Abstract: We analyzed the interactivity time, defined as the duration between two consecutive tasks such as sending emails, collecting friends and followers and writing comments in online social networks (OSNs).The distributions of these times are heavy tailed and often described by a power-law distribution. However, power-law distributions usually only fit the heavy tail of empirical data and ignore the information in the smaller value range. We argue that the durations between writing emails or comments, adding friends and receiving followers are likely to follow a lognormal distribution, discussing the similarities between power-law and lognormal distributions, and show that binning of data can deform a lognormal to a power-law distribution. An explanation for the appearance of lognormal interactivity times will be discussed and the influence of non-Markovian infection spread on the Susceptible-Infected-References:- C. Doerr, N. Blenn, and P. Van Mieghem. Lognormal Infection Timesof Online Information Spread. PLoS ONE, 8(5):e64349, 05 2013.- E. Cator, R. van de Bovenkamp, and P. Van Mieghem.Susceptible-infected-infection and cure times. Physical Review E, 87:062816, Jun 2013.- P. Van Mieghem and R. van de Bovenkamp. Non-Markovian InfectionSpread Dramatically Alters the Susceptible-Infected-Threshold in Networks. Physical Review Letters, 110:108701, Mar 2013.

Abstract: A number of human activities exhibit a bursty pattern, namely periods of very high activity that are followed by rest periods. Records of these processes generate time series of events whose inter- event times follow a probability distribution that displays a fat tail. The grounds for such phenomenon are not yet clearly understood. In this talk I will present some results concerning the use the freely available Wikipedia?s editing records to unravel some features of this phenomenon. We show that even though the probability to start editing is conditioned by the circadian 24 hour cycle, the conditional probability for the time interval between successive edits at a given time of the day is independent from the latter. We confirm our findings with the activity of posting on the social network Twitter. Our result suggests there is an intrinsic humankind scheduling pattern: after overcoming the encumbrance to start an activity, there is a robust distribution of new related actions, which does not depend on the time of day. Some simulations were performed in order to understand the effect of circadian patterns in the activity, in particular in the stationarity of the power-law inter-event distributions.

Abstract: Empirical studies revealed a number of features of bursty time series [1,2]. We implemented a simple task-queuing model, which produces bursty time series due to the non-trivial dynamics of the task list. We give exact results on the asymptotic behaviour of the model and we show that the inter-event time distribution (IETD) is power-law decaying for any kind of input distributions that remain normalizable in the infinite list limit, with exponents tuneable between 1 and 2. The model satisfies a scaling law between the exponents of inter-event time distribution (?) and autocorrelation function (?):???+???=?2. This law is general for renewal processes with power-law decaying inter-event time distribution and a departure from it indicates long-range dependence between the inter-event times [3]. We investigated another model based on self-exciting point processes with variable memory range. We found that in an intermediate range of memory effect the generated correlated bursts are comparable to empirical findings [4]. Empirical studies show that burstiness has major impact on the spreading processes on networks [5]. We solve the SI model on the infinite complete graph and show that fat tailed IETD causes always acceleration [6]. In order to understand the role of these influencing factors we studied the SI model on temporal networks with different aggregated topologies and different IETDs. Based on analytic calculations and numerical simulations, we show that if the stationary bursty process is governed by power-law IETD, the spreading can be slowed down or accelerated as compared to a Poisson process; the speed being determined by the short time behaviour, which in our model is controlled by the exponent. We demonstrate that finite, so called 'locally tree-like' networks, like the Barab?si?Albert networks behave very differently from real tree graphs if the IETD is strongly fat-tailed. Furthermore, non-stationarity of the dynamics has a significant effect on the spreading speed for strongly fat-tailed power-law IETDs [7].References:[1] M?rton Karsai, Kimmo Kaski, Albert-L?szl? Barab?si, J?nos Kert?sz: Universal features of correlated bursty behaviour, Scientific Reports, 2 397 (2012)[2] M?rton Karsai, Kimmo Kaski, J?nos Kert?sz: Correlated dynamics in egocentric communication networks, PloS ONE, 7, e40612 (2012)[3] Szabolcs Vajna, B?lint T?th, J?nos Kert?sz: Modelling bursty time series, New Journal of Physics, 15, 103023 (2013)[4] Hang-Hyun Jo, Juan I Perotti, Kimmo Kaski, J?nos Kert?sz: Correlated bursts and the role of memory range, Physical Review E, 92, 022814 (2015)[5] M?rton Karsai, Mikko Kivel?, Raj Kumar Pan, Kimmo Kaski, J?nos Kert?sz, A-L Barab?si, Jari Saram?ki: Small but slow world: How network topology and burstiness slow down spreading, Phys. Rev. E, 83, 025102 (2011)[6] Hang-Hyun Jo, Juan I Perotti, Kimmo Kaski, J?nos Kert?sz: Analytically solvable model of spreading dynamics with non-Poissonian processes, Phys. Rev. X, 011041 (2014)[7] D?vid X. Horv?th, J?nos Kert?sz: Spreading dynamics on networks: the role of burstiness, topology and non-stationarity, New Journal of Physics, 16, 073037 (2014)

Abstract: A diverse variety of processes?including recurrent disease episodes, neuron firing, and communication patterns among humans?can be described using inter-event time (IET) distributions. Many such processes are ongoing, although event sequences are only available during a finite observation window. Because the observation time window is more likely to begin or end during long IETs than during short ones, the analysis of such data is susceptible to a bias induced by the finite observation period. In this talk, I illustrate how this length bias is born, how it can be corrected, and formulate simple heuristic for determining the severity of the bias. This can be donewithout assuming any particular shape for the IET distribution, but one needs to assume that the event sequences are produced by (stationary) renewal processes. I illustrate the method for several well-known empirical communication networks from the literature. It turns out that in these data sets the resulting bias can lead to systematic underestimates of the variance in the IET distributions and that correcting for the bias can lead to qualitatively different results for the tails of the IET distributions.

Abstract: Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external perturbation to the system. In this paper we propose a novel procedure for the detection of intensity bursts within the Hawkes process framework. By using a model selection scheme we show that our procedure can be used to detect intensity bursts when both their occurrence time and their total number is unknown. Moreover the initial time of the burst can be determined with a precision given by the typical inter-event time. We apply our methodology to the mid-price change in FX markets showing that these bursts are frequent and that only a relatively small fraction is associated to news arrival. We show lead-lag relations in intensity burst occurrence across different FX rates and we discuss their relation with price jumps.

Abstract: When modelling dynamical systems on networks, it is often assumed that the process is Markovian, that is future states depend only upon the present state and not on the sequence of events that preceded it. Examples include diffusion of ideas or diseases on social networks, or synchronisation of interacting dynamical units. In each case, the dynamics is governed by coupled differential equation, where the coupling is defined by the adjacency matrix of the underlying network. The main purpose of this talk is to challenge this Markovian picture. We will argue that non-Markovian models can provide a more realistic picture in the case of temporal networks where edges change in time, or in situations when pathways can be measured empirically. We will focus on the importance of non-Poisson temporal statistics, and show analytically the impact of burstiness on diffusive dynamics, before turning to applications and incorporating memory kernels in predictive models of retweet dynamics.

Abstract: We analyze several temporal aspects of a large dataset of crimes and their suspects. The dataset covers all crimes recorded by the Swedish police from 1992 to 2012, it covers 460,846 crimes involving 1,250,535 individuals. The crimes are categorized into about 400 categories and are time stamped. We extract several types of temporal structures, from interevent times to the more long-scale structures related to criminal careers. We discuss the connections between the various extracted time scales and to the social phenomenon of crime. Some quantities are even scale-free (with exponent around 2.5)?like the distribution of collaboration trees (where a crime is connected to the previous if there is a significant overlap of criminals involved (see the figurebelow). Most quantities do, however, have scales. We discuss how these temporal effects can help preventive police works.

Abstract: Several biological and natural systems appear to operate close to a critical point, as evidenced by the absence of a characteristic size in the phenomenon. Indeed, the existence of power law distributions has been detected in several contexts, as different as earthquakes, solar flares or spontaneous brain activity, and, surprisingly, with similar scaling behaviour. We propose that the specific features of each phenomenon are imbedded in the temporal organization of events in time. A detailed analysis of time-energy correlations detrending statistical noise is able to enlighten the difference between the physical mechanisms controlling different phenomena, as for instance earthquakes and solar flares. Conversely, the temporal organization of neuronal avalanches in the rat cortex in vitro exhibits a distribution of waiting times between successive events with a non-monotonic behavior, not usually found in other natural processes. Numerical simulations provide evidence that this behavior is a consequence of the alternation between states of high and low activity, leading to a dynamic balance between excitation and inhibition. This behavior is also detected at a larger scale, i.e., on fMRI data from resting patients. By monitoring temporal correlations in high amplitude BOLD signal, we find that the activity variations with opposite sign are correlated over a temporal scale of few seconds, suggesting a critical balance between activity excitation and depression in the brain.

Abstract: Particle-laden flows experience deposition and erosion when passing through a porous medium, a common situation in many fields, ranging from environmental sciences to industrial filters and petroleum recovery. We experimentally study dense suspensions during deep bed filtration and find that the time evolution of pressure losses through the filter is characterized by jumps separated bytime delays. These jumps are related to erosive events inside the porous medium and are preceded and followed by deposition. A statistical analysis shows that the events are independent whose size distribution scales with a power law. The detection of such jumps provides new insight into the dynamics of particle-laden flows through porous media, specifically as they can be considered analogous to sand avalanches occurring in petroleum wells. The above phenomenon can be reproduced in an electrical network of fuse-anti- fuse devices, which become insulators within acertain finite interval of local applied voltages. As a consequence, the macroscopic current exhibits temporal fluctuations which increase with system size. We determine the conditions under which this itinerant conduction appears by establishing a phase diagram as a function of the applied field and the size of the insulating window.

Abstract: In the traditional ?bare-bones? network approach, nodes are nodes and links and links, and that is all there is. For social networks, this means that individuals are distinguishable only on the basis of their network characteristics (degree, centrality, etc). However, we all know that people are different and behave in different ways. These differences can be approached with more fine-grained behavioural data, in particular with the help of data on time-stamped interactions that allow constructing dynamic and temporal social networks. In this talk, I will focus on exploring individual differences with the help of temporal data on electronic interactions (calls, emails, etc). I will first talk about longer timescales and the similarities and differences in how we maintain our personal networks. Then, I will focus on shorter timescales of circadian patterns, and show how various data sets reveal chronotypes of individuals (morning/evening-active persons) and chronotype compositions of populations.

Abstract: Bursty dynamical patterns characterise not only individual human behaviour but also appear on the level of dyadic interactions and even in case of collective phenomena. The first observations of human bursty patterns were commonly addressed the activity of individuals, although many observations were made on interaction datasets. All these studies reported heterogeneous non-Poissonian dynamical patterns characterised by broad inter-event time distributions, which emergence was explained in various ways: due to intrinsic correlations via decision mechanisms; due to independent actions influenced by circadian patterns; or other underlying mechanisms. In addition several combinations of these modelling directions were proposed together with phenomenological models aiming at simply reproducing signals with similar temporal features. In this talk our aim is to give a brief introduction to these modelling efforts and to provide an overview about their development during the last decay.

Abstract: Over the past two decades, school shootings within the United States have repeatedly devastated communities and shaken public opinion. Many of these attacksappear to be ?lone wolf? ones driven by specific individual motivations, and the identification of precursor signals and hence actionable policy measures would thusseem highly unlikely. Here, we take a system-wide view and investigate the timing of school attacks and the dynamical feedback with social media. We identifya trend divergence in which college attacks have continued to accelerate over the last 25 years while those carried out on K-12 schools have slowed down. We estab-lish the copycat effect in school shootings and use a Hawkes process to model the statistical association between social media chatter and the probability of an attackin the following days. While hinting at causality, this relationship may also help mitigate the frequency and intensity of future attacks.