The patterns of motion of mobile agents has received recently wide attention in the literature. There is a number of recent studies centered around the motion behavior of many agents ranging from albatrosses to human beings. Special attention has bee
n given to the covered distances statistical distributions. In some cases, due to the lack of accurate data about the motion of the agents it has been necessary to plan very clever experiments to obtain them. These experiments try to infer the statistical properties of the agents real motion from the observed positions in consecutive time intervals. The length of the time intervals is a random variable taking values from a previously known statistical distribution or from a distribution deduced from empirical data. The aim of this work is to demonstrate that for a Gaussian Random Walker it is, in general, impossible to recover the real motion patterns distribution from the stroboscopic observation of the agents. Moreover, it is also shown that the distances distribution strongly depends on the agents observation time intervals. These claims are sustained by numerical experiments.
The network of 5823 cities of Mexico with a population more than 5000 inhabitants is studied. Our analysis is focused to the spectral properties of the adjacency matrix, the small-world properties of the network, the distribution of the clustering co
efficients and the degree distribution of the vertices. The connection of these features with the spread of epidemics on this network is also discussed.
