Table 1.
Summary of the studied emergencies and non-emergencies.
Figure 1.
Call anomalies during emergencies.
A, The time dependence of call volume in the vicinity of four emergencies and two non-emergencies (See Table 1). B, The temporal behavior of the relative call volume
of the events shown in A, where
, Vevent is the call volume on the day of the event (shown in red in A), and
is the average call volume during the same period of the week (the call volume during the previous week is shown in black in B). C, The relative change in the average number of calls placed per user (
) and the total number of users (
) making calls from the region indicates that the call anomaly is primarily due to a significant increase in the number of users that place calls during the events.
Figure 2.
The spatial impact of an emergency.
A, Maps of total anomalous call activity (activity during the event minus expected normal activity) for two-hour periods before (), during (
), and after (
) the bombing. The color code corresponds to the total change
, where the sum runs over the particular time period. B, Changes in call volume in regions at various distances
from the event epicenter. Note that the peak of the call volume anomaly for the bombing within the observed
km region is delayed by approximately 10 minutes compared to the
km epicenter region. No call anomaly is observed for
km. The earthquake covers a large spatial range so we instead choose three event regions A–C, at distances of 310 km, 340 km, and 425 km from the seismic epicenter (which was outside the studied region). C, To measure the distance dependence of the anomaly, we computed the total anomalous call volume in B before (
) and after (
) each event as a function of the distance
, revealing approximately exponential decay,
. Non-emergencies are spatially localized, with
km.
Figure 3.
Social characteristics of information cascades.
A, Changes in call volume for users directly affected by the event (), users that receive calls from
but are not near the event (
), users contacted by
but not in
or
(
), etc. For the bombing and plane crash, populations respond very rapidly, within minutes. B, The total amount of anomalous call activity in A before (during
) and after (during
) the event for each user group
quantifies the impact on the social network. We see that information propagates deeply into the social network for the bombing and plane crash. C, Top panel: the contact network formed between affected users during the bombing. Bottom panel: the call pattern between users that are active during the emergency during the previous week, indicating that the information cascade observed during the bombing is out of the ordinary. D, The distribution of shortest paths within the contact network quantifies the anomalous information cascade induced by the bombing.
Figure 4.
Analyzing a composite event (evacuation preceding an explosion).
A, Call activity increases during the evacuation () but levels off after the initial warning, until the explosion at
causes a much larger increase in call activity. B, Spatially, the evacuation causes a sharply localized activity spike (
km), but the explosion increases the spatial extent dramatically (
km). C–D, The evacuation only activates the
(eyewitness) and
groups, meaning that information fails to propagate significantly beyond the initial group and their immediate ties. However, the blast not only leads to a further increase in call activity in the
and
groups, but also triggers the second neighbors
.
Figure 5.
Systematic response mechanisms during emergencies.
A, The midpoint fraction quantifying the onset speed of anomalous call activity (a lower
indicates a faster onset). Emergencies display a more abrupt call anomaly than non-emergencies, which feature gradual buildups of anomalous call activity. B, The spatial extent of the events, quantified by
, indicates that non-emergency events are far more centrally localized than unexpected emergencies. C, The relative cascade size
, where
is the number of users in the social cascade. D,
, where
is the probability of calling an acquaintance and
is the standard deviation of
.