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Math

+ - World's Subways Share Common Mathematical Structure

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Hugh Pickens writes
Hugh Pickens writes writes "No two subway systems have the same design. New York City’s haphazard rail system differs markedly from the highly organized Moscow Metro, or the tangled spaghetti of Tokyo’s subway network. Now BBC reports that a study analyzing 14 subway networks around the world has discovered that the distribution of stations within each of the subway networks, as well as common proportions of the numbers of lines, stations, and total distances seem to converge over time to a similar structure regardless of where the networks were, when they were begun, or how quickly they reached their current layout. "Although these (networks) might appear to be planned in some centralized manner, it is our contention here that subway systems like many other features of city systems evolve and self-organize themselves as the product of a stream of rational but usually uncoordinated decisions taking place through time," write the study authors. The researchers uncovered three simple features that make subway system topologies similar all around the world. First, subway networks can be divided into a core and branches, like a spider with many legs. The “core” typically sits beneath the city’s center, and its stations usually form a ring shape. Second, the branches tend to be about twice as long as the width of the core. The wider the core, the longer the branches. Last, an average of 20 percent of the stations in the core link two or more subway lines, allowing people to make transfers. "The apparent convergence towards a unique network shape in the temporal limit suggests the existence of dominant, universal mechanisms governing the evolution of these structures.""
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World's Subways Share Common Mathematical Structure

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