Search

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.

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. (C) 2018 Elsevier B.V. All rights reserved.

High-casualty fires (HCFs) involving 3 or more fatalities from the Fire Statistical Year Book of China and the Chinese Fire Services from 2002 to 2009 were analyzed. This study investigates the frequency-size power-law distribution and time-scaling property of HCFs. The results show that HCFs exhibit a frequency-size power-law distribution regardless of whether the fire size is represented by fatalities, direct loss or burned area. The frequency-fatality power-law distribution is a common phenomenon in fire accidents, even in international data. Six factors (place, cause, time of day, season, year and region of the fire) were analyzed to assess their effects on the frequency-fatality distribution and compared using the scaling exponent. Factors, such as a non-residential place, an electrical cause, the winter season and regions with strong economies, cause fire frequency to decrease slowly with increases in fatalities. That is, these factors are associated with higher fatalities. The time-scaling properties were detected using the Fano Factor and Allan Factor, and the results illustrate that HCFs exhibit obvious time-scaling behavior after the fractal onset times. The results of the fractal onset times imply that the time-scaling behaviors of HCFs exhibit daily and monthly periodicity. The 1-day onset time is consistent with previous studies, but the 1-month onset time is different from that reported previously. The time-scaling exponent decreases significantly with increasing fatalities, which indicates that fire sequences with more fatalities tend to behave as Poisson processes.

High-casualty fires (HCFs) involving ≥ 3 fatalities derived from the Fire Statistical Year Book of China and Chinese Fire Services from 2002-2010 were analyzed. The aim of this study was to investigate the time-scaling properties of HCFs. The time-scaling properties were detected by means of Fano Factor (FF), Allan Factor (AF) and detrended fluctuation analysis (DFA). The results of FF and AF show that the HCF sequences with death ≥ 3 and death ≥ 4 exhibit obvious time scaling behavior after the fractal onset times. The scaling exponents of FF and AF decrease significantly with increasing fatality, which reflects that HCF sequences with more fatalities tend to behave as Poisson process. The sequence of HCFs with death ≥ 6 can be considered as a Poisson process according to the comparison of FF (AF) curve and Poissonian 95% confidence curve. The DFA scaling exponent of HCF sequence involving fatality ≥ 3 is approximate 0.551±0.005, indicating that this sequence exhibits long-range correlations. With the increase of fatality threshold the DFA scaling exponent gradually decreases to about 0.5, which reflects that the HCFs with high fatality levels are likely to be uncorrelated. Furthermore, the sequence of HCFs with death ≥ 6 can be regarded as uncorrelated because its DFA scaling exponent is 0.496±0.003. © 2013 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Asia-Oceania Association for Fire Science and Technology.

Sharp fluctuations (in particular, extreme fluctuations) of asset prices have a great impact on financial markets and risk management. Therefore, investigating the time dynamics of sharp fluctuation is a challenge in the financial fields. Using two different representations of the sharp fluctuations (inter-event times and series of counts), the time clustering behavior in the sharp fluctuation sequences of stock markets in China is studied with several statistical tools, including coefficient of variation, Allan Factor, Fano Factor as well as R/S (rescaled range) analysis. All of the empirical results indicate that the time dynamics of the sharp fluctuation sequences can be considered as a fractal process with a high degree of time-clusterization of the events. It can help us to get a better understanding of the nature and dynamics of sharp fluctuation of stock price in stock markets.

The time dynamics of seismicity of Aswan area (Egypt) from 2004 to 2010 was investigated by means of the (i) Allan Factor, which is a powerful tool allowing the capture of time-clusterized properties of temporal point processes; and the (ii) detrended fluctuation analysis, which is capable of detecting scaling in nonstationary time series. The analysis was performed varying the depth and the magnitude thresholds. The 2004–2010 Aswan seismicity is characterized by significant three-fold time-clustering behaviors with scaling exponents ~0.77 for timescales between 104.16 s and 105.14 s, ~0.34 for timescales between 105.14 s and 106.53 s, and ~1 for higher timescales. The seismic interevent times and distances are characterized by persistent temporal fluctuations for most of the magnitude and depth thresholds.

The seismicity observed in the Aswan area (Egypt) between 1986 and 2003 was deeply investigated by means of time-fractal methods. The time dynamics of the aftershock-depleted seismicity, investigated by means of the Allan Factor, reveals that the time-clustering behavior for events occurred at shallow depths (down to 12.5 km from the ground) as well as for events occurred at larger depths (from 15 km down to 27.5 km) does not depend on the ordering of the interevent times but mainly on the shape of the probability density functions of the interevent intervals. Moreover, deep seismicity is more compatible with a Poissonian dynamics than shallow seismicity that is definitely more super-Poissonian. Additionally, the set of shallow events shows a periodicity at about 402 days, which could be consistent with the cyclic loading/unloading operations of the Lake Naser Dam. Such findings contribute to better characterize the seismicity of the Aswan area, which is one of the most interesting water reservoirs in the world, featured by reservoir-induced earthquakes.

The time-clustering behavior of the 1996–2005 seismicity of Koyna–Warna region (India), a unique site where reservoir-triggered earthquakes have been continuously occurring over the last about 50 year, has been analyzed. The scaling exponent α, estimated by using the Allan Factor method, a powerful tool to investigate clusterization in point processes, shows co-seismic and pre-seismic enhancements associated with the occurrence of the major events.

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.

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.

The series of lightning measured during 2002 and 2003 in two areas of Italy, Lombardia (northern Italy) and Campania (southern Italy), has been deeply investigated to detect and quantify time-clustering structures by using several methods. Our results suggest the existence of time-clustering in the sequence of lightning time-occurrences, characterized by the presence of two scaling regions, respectively related with clustering effect inside a single thunderstorm and among successive thunderstorms.

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.

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.

Temporal point processes can be used to model rain event sequences. Time-scaling analysis of rainfall data has been performed by means of the statistical approaches of Fano Factor analysis (FF) and Allan Factor analysis (AF). The obtained results suggest the presence of clustering in the time distribution of the sequence of rain events, with scaling exponents alpha(FF)similar to 0.33-0.47 and alpha(AF) similar to 0.41-0.48.

The time-scaling behavior of the 1970-2003 seismicity of southern Aegean area has been investigated by means of the Allan Factor analysis, which allows the detection and the quantification of time-clustering structures in point processes. The analysis of the time variation of the scaling exponent, defined by means of this statistics, has revealed precursory patterns related with the largest event (M = 6.1) of the sequence investigated. (c) 2005 Elsevier Ltd. All rights reserved.

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.

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.

Two years of lightning data, measured during 2002 and 2003 in an area of southern Italy, have been analyzed in order to reveal scaling behaviour in their time dynamics. We used the Allan Factor method to evidence the presence of time-clustering in the lightning data. We found that i) 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. A crossover timescale is identified, which is connected with the mean duration of a thunderstorm. We investigated intra- and inter-cluster time-dynamics for the whole sequence as well as the sequence of only positive and only negative flashes. The negative lightning show a time-clustering feature stronger than that of the positive lightning.

We performed the Allan factor analysis on the temporal distribution of seismicity of Italy from 1983 to 2002. Significant power-law temporal behaviour has been identified analyzing both the full and the aftershock-depleted seismic catalogues of Italy; this suggests that the correlated behaviour is due not only to the generation of aftershocks, following the occurrence of large shocks, but is a feature of the background seismicity.

Muscle sympathetic nerve activity (MSNA) in resting humans is characterized by cardiac-related 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.

We investigate the time dynamics of sequences of earthquakes occurred in three different seismic zones in Italy. All the series analyzed present 1/f α temporal fluctuations, shown by the power-law behaviour of several statistics (Fano Factor, Allan Factor and Count-based Periodogram), that allow to detect correlation properties in point processes.

The temporal distribution of aftershock sequences can be analyzed by means of new parameters other than the Omori's p-value. A deep analysis of the temporal properties of six aftershock sequences occurred in Greece from 1980 to 1997 has been carried out by means of fractal tools. We performed the Omori's law, the R/S and the Allan Factor analyses in order to estimate the p-value of the aftershock rate, the Hurst exponent (H) of the interevent-time series, and the spectral exponent (α) respectively. Our results show a significant variability of the p-value from 0.89 to 1.48, of H from 0.78 to 1.186 and of α from 0.49 to 1.44. The variation of the normalized α with the threshold magnitude for all the aftershock sequences examined has displayed almost the same decreasing behaviour. The temporal fractality of aftershock sequences is primarily due to the power-law decay of the aftershock rate.

Fractal stochastic point processes are described by power-law statistics, and therefore, are suited to model the time-occurrence sequence of seismic events, that are generally characterized by a time-clustering phenomenon. In this paper we quantified the temporal clustering in earthquake sequences by means of the Fano factor and the Allan factor, that can be used to reveal the fractality of such processes. These methods are applied to model the fractality of the 1983–1997 seismicity of one of the most seismically active area of southern Apennine Chain (southern Italy), that has shown the presence of temporal clusterization.

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.

Both fluctuations and distributions of spontaneous neural spiking activity have been observed to closely follow a variety of power laws. Multiple explanations have been offered for each observation, but few lead to mechanisms that encompass their widespread occurrence. A canonical, leaky integrate-and-fire model is presented in which synapses are updated based on the timing of pre- and post-synaptic spikes in order to maintain a state of critical branching. Results showed that 1) the self-tuning algorithm maintained critical branching under a range of parameters; 2) power laws were obtained in spiking activity fluctuations (1/f scaling), size distributions of network bursts (neural avalanches), and temporal correlations in interspike intervals (Allan factor); 3) power laws disappeared once the self-tuning algorithm was disabled; and 4) critical branching was adaptive in that it maximized the network’s memory capacity when assessed as a liquid state machine.

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.

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.

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.

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.

The present study was designed to characterize respiratory fluctuations in awake, healthy humans under resting conditions. Specifically, we used Allan factor and dispersional analysis to test whether the fluctuations in breath number, respiratory period, and breath amplitude were fractal or random in nature. The results can be summarized as follows. Fluctuations in all three parameters were fractal in nine subjects. There were four subjects in whom only the fluctuations in breath number and amplitude were fractal, three subjects in whom only fluctuations in breath number were fractal, and two subjects in whom only fluctuations in breath number and respiratory period were fractal. Fluctuations in the three parameters occurred randomly in the remaining two subjects. The data suggest that fractal fluctuations in breath number, respiratory period, and breath amplitude are controlled by separate processes.

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).

Heart-failure patients can be identified by computing certain statistics of the sequence of heartbeats, such as the Allan factor (AF) and its generalization, the wavelet Allan factor (WAF). These measures successfully determine whether a given patient suffers from heart failure or not. They succeed because they are jointly sensitive to both short-term, and long-term fractal, characteristics of the heartbeat time series.

Temporal clustering structures were identified and quantified in fire sequences recorded from 1980 to 2005 in Continental Portugal, by using the Allan Factor statistics, a statistical tool suited to reveal clustering behaviour in point processes. The obtained results show the presence of daily and annual periodicities, superimposed onto a scaling behaviour, which features the sequence of wildfires as a fractal time process with a rather high degree of time-clusterization of the events.

Temporal dynamical analysis in fire sequences recorded from 1969 to 2008 in Canton Ticino (Switzerland) was carried out by using the Allan Factor statistics. The obtained results show the presence of daily periodicities, superimposed to two time-scaling regimes. The daily cycle vanishes for sequences of higher altitude fires, for which a single scaling behaviour is observed.