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The master equation approach is proposed to describe the evolution of passengers in a subway system. With the transition rate constructed from simple geographical consideration, the evolution equation for the distribution of subway passengers is found to bear skew distributions including log-normal, Weibull, and power-law distributions. This approach is then applied to the Metropolitan Seoul Subway system: Analysis of the trip data of all passengers in a day reveals that the data in most cases fit well to the log-normal distributions. Implications of the results are also discussed.
The Metropolitan Seoul Subway system, consisting of 380 stations, provides the major transportation mode in the metropolitan Seoul area. Focusing on the network structure, we analyze statistical properties and topological consequences of the subway s
Network growth as described by the Duplication-Divergence model proposes a simple general idea for the evolution dynamics of natural networks. In particular it is an alternative to the well known Barabasi-Albert model when applied to protein-protein
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous efforts at a
Recently, with the availability of various traffic datasets, human mobility has been studied in different contexts. Researchers attempt to understand the collective behaviors of human movement with respect to the spatio-temporal distribution in traff
A derivation of the Dirac equation in `3+1 dimensions is presented based on a master equation approach originally developed for the `1+1 problem by McKeon and Ord. The method of derivation presented here suggests a mechanism by which the work of Knut