Measuring burstiness for finite event sequences

Kim, Eun Kyeong; Jo, Hang-Hyun

doi:10.1103/physreve.94.032311

Cited by 55 publications

(57 citation statements)

References 33 publications

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“…For the numerical simulations, the event sequences were generated using the implementation method of the BGB mechanism in Subsection II B, but using Eq. (30). We confirm the tendency that the larger positive value of M is associated with the smaller value of β, i.e., the heavier tail.…”

Section: Limits Of the Memory Coefficient In Measuring Correlationssupporting

confidence: 79%

Bursty Time Series Analysis for Temporal Networks

Hiraoka

2019

Computational Social Sciences

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Characterizing bursty temporal interaction patterns of temporal networks is crucial to investigate the evolution of temporal networks as well as various collective dynamics taking place in them. The temporal interaction patterns have been described by a series of interaction events or event sequences, often showing non-Poissonian or bursty nature. Such bursty event sequences can be understood not only by heterogeneous interevent times (IETs) but also by correlations between IETs. The heterogeneities of IETs have been extensively studied in recent years, while the correlations between IETs are far from being fully explored. In this Chapter, we introduce various measures for bursty time series analysis, such as the IET distribution, the burstiness parameter, the memory coefficient, the bursty train sizes, and the autocorrelation function, to discuss the relation between those measures. Then we show that the correlations between IETs can affect the speed of spreading taking place in temporal networks. Finally, we discuss possible research topics regarding bursty time series analysis for temporal networks. * This is a preprint for a chapter to appear in Temporal Network Theory edited by P. Holme and J. Saramäki (https: //www.springer.com/gp/book/9783030234942).

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Section: Limits Of the Memory Coefficient In Measuring Correlationssupporting

confidence: 79%

Bursty Time Series Analysis for Temporal Networks

Hiraoka

2019

Computational Social Sciences

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“…The burstiness coefficient 28 is used to quantify the deviation of a given time series from a Poissonian signal, and is based on measuring the extent to which the coefficient of variation deviates from unity. In order to avoid finite-size effects in measuring the burstiness parameter 6 , 35 , we collect the IETs from all nodes/edges and measure burstiness for this aggregated sequence of IETs. For a sequence of IETs with mean m and standard deviation σ , the burstiness coefficient is defined as …”

Section: Methodsmentioning

confidence: 99%

Lifetime-preserving reference models for characterizing spreading dynamics on temporal networks

Rao

Gernat

et al. 2018

Sci Rep

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To study how a certain network feature affects processes occurring on a temporal network, one often compares properties of the original network against those of a randomized reference model that lacks the feature in question. The randomly permuted times (PT) reference model is widely used to probe how temporal features affect spreading dynamics on temporal networks. However, PT implicitly assumes that edges and nodes are continuously active during the network sampling period – an assumption that does not always hold in real networks. We systematically analyze a recently-proposed restriction of PT that preserves node lifetimes (PTN), and a similar restriction (PTE) that also preserves edge lifetimes. We use PT, PTN, and PTE to characterize spreading dynamics on (i) synthetic networks with heterogeneous edge lifespans and tunable burstiness, and (ii) four real-world networks, including two in which nodes enter and leave the network dynamically. We find that predictions of spreading speed can change considerably with the choice of reference model. Moreover, the degree of disparity in the predictions reflects the extent of node/edge turnover, highlighting the importance of using lifetime-preserving reference models when nodes or edges are not continuously present in the network.

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“…where σ τ is the standard deviation of the inter-onset interval distribution and μ τ is the mean of the inter-onset interval distribution. A recent addition to the burstiness analysis includes an updated equation that takes into account the amount of inter-onset intervals in a distribution and therefore is more relevant for empirical work using finite time series ( Kim and Jo, 2016 ). Estimates from both equations converge when the inter-onset interval distributions include τ length > 100 intervals.…”

Section: Module 3: Tapping Into the Temporal Structure Of Developmentmentioning

confidence: 99%

Finding Structure in Time: Visualizing and Analyzing Behavioral Time Series

Barbaro

Abney

et al. 2020

Front. Psychol.

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The temporal structure of behavior contains a rich source of information about its dynamic organization, origins, and development. Today, advances in sensing and data storage allow researchers to collect multiple dimensions of behavioral data at a fine temporal scale both in and out of the laboratory, leading to the curation of massive multimodal corpora of behavior. However, along with these new opportunities come new challenges. Theories are often underspecified as to the exact nature of these unfolding interactions, and psychologists have limited ready-to-use methods and training for quantifying structures and patterns in behavioral time series. In this paper, we will introduce four techniques to interpret and analyze high-density multi-modal behavior data, namely, to: (1) visualize the raw time series, (2) describe the overall distributional structure of temporal events (Burstiness calculation), (3) characterize the non-linear dynamics over multiple timescales with Chromatic and Anisotropic Cross-Recurrence Quantification Analysis (CRQA), (4) and quantify the directional relations among a set of interdependent multimodal behavioral variables with Granger Causality. Each technique is introduced in a module with conceptual background, sample data drawn from empirical studies and ready-to-use Matlab scripts. The code modules showcase each technique's application with detailed documentation to allow more advanced users to adapt them to their own datasets. Additionally, to make our modules more accessible to beginner programmers, we provide a "Programming Basics" module that introduces common functions for working with behavioral timeseries data in Matlab. Together, the materials provide a practical introduction to a range of analyses that psychologists can use to discover temporal structure in high-density behavioral data.

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Measuring burstiness for finite event sequences

Cited by 55 publications

References 33 publications

Bursty Time Series Analysis for Temporal Networks

Bursty Time Series Analysis for Temporal Networks

Lifetime-preserving reference models for characterizing spreading dynamics on temporal networks

Finding Structure in Time: Visualizing and Analyzing Behavioral Time Series

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