fractal time processes with a rather high degree of time-clusterization of the events. [Copyright &y& Elsevier]

It has been found that many natural systems are characterized by scaling behavior. In such systems natural factors dominate the event dynamics. But in countries with high population density such as China and Japan, more than 95% of the forest fire disasters are caused by human activities. Furthermore, with the development of society, the wildland–urban interface (WUI) area is becoming more and more populated, and the forest fire is much connected with urban fire. Therefore exploring the scaling behavior of fires dominated by human-related factors is very challenging. The present paper explores the temporal scaling behavior of forest fires and urban fires in Japan. Our findings point out that although the human factors are the main cause, both the forest fires and urban fires exhibit time-scaling behavior. Similar distribution law characterizes the relative humidity. [Copyright &y& Elsevier]

The investigation of the temporal fluctuations in forest fires is an important topic in the context of environmental sciences. Time-scaling scale-invariant methodologies have been used to characterize the temporal properties of forest-fire sequences detected in the Italian territory. Our findings reveal that the fire sequences can be considered as fractal processes with a high degree of time-clusterization of the events. The time-clustering phenomenon is clearly visible from timescales of order of days. Furthermore the fire sequences observed with decreasing latitude tend to be more time-clusterized. [Copyright &y& Elsevier]

Abstract: In this paper we study the time-clustering behavior of sequences of car accidents, using data from a freely available database in the internet. The Allan Factor analysis, which is a well-suited method to investigate time-dynamical behaviors in point processes, has revealed that the car accident sequences are characterized by a general time-scaling behavior, with the presence of cyclic components. These results indicate that the time dynamics of the events are not Poissonian but long range correlated with periodicities ranging from 12 h to 1 year. [Copyright &y& Elsevier]

Abstract: Time-clustering behavior in the sequence of solar flare hard X-ray bursts from April 1991 to May 2000 obtained from BATSE/GRO (Burst and Transient Source Experiment aboard the Compton Gamma Ray Observatory satellite) was investigated by using the Allan Factor statistics. The presence of different timescale regimes ranging from Poissonian to rather strong long-range correlated behaviors has been revealed. [Copyright &y& Elsevier]

Abstract: A sequence of aircraft accidents has been analyzed using an Internet freely available database. By means of the Allan Factor (AF) statistics, time-clustering phenomenon was detected in the sequence, and this indicates that at certain timescales the time dynamics of the events is not Poissonian but long-range correlated. [Copyright &y& Elsevier]

Abstract: Arrival sequences for several marathon races, including New York City and Chicago ones, have been analyzed using an internet freely available database. By means of the Allan factor statistics, time-clustering phenomena has been detected in the sequence and this indicates that at certain time scales the dynamics of the arriving events is not Poissonian but long-range correlated. [Copyright &y& Elsevier]

Abstract: Is there any kind of “memory” in the sequence of terror attacks worldwide? Are the terrorist attacks non-randomly time distributed? Our analysis suggests that they are correlated, which means that a terror event is not independent from the time elapsed since the previous event. But, if we consider terror attacks with a large severity index (number of fatalities or injured), the phenomenon is unpredictable, since it approaches a Poisson process (random, independent and uncorrelated). [Copyright &y& Elsevier]

Lightning data, measured from April to October 2002 in an area of northern Italy, have been analyzed by using the Allan Factor statistics. The sequence of lightning time-occurrences is characterized by two scaling regions, which reveal intra-cluster (inside an individual thunderstorm) and inter-cluster (among successive thunderstorms) time-clustering properties of lightning data. We investigated intra- and inter-cluster correlations for three classes of lightning: (i) the whole series, (ii) the sequence of only negative flashes and (iii) that of only positive flashes. Furthermore, we performed the analysis of the scaling behavior of the three classes of lightning varying the current intensity threshold. [ABSTRACT FROM AUTHOR]

Abstract: Temporal regimes in fire data recorded from 1997 to 2003 in an area of central Italy have been detected by using the Allan Factor statistics. Our findings reveal the presence of meteo-climatic-related periodicities; furthermore time-scaling behaviour characterizes the point process of the fire sequence as a fractal process with a high degree of time-clusterization of the events. [Copyright &y& Elsevier]

Abstract: The time-clustering behavior of lightning data measured from April to October 2002 in an area of southern Italy has been analyzed by using the Allan factor statistics. The results point out to the presence of two time-scaling regions, which reveal intra-cluster (inside an individual thunderstorm) and inter-cluster (among successive thunderstorms) time-correlation properties of lightning data. [Copyright &y& Elsevier]

The time-clustering behavior of the neutron star SGR1806-20 burst sequence (detected by the International Cometary Explorer, ICE) has been analyzed. The presence of two different timescaling regions, related to the "foreshock" and "aftershock" phases, separated by the largest event occurred on November 16, 1983, 8:34 GMT, E = 5.17 · 1041erg, has been evidenced. The results highlight that starquake foreshocks involve medium timescales from about 30 minutes to approximately 5 days, while starquake aftershocks involve longer timescales ranging up 4 months. [ABSTRACT FROM AUTHOR]

Abstract: Investigating the time dynamics of forest-fires is a challenge in the environmental sciences. Time-scaling scale-invariant approaches have been used to characterize the temporal distribution of forest-fire sequence detected in Gargano area (southern Italy), which is characterized by high level of wildfire density. Our findings reveal that the point process of the fire sequence can be considered as a fractal process with a high degree of time-clusterization of the events. The time-clustering phenomenon is visible from timescales of order of few days. Furthermore, the fire process tends to be less time-clusterized with the increase of the burned area. [Copyright &y& Elsevier]

Abstract: We performed the Allan factor analysis on the 1986–2001 seismicity of the 80 seismogenetic zones in which the Italian territory has been subdivided by the Gruppo Nazionale Difesa dai Terremoti (GNDT), in order to investigate the presence of time-correlated behaviour. Power-law time-correlated areas have been identified analyzing the aftershock-depleted seismicity. Strong variability in the scaling properties has been found, suggesting that different dynamical mechanisms govern the seismic activity of the Italian seismogenetic zones. [Copyright &y& Elsevier]

Point processes, like other geophysical phenomena, such as earthquakes or avalanches, are well suited to model rain event sequences. Time-clustering analysis has been performed over rainfall sequences by using the statistical approaches of Fano Factor and Allan Factor. The obtained results suggest the presence of clustering in the time distribution of the sequence of rain events, with scaling exponent α ranging between ~0.35 and ~0.42. [ABSTRACT FROM AUTHOR]

Rain events can be described in terms of point processes, analogously to other geophysical phenomena, such as earthquakes or avalanches. Power-law behaviors have been identified in the distribution of sizes, of rain event durations and drought durations, with scaling exponents 1.4, 2.4 and 1.3, respectively. Time-fractal approaches, like Fano Factor and Allan Factor, well suited to reveal scaling behavior in point processes, allow to detect power-law behavior in rainfall data, pointing out to the presence of clustering in the time distribution of the sequence of rain events. [Copyright &y& Elsevier]

Muscle sympathetic nerve activity (MSNA) in resting humans is characterized by cardiacrelated bursts of variable amplitude that occur sporadically or in clusters. The present study was designed to characterize the fluctuations in the number of MSNA bursts, interburst interval, and burst amplitude recorded from the peroneal nerve of 15 awake, healthy human subjects. For this purpose, we used the Allan and Fano factor analysis and dispersional analysis to test whether the fluctuations were time-scale invariant (i.e., fractal) or random in occurrence. Specifically, we measured the slopes of the power laws in the Allan factor, Fano factor, and dispersional analysis curves. In addition, the Hurst exponent was calculated from the slope of the power law in the Allan factor curve. Whether the original time series contained fractal fluctuations was decided on the basis of a comparison of the values of these parameters with those for surrogate data blocks. The results can be summarized as follows. Fluctuations in the number of MSNA bursts and interburst interval were fractal in each of the subjects, and fluctuations in burst amplitude were fractal in four of the subjects. We also found that fluctuations in the number of heartbeats and heart period (R-R interval) were fractal in each of the subjects. These results demonstrate for the first time that apparently random fluctuations in human MSNA are, in fact, dictated by a time-scale-invariant process that imparts "long-term memory" to the sequence of cardiac-related bursts. Whether sympathetic outflow to the heart also is fractal and contributes to the fractal component of heart rate variability remains an open question. [ABSTRACT FROM AUTHOR]

An earthquake catalog derived from the detection of seismically-generated T-waves is used to study the time-clustering behavior of moderate-size (&gsim;3.0 M) earthquakes between 15 and 35°N along the Mid-Atlantic Ridge (MAR). Within this region, the distribution of inter-event times is consistent with a non-periodic, non-random, clustered process. The highest degrees of clustering are associated temporally with large mainshock-aftershock sequences; however, some swarm-like activity also is evident. Temporal fluctuations characterized by a power spectral density P(f) that decays as 1/fα are present within the time sequence, with α ranging from 0.12 to 0.55 for different regions of the spreading axis. This behavior is negligible at time scales less than ∼5×103 s, and earthquake occurrence becomes less clustered (smaller α) as increasing size thresholds are applied to the catalog. A power-law size-frequency scaling for Mid-Atlantic Ridge earthquakes also can be demonstrated using the distribution of acoustic magnitudes, or source levels. Although fractal seismic behavior has been linked to the structure of the underlying fault population in other environments, power–law fault size distributions have not been observed widely in the mid-ocean ridge setting. [Copyright &y& Elsevier]

Much recent work has been focused on understanding the statistical properties of time-occurrence series of earthquakes. Investigating into the patterns of seismic sequences reveals evidence of scaling features in temporal behavior. This is shown in the clustering properties of seismicity of the western Corinth graben, Greece from 1983 to 2000. Power-law behavior has been found by means of Allan factor analysis and Fourier spectra for the earthquake sequence, with consistent values for the scaling exponents, that decrease with the threshold magnitude. The analysis of the temporal variation of the scaling exponent, performed with different threshold magnitudes, reveals an enhancing of the clusterization in correspondence to larger events. The multifractal analysis of the temporal distribution of the events has shown a decrease of the intermittent character with the threshold magnitude. [Copyright &y& Elsevier]