Source-linked AI summary
Circadian pattern and burstiness in mobile phone communication
Hang-Hyun Jo, Márton Karsai, János Kertész, Kimmo Kaski
TL;DR
The paper examines whether bursty, heavy-tailed mobile-phone communication patterns arise only from circadian and weekly cycles or also from task-execution correlations. It systematically removes those cycles by rescaling event times and finds that heavy tails remain, identifying task execution as a possible source of residual burstiness.
Problem
The paper asks whether communication burstiness reflects only circadian and weekly cycles or also correlations from human task execution.
Method
The study extracts circadian and weekly patterns, removes them by rescaling mobile-phone call and message event times, and compares the resulting inter-event distributions with the originals.
Results
Heavy-tailed inter-event distributions remain after de-seasoning, while burstiness decreases but generally persists across individual and grouped analyses.
Takeaways & Limitations
The remaining burstiness is not only a consequence of circadian and weekly cycles and may also reflect correlations in human task execution.
Takeaways & Limitations
Using averaged event rates for individual de-seasoning may cause systematic errors when individual and group activity patterns differ.
Abstract
from arXiv · showhide
The temporal communication patterns of human individuals are known to be inhomogeneous or bursty, which is reflected as the heavy tail behavior in the inter-event time distribution. As the cause of such bursty behavior two main mechanisms have been suggested: a) Inhomogeneities due to the circadian and weekly activity patterns and b) inhomogeneities rooted in human task execution behavior. Here we investigate the roles of these mechanisms by developing and then applying systematic de-seasoning methods to remove the circadian and weekly patterns from the time-series of mobile phone communication events of individuals. We find that the heavy tails in the inter-event time distributions remain robustly with respect to this procedure, which clearly indicates that the human task execution based mechanism is a possible cause for the remaining burstiness in temporal mobile phone communication patterns.
1. Introduction
Human communication is bursty, with heavy-tailed inter-event times whose origins may include circadian and weekly cycles as well as task-execution correlations. The paper de-seasons mobile-phone data to test whether burstiness remains after removing these cycles.
- Human activity across communication channels is inhomogeneous or bursty, producing heavy-tailed inter-event time distributions.
- Circadian and weekly inactivity have been proposed to explain apparent power-law behavior through an inhomogeneous Poisson process.The model combines a time-dependent activity rate with shorter-timescale cascading bursty behavior.
- The paper asks whether human task execution contributes additional correlations beyond circadian- and weekly-cycle-driven inhomogeneities.
- The study removes circadian and weekly patterns from mobile-phone event data before examining the remaining temporal structure.Its motivation is to distinguish the origins of inhomogeneity when modeling human communication behavior.
- The proposed workflow extracts temporal patterns, rescales event timings to remove them, and compares de-seasoned with original inter-event distributions.The reported result is that heavy-tail power-law scaling remains, indicating task execution as a possible source of residual burstiness.
2. De-seasoning analysis
The paper systematically removes circadian and weekly activity patterns by rescaling mobile-phone communication event times, then evaluates how inter-event distributions and burstiness change. De-seasoning removes targeted periodic components but leaves heavy tails and bursty behavior largely intact.
- Data and observables: The analysis uses mobile-phone call records from 5.2×10^6 users, 10.6×10^6 links, and 322×10^6 events collected over 119 days.The dataset comes from a European operator with approximately 20% national market share.
- De-seasoning method: The method extracts periodic event rates and rescales event timings so high-activity intervals expand and low-activity intervals contract, producing a constant rescaled rate.The rescaled-time transformation is defined by ρ*(t*)dt* = ρ(t)dt with ρ*(t*) = 1.
- Burstiness measure: Burstiness compares the standard deviation and mean of inter-event times, with B0 denoting original burstiness and BT denoting burstiness after de-seasoning period T.B ranges from −1 for completely regular behavior to 1 for maximally bursty behavior, with B = 0 representing homogeneous Poisson behavior.
- Individual de-seasoning: Rescaled individual inter-event distributions retain heavy tails, while burstiness decreases from B0 ≈ 0.202 to B7 ≈ 0.174 and B28 ≈ 0.104 for a user with strength 200.For strength 3197, the corresponding values are B0 ≈ 0.469, B7 ≈ 0.254, and B28 ≈ 0.219; burstiness remains higher for the more active user.
- Individual de-seasoning: Across individual users, de-seasoning circadian and weekly patterns does not destroy bursty behavior irrespective of user strength.More active users have larger burstiness values, with strength-dependent decay rates changing around T = 7 days.
- Grouped de-seasoning: For same-strength groups, burstiness decreases only slightly as T increases but remains below the original group burstiness; group-level averaging can introduce systematic errors.These errors may arise because individual users and groups can have different circadian and weekly patterns; clustering users by activity patterns is suggested as a remedy.
- Power spectra analysis: Power spectra show that de-seasoning removes the periodic peak matching T while leaving longer cycles unaffected.T = 1 day removes the circadian peak, T = 7 days removes the weekly peak, and cycles longer than T remain.
3. Summary
The study removes circadian and weekly inhomogeneities from mobile phone communication data and finds that heavy-tailed inter-event times and burstiness remain. This supports human task-execution correlations as a possible source of the residual burstiness.
- The authors systematically de-season circadian and weekly patterns in mobile phone communication data to examine remaining temporal correlations.The procedure rescales event timings using extracted activity patterns.
- Heavy tails and burstiness remain after de-seasoning circadian and weekly cycle-driven inhomogeneities.The result is reported for both mobile phone calls and Short Messages.
- The remaining burstiness is consistent with correlations rooted in human task execution.The paper presents this as a possible mechanism rather than a definitive causal explanation.
- The circadian and weekly peaks are successfully removed from original power spectra by de-seasoning.
Appendix
The appendix applies de-seasoning to a large bidirectional Short Message dataset and examines how circadian and weekly cycles affect burstiness. Heavy-tailed inter-event distributions and burstiness remain largely robust after de-seasoning, while cycles longer than the chosen period persist.
- Dataset: The Short Message dataset contains 4.2 × 10^6 users, 8.5 × 10^6 links, and 114 × 10^6 events after retaining bidirectional interactions.Consecutive messages sent within 10 seconds were merged into one event.
- Activity patterns: Individual users and strength-based groups show varied circadian activity patterns, with the Short Message activity peak occurring around 11 PM.Averaged event rates are also examined for groups with equal or broad strength ranges.
- Inter-event distributions: Inter-event distributions follow a bimodal combination of power-law and Poisson components rather than a simple power law.The analysis compares original and rescaled distributions across users and strength-defined groups.
- Burstiness: Burstiness slowly decreases as the de-seasoning period T increases up to 7 days, indicating that removing circadian and weekly patterns does not considerably affect bursty behavior.Burstiness is evaluated for individual users and groups with equal or broad strength ranges.
- Power spectra and conclusion: Power-spectrum analysis removes circadian and weekly peaks, but cycles longer than T remain; the results support additional correlations such as human task execution as contributors to burstiness.The conclusion is based on the persistence of heavy tails and burstiness after de-seasoning.