# Event Sequences and time intervals between places:

• There are different ways to extract temporal distances from the individual event sequences
• the time between consecutive events

E1          E2         E3          E4
d12           +--------+
d23                         +-------+
d34                                      +---------+

• we also can add  the temporal distances between non-consecutive events
E1          E2         E3          E4
d13          +--------------------+
d14          +--------------------------------+
d24                          +--------------------+

• both  result in different distributions of   temporal distances  between pairs of  events
• a simple way to characterize these distributions is to use their means to describe the transitions between different places
• is the resulting matrix of mean time differences symmetric ? (what could that mean ??) otherwise symmetrize

•

# Analysis

• We propose to analyze the temporal distances in relation to geographic space
• we use the geographical coordinates of the places for the layout the nodes of the graph
• for any place we additionally have a vector of  mean time differences to all places
• a vector of arbitrary time-thresholds can now be used to determine the sets of all places that can be reached from a given source in a given time intervall.
• this results in a number of sets
• each of these sets contains all places that have been visited from this place in a given time intervall
• sets for smaller time threshholds are subsets of places of those for larger time-intervalls
• using the geographical coordinates of the places in each set allows to compute their convex hulls. These describe the area in geographic space that has been accessed from a start point in a given time.
• Repeating the analysis for several places allows to study the intersection of places that are reached from different places in similar times.

# A Sketch of a potential Solution

• Three locations (100, 113, 51) have been chosen as start points of the analysis
• Three convex hulls show for each of the places the geographical domains (the set of nodes) that have been visited in the next five hours, the next day .. the next two days