Abstract
In this paper we aim to demonstrate how physical perspective enriches statistical analysis when dealing with a complex system of many interacting agents of non-physical origin. To this end, we discuss analysis of urban public transportation networks viewed as complex systems. In such studies, a multi-disciplinary approach is applied by integrating methods in both data processing and statistical physics to investigate the correlation between public transportation network topological features and their operational stability. These studies incorporate concepts of coarse graining and clusterization, universality and scaling, stability and percolation behavior, diffusion and fractal analysis.
Highlights
One of the most prominent scientists of our time, Steven Hawking, when asked about the main trends of science in the twenty-first century replied that he thinks it will be the century of complexity
In the case study discussed in this paper, we aim to demonstrate how a physical perspective can enrich statistical analysis and data processing when dealing with a complex system of many interacting agents “non-physical” in nature
Special systematization is being suggested, it classifies power-law statistics observed in different systems according to certain archetypal reasons that cause it [16, 51, 54, 65]. In this respect it is similar to distinguishing different universality classes in the theory of critical phenomena, see e.g. [40, 45]. Such power laws have been observed for the public transport network (PTN) too, as we show in several examples given below
Summary
One of the most prominent scientists of our time, Steven Hawking, when asked about the main trends of science in the twenty-first century replied that he thinks it will be the century of complexity (see [61]). The latter serves as a framework to formalize a system of interacting agents by allowing each agent to act as network node, where various kinds of interaction can be described as (weighted or unweighted, directed or undirected, multiple or unique) links The former equips complexity science with an arsenal of tools and concepts traditionally used in physics to describe collective phenomena. In the case study discussed in this paper, we aim to demonstrate how a physical perspective can enrich statistical analysis and data processing when dealing with a complex system of many interacting agents “non-physical” in nature To this end, we have chosen to consider public transportation networks where the data for each public transport network (PTN) includes information about the routes and the locations of each station. This motivated us in choosing the topic for this paper
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