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Many astrophysical bursts can recur, and their time series structure or pattern could be closely tied to the emission and system physics. While analysis of periodic events is well established, some sources, e.g. some fast radio bursts and soft gamma-ray emitters, are suspected of more subtle and less explored periodic windowed behavior: the bursts themselves are not periodic, but the activity only occurs during periodic windows. We focus here on distinguishing periodic windowed behavior from merely clustered events through time clustering analysis, using techniques analogous to spatial clustering, demonstrating methods for identifying and characterizing the behavior. An important aspect is accounting for the ``curious incident of the dog in the night time'' - lack of bursts carries information. As a worked example, we analyze six years of data from the soft gamma repeater SGR1935+2154, deriving a window period of 231 days and 55% duty cycle; this has now successfully predicted both active and inactive periods., 12 pages, 11 figures; v2 highlights successful burst prediction, improves uncertainty quantification, adds comparison to other optimization results, PRD accepted

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.

Advancements in intelligent aircraft controller design, paired with increasingly flexible and efficient aircraft concepts, create the need for the development of novel (smart) adaptive sensing suitable for aeroelastic state estimation. In contrast to rigid states, aeroelastic state estimation requires more measurement points (displacements and forces) across the span to capture the vibrational shapes of the wing undergoing excitations. A potentially universal and non-invasive approach is visual tracking. However, many tracking methods require manual selection of initial marker locations as the start of a tracking sequence. This study is part of a larger study in the field of smart sensing and aims to cover the gap by investigating a robust machine learning approach for unsupervised automatic labelling of visual markers. The method utilizes fast DBSCAN and adaptive image segmentation pipeline with HSV colour filter to extract and label the marker centres under the presence of marker failure. A comparison is made with Disjoint-set data structure for clustering of the data. The segmentation-clustering pipeline with DBSCAN shows the capability to act as a visual tracking method on its own, capable of running real-time at 250 fps on an image sequence of a single camera with a resolution of 1088×600 pixels. To increase the robustness against noise, a novel formulation of DBSCAN better suited against noise, the inverse DBSCAN (DBSCAN −1), is proposed, allowing to cast the clustering problem into noise filtering problem with an additional MaxPts parameter. Furthermore, observations are made regarding the frequency content of the image pixel intensities across time, and how this can be utilized to estimate the natural frequency of the system and adjust the segmentation-clustering pipeline with a sliding DFT (Discrete Fourier Transform).

After lying dormant for 36 yr, the Tolbachik volcano of the Klyuchevskoy group started to erupt on 27 November 2012. We investigate the preparatory phase of this eruption via a statistical analysis of the temporal behavior of long-period (LP) earthquakes that occurred beneath this volcanic system. The LP seismicity occurs close to the surface beneath the main volcanic edifices and at 30 km depth in the vicinity of a deep magmatic reservoir. The deep LP earthquakes and those beneath the Klyuchevskoy volcano occur quasi-periodically, while the LP earthquakes beneath Tolbachik are clustered in time. As the seismicity rate increased beneath Tolbachik days before the eruption, the level of the time clustering decreased. We interpret this as a manifestation of the evolution of the volcano plumbing system. We suggest that when a plumbing system awakes after quiescence, multiple cracks and channels are reactivated simultaneously and their interaction results in the strong time clustering of LP earthquakes. With time, this network of channels and cracks evolves into a more stable state with an overall increased permeability, where fluids flow uninhibited throughout the plumbing system except for a few remaining impediments that continue to generate seismic radiation. The inter-seismic source interaction and the level of earthquake time clustering in this latter state is weak. This scenario suggests that the observed evolution of the statistical behavior of the shallow LP seismicity beneath Tolbachik is an indicator of the reactivation and consolidation of the near-surface plumbing system prior to the Tolbachik eruption. The parts of the plumbing system above the deep magmatic reservoir and beneath the Klyuchevskoy volcano remain in nearly permanent activity, as demonstrated by the continuous occurrence of the deep LP earthquakes and very frequent Klyuchevskoy eruptions. This implies that these parts of the plumbing system remain in a stable permeable state and contain a few weakly interacting seismogenic sources. Our results provide new constraints on future mechanical models of the magmatic plumbing systems and demonstrate that the level of time clustering of LP earthquakes can be a useful parameter to infer information about the state of the plumbing system.

Displaying geo-referenced data in web mapping systems has become popular. However, most existing systems suffer from three annoying problems: (1) clutter when trying to visualize large amount of data; (2) slowness of transferring data over internet; (3) lack of support for dynamic queries. To solve these problems, we propose a real-time system using server-side clustering, transferring only the clustered data, and client-side visualization using existing map tools. As far as we know, there is no other scientific paper describing such real-time system that allows dynamic database queries without limiting to predefined queries. Experiments show that it can handle up to 1 million objects whereas all existing systems are either limited to pre-defined queries, or they support only a very small number of free parameters in the query whereas the proposed system has no such limitations.

Very often damage and fracture in heterogeneous materials exhibit bursty dynamics made of successive impulse-like events which form characteristic aftershock sequences obeying specific scaling laws initially derived in seismology: Gutenberg-Richter law, productivity law, B\r{a}th's law and Omori-Utsu law. We show here how these laws naturally arise in the model of the long-range elastic depinning interface used as a paradigm to model crack propagation in heterogeneous media. We unravel the specific conditions required to observe this seismic-like organization in the crack propagation problem. Beyond failure problems, the results extend to a variety of situations described by models of the same universality class: contact line motion in the wetting problem or domain wall motion in dirty ferromagnet, to name a few., Comment: 12 pages

With the development of population aging, the recognition of elderly activity in smart homes has received increasing attention. In recent years, single-resident activity recognition based on smart homes has made great progress. However, few researchers have focused on multi-resident activity recognition. In this paper, we propose a method to recognize two-resident activities based on time clustering. First, to use a de-noising method to extract the feature of the dataset. Second, to cluster the dataset based on the begin time and end time. Finally, to complete activity recognition using a similarity matching method. To test the performance of the method, we used two two-resident datasets provided by Center for Advanced Studies in Adaptive Systems (CASAS). We evaluated our method by comparing it with some common classifiers. The results show that our method has certain improvements in the accuracy, recall, precision, and F-Measure. At the end of the paper, we explain the parameter selection and summarize our method.

The analysis of time-clustering behaviour of the sub-crustal seismicity (depth larger than 60 km) of the Vrancea region has been performed. The time span of the analyzed catalogue is from 1978 to 2008, and only the events with a magnitude of Mw ≥ 3 have been considered. The analysis, carried out on the full and aftershock-depleted catalogues, was performed using the Allan Factor (AF) that allows the identificatiion and quantification of correlated temporal structures in temporal point processes. Our results, whose significance was analysed by means of two methods of generation of surrogate series, reveal the presence of time-clustering behaviour in the temporal distribution of seismicity data of the full catalogue. The analysis performed on the aftershock-depleted catalogue indicates that the time-clustering is associated mainly to the aftershocks generated by the two largest events occurred on 30 August 1986 (Mw = 7.1) and 30 May 1990 (Mw = 6.9).

Nowadays with the development of smart infrastructure for water resource management, there is an increased need for efficient operation and management of water distribution infrastructures. In this paper, we propose a system for real-time clustering system priority evaluation in a water distribution system. Data clustering algorithms are modified for real-time scenarios providing decision support for management of water distribution system. The proposed method is compared to the standard clustering methods in terms of accuracy and real-time capabilities.

Brittle fractures of inhomogeneous materials like rocks, concrete, or ceramics are of two types: Nominally brittle and driven by the propagation of a single dominant crack or quasi-brittle and resulting from the accumulation of many microcracks. The latter goes along with acoustic noise, whose analysis has revealed that events form aftershock sequences obeying characteristic laws reminiscent of those in seismology. Yet, their origin lacks explanation. Here we show that such a statistical organization is not only specific to the multi-cracking situations of quasi-brittle failure and seismology, but also rules the acoustic events produced by a propagating crack. This simpler situation has permitted us to relate these laws to the overall scale-free distribution of inter-event time and energy and to uncover their selection by the crack speed. These results provide a comprehensive picture of how acoustic events are organized upon material failure in the most fundamental of fracture states: single propagating cracks., 30 pages

Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of high frequency cojumps. We show that the dynamics of these jumps is described neither by a multivariate Poisson nor by a multivariate Hawkes model. We introduce a Hawkes one factor model which is able to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets., Comment: 11 figures, 8 tables, block bootstrap section removed, some typos corrected

We observe two distinct interevent time patterns in the slip avalanches of compressed bulk metallic glasses (BMGs). Small slip avalanches cluster together in time, but large slip avalanches recur roughly periodically. We compare the timing patterns of BMG slip avalanches with timing patterns of earthquakes and with the predictions of a mean-field model. The time clustering of small avalanches is similar to the known time clustering of earthquake foreshocks and aftershocks.

International audience; In the context of Web A/B testing, dynamic assignment of traffic aims to promote the best variation (A or B) as quickly as possible. However, dynamic assignment is difficult to use when the difference between A and B affects the visitor differently according to his / her personal characteristics and his / her history (number of visits, navigation on the website ...). In this paper, we propose a dynamic assignment strategy based on a visitor segmentation determined automatically from the visitors navigation and characteristics.

Pedestrian stampede happened more and more often during these years, such as Love Parade disaster in Germany 2010, trampling in Shanghai bund 2014 and crowd stampede in pilgrimages. Love Parade disaster 2010 stands out for well recorded videos, which are HD quality and available for researchers. There were totally seven surveillance cameras capturing the whole festival progress and the video we study is just before the disaster happened. Pedestrian motion was special and a small disturbance would lead the group to an avalanche in this kind of critical situation. Here we focus on the individual movement pattern. The trajectories of each pedestrian involved were extracted by a mean-shift algorithm. We analyzed the space-time patterns of the pedestrians involved in the Love Parade stampede by using the detrended fluctuation analysis and the coefficient of variation. Our results reveal that the pedestrians' movement in crowd-quakes is persistent in space, globally time-clusterized but locally regular or quasi-periodic behavior. Pedestrian movement was treated as stop and go state by point process-based representation. When the threshold increases, this means that the "go" state is longer and pedestrians keep on walking in several consecutive time frames; this is difficult in crowded situations and lead to special time-clustering behavior of the sequence of "go" events. The study reveals pedestrian motion characteristics in critical situations, which will enhance the understanding of pedestrian behaviors and supply early warning features for not only Love Parade Disaster, but also other similar large events. (C) 2016 Published by Elsevier B.V.

A plethora of infinite data is generated from the Internet and other information sources. Analyzing this massive data in real-time and extracting valuable knowledge using different mining applications platforms have been an area for research and industry as well. However, data stream mining has different challenges making it different from traditional data mining. Recently, many studies have addressed the concerns on massive data mining problems and proposed several techniques that produce impressive results. In this paper, we review real time clustering and classification mining techniques for data stream. We analyze the characteristics of data stream mining and discuss the challenges and research issues of data steam mining. Finally, we present some of the platforms for data stream mining.

Clustering queries over sliding windows require maintaining cluster memberships that change as windows slide. To address this, the Generic 2-phase Continuous Summarization framework (G2CS) utilizes a generation based window maintenance approach where windows are maintained over different time intervals. It provides algorithm independent and efficient sliding mechanisms for clustering queries where the clustering algorithms are defined in terms of queries over cluster data represented as temporal tables. A particular challenge for real-time detection of a high number of fastly evolving clusters is efficiently supporting smooth re-clustering in real-time, i.e. to minimize the sliding time with increasing window size and decreasing strides. To efficiently support such re-clustering for clustering algorithms where deletion of expired data is not supported, e.g. BIRCH, G2CS includes a novel window maintenance mechanism called Sliding Binary Merge (SBM), which maintains several generations of intermediate window instances and does not require decremental cluster maintenance. To improve real-time sliding performance, G2CS uses generation-based multi-dimensional indexing. Extensive performance evaluation on both synthetic and real data shows that G2CS scales substantially better than related approaches.

By using the global and local coefficient of variation and the Allan Factor we investigated the time-clustering properties of the time dynamics of fluid-injection–induced microseismicity. The experiment consists of a microseismic monitoring through a nearly vertical borehole of 12 receivers of a hydraulic fracturing stimulation along a horizontal well separated into more than 20 sections (stages) The main finding of the applied methodology is the discrimination between fault triggering and new fracturing, being the first characterized by a clusterization of the induced microseismic events and the second by a Poissonian behaviour of the generated events.

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.

Problem statement: In this study, the inequality of apnea rates during sleep was investigated. Approach: This study used a database comprising 13 patients with apnea problems. The data was extracted from the MIT-BIH database. The Lorenz curve and Gini index were used to determine the inequality of apnea rates. In order to test for cluster, random or regular patterns of apnea, an index of runs was used. Results: The Lorenz curve showed that the distribution of apnea events for every 10% period of sleep varied between each patient. The Gini index ranged between 0.148 and 0.614. Most of the patients had a Gini coefficient lower than 0.5. The index of runs was between 0.115 and 0.353, which indicates that most patients had a regular pattern of apnea and that it is not random. Conclusion: The distribution of the apnea is almost equal and most patients have regular patterns of occurrence of apnea.

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.

Introduction Congenital hypothyroidism (CH) is a condition of thyroid hormone deficiency present at birth. Based on data recorded by the South-eastern France newborn screening center, an unusually large number of cases were observed in 1986, the year when radioactive iodine from the Chernobyl disaster was released. We sought to investigate the time clustering pattern of CH cases in this area using 31 years of data to study whether this cluster is unlikely to have arisen by chance. Methods The study included all cases of CH with eutopic thyroid gland and thyroid dysgenesis screened from 1982 to 2012 in Provence-Alpes-Cote-d’Azur and the island of Corsica. Statistical tests (Naus and Kulldorff scan tests) to retrospectively investigate an unusual temporal clustering of cases were applied, adjusting for the temporal incidence trend and variation of the neonatal population size. CH with eutopic thyroid gland were analyzed separately from thyroid dysgenesis, as an anomaly in thyroid development following radiation would be expected to present itself as thyroid dysgenesis. Results Thyroid dysgenesis was the underlying cause in 73% of the 522 cases of CH in newborn infants registered in the studied geographical area between 1982–2012. A statistically annual average increase was observed for CH with eutopic gland only (+3.4%, confidence interval: 1.2, 6.3). Irrespective of the type of CH or alternative hypothesis investigated for the clustering pattern, no statistically significant temporal clusters of cases were found. Conclusions Our results indicate that the perceived excess of cases in 1986 in South-Eastern France was not statistically unusual. This finding does not suggest a role for radioactive fallout of Chernobyl in the incidence of CH cases.

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.

This paper addresses the following question: Are the hazardous materials pipeline incidents non-randomly time distributed? Our analysis suggests that they are correlated, which means that a hazardous materials pipeline incident is not independent from the time elapsed since the previous event. That is, our statistical tests suggest that previous accident counts correlate with future counts. But, if we consider incidents with a large severity index (spills and property damage), the phenomenon is unpredictable, since it approaches a Poissonian process (random, independent and uncorrelated).

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.

National audience; In this paper, we focus on the stochastic block model (SBM),a probabilistic tool describing interactions between nodes of a network using latent clusters. The SBM assumes that the networkhas a stationary structure, in which connections of time varying intensity are not taken into account. In other words, interactions between two groups are forced to have the same features during the whole observation time. To overcome this limitation,we propose a partition of the whole time horizon, in which interactions are observed, and develop a non stationary extension of the SBM,allowing to simultaneously cluster the nodes in a network along with fixed time intervals in which the interactions take place. The number of clusters (K for nodes, D for time intervals) as well as the class memberships are finallyobtained through maximizing the complete-data integrated likelihood by means of a greedy search approach. After showing that the model works properly with simulated data, we focus on a real data set. We thus consider the three days ACM Hypertext conference held in Turin,June 29th - July 1st 2009. Proximity interactions between attendees during the first day are modelled and an interestingclustering of the daily hours is finally obtained, with times of social gathering (e.g. coffee breaks) recovered by the approach. Applications to large networks are limited due to the computational complexity of the greedy search which is dominated bythe number $K_{max}$ and $D_{max}$ of clusters used in the initialization. Therefore,advanced clustering tools are considered to reduce the number of clusters expected in the data, making the greedy search applicable to large networks.; Le modèle à blocs stochastiques (SBM) décrit les interactions entre les sommets d'un graphe selon une approche probabiliste, basée sur des classes latentes. SBM fait l'hypothèse implicite que le graphe est stationnaire. Par conséquent, les interactions entre deux classes sont supposées avoir la même intensité pendant toute la période d'activité. Pour relaxer l'hypothèse de stationnarité, nous proposons une partition de l'horizon temporel en sous intervalles disjoints, chacun de même longueur. Ensuite, nous proposons une extension de SBM qui nous permet de classer en même temps les sommets du graphe et les intervalles de temps où les interactions ont lieu. Le nombre de classes latentes (K pour les sommets, D pour les intervalles de temps) est enfin obtenu à travers la maximisation de la vraisemblance intégrée des données complétées (ICL exacte). Après avoir testé le modèle sur des données simulées, nous traitons un cas réel. Pendant une journée, les interactions parmi les participants de la conférence HCM Hypertext (Turin, 29 Juin – 1er Juillet 2009) ont été traitées. Notre méthodologie nous a permis d'obtenir une classifications intéressante des 24 heures: les moments de rencontre tels que les pauses café ou buffets ont bien été détectés. La complexité de l'algorithme de recherche, linéaire en fonction du nombre initial de clusters ($K_{max}$ et $D_{max}$ respectivement), nous oriente vers l'utilisation d'instruments avancés de classification, pour réduire le nombre attendu de classes latentes et ainsi pouvoir utiliser le modèle pour des réseaux de grand dimension.

Motivated by the problem of computing investment portfolio weightings we investigate various methods of clustering as alternatives to traditional mean-variance approaches. Such methods can have significant benefits from a practical point of view since they remove the need to invert a sample covariance matrix, which can suffer from estimation error and will almost certainly be non-stationary. The general idea is to find groups of assets which share similar return characteristics over time and treat each group as a single composite asset. We then apply inverse volatility weightings to these new composite assets. In the course of our investigation we devise a method of clustering based on triangular potentials and we present associated theoretical results as well as various examples based on synthetic data., Comment: AIFU15

Natural hazards can be represented as point processes that are characterized by the occurrence times of the events and their intensities. It is crucial to investigate the correlation properties of these processes in order to gain a deep knowledge of the dynamical mechanisms which underlie hazardous phenomena. To this end, suitable methodologies must be developed to perform these correlation analyses on processes, which are described as point-like processes. The concept of time-clustering implies a time-structured organization of these processes, and is in direct opposition to the pure randomness typical of Poissonian processes in which the events are uncorrelated. This article reports several examples of natural hazards within the framework of time-clustering.

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.

In recent years there has been deep development in the use of techniquesto analyse the statistical properties of point process time series. Furthermoremany efforts have been made to establish robust methods to identify timeclustering structures in the temporal distribution of seismic events. In thispaper we intend to give a systematic review of some common usedtechniques to characterise the temporal properties of an earthquakesequence; we also present new methods, commonly used in other scientificfields, to reveal time clustering structures in a seismic sequence and toclearly identify non-poissonian behaviours at different time scales. Anapplication of these methods has been performed on the seismicity ofIrpinia-Basilicata area (Southern Italy).

The present study assessed landslide events over a time span of fifty years in the prefecture of Ioannina. Historical data analysis commonly provides valuable data for understanding distribution of landslides. The methodology included collection and analysis of articles about landslides events found in the local newspapers between 1960 and 2008, also in the national newspapers (1960-1967) and in the contemporary national newspapers (1995-2008). The time interval selected in this study is representative of the entire time period of systematic newspapers publication. During this time spam, eighty nine historical landslides were identified. Newspaper articles annotate the time and the location of the landslides as well as primarily the role of weather conditions in triggering the landslides. In addition, published articles provide information on the damages caused by the landslides. The study shows that these events occurred due to extremely high precipitation, snowstorms or prolonged rainfall. The monthly distribution of the recorded phenomena shows an increase of landslide events during January-March and November-December, as these are the months with the highest precipitation and snowing in the prefecture. Although time clustering of the landslides within the Ioannina Prefecture in the time interval 1960 to 2006 was found to be repeated every forty years, their spatial clustering appears to change.

We develop a theory that links stress interaction between earthquakes and the occurrence of temporal clustering. Coseismic static stress change in the vicinity (50 km) of large earthquakes suggests that perturbations of 0.1 to 1 bars may affect the occurrence of other earthquakes. At larger distances, interactions also seem to exist: four M 8 earthquakes have occurred in Mongolia on distant faults (400 km) during the last century. Also, paleoseismic observations documenting much longer time periods display a time clustering of major events. We demonstrate with simple mechanical concepts that postseismic stress relaxation magnifies the coseismic stress change and has a major effect on fault interaction during the seismic cycle. In the simple case where two distant faults are coupled, the probabilistic occurrence of triggered earthquakes may increase dramatically due to long range postseismic coupling.

We investigate the time self-similarity properties of seismicity in the Hellenic are, which is one of the most rapidly deforming and seismically active regions of the Mediterranean area. The presence of time-scale-invariance properties in the shallow and intermediate depth seismicity is revealed. In particular, 1/f(beta) fluctuations are detected from the analysis of earthquake sequences using the counting statistics methodology. The shallow seismicity is characterized by a time clustering effect and shows a beta value that is a typical fingerprint of self-similar behaviours, whereas the intermediate seismicity can be considered as a realization of a purely poissonian process. The investigations cover instrumentally recorded earthquakes occurring between 1964 and 1996, and the analyses have been carried out, selecting different magnitude thresholds. The beta value for shallow seismicity decreases from almost 0.5 to 0.2 as the threshold magnitude increases from 3.3 to 4.5. (C) 2000 Elsevier Science B.V. All rights reserved.

During the time interval of 4 May–15 June 1995 four independent mainshocks occurred in the Greek mainland: 4/5/95, M s = 5.5; 9/5/95, M s = 5.2; 13/5/95, M s =6.6; 15/6/95, M s = 6.1. The seismicity rate within this 43-day interval is increased by a factor of 34 and 71 with respect to the mean, long-term seismicity for M s ≥ 5.2 and M s ≥ 6.1, respectively. In terms of probability, it has been found out that the probability of observing by chance four events of M s ≥ 5.2 or two events of M s ≥ 6.1 in the Greek mainland is equal to only 7.12 × 10 −6 and 3.82 × 10 −4 , respectively. These results imply that the observed seismicity has been a non-random time clustering. Similar earthquake time clusters were identified to have occurred in the Greek mainland in 1911 and 1931. A triggering mechanism has been modeled to interprete the earthquake clustering: the first event of the earthquake sequence produces transient stress changes that cause an acceleration to the stress loading, and then to seismic failure, to remote highly prestressed regions.

The clustering structure of the Vesuvian earthquakes occurring is investigated by means of statistical tools: the inter-event time distribution, the running mean and the multifractal analysis. The first cannot clearly distinguish between a Poissonian process and a clustered one due to the difficulties of clearly distinguishing between an exponential distribution and a power law one. The running mean test reveals the clustering of the earthquakes, but looses information about the structure of the distribution at global scales. The multifractal approach can enlighten the clustering at small scales, while the global behaviour remains Poissonian. Subsequently the clustering of the events is interpreted in terms of diffusive processes of the stress in the earth crust.

Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of high frequency cojumps. We show that the dynamics of these jumps is described neither by a multivariate Poisson nor by a multivariate Hawkes model. We introduce a Hawkes one factor model which is able to capture simultaneously the time clustering of jumps and the high synchronization of jumps across assets.