roomthily

comparison of Census data, the gravity model and the radiation model to predict the movement between cities (Northeastern, MIT, University of Padua)

via The Atlantic Cities

The “gravity law” has several other limitations, most of which should be obvious to even the most dimwitted individual with an advanced dual degree in complex network mathematics and physics, and suffice it to say these setbacks have inspired other researchers to look for a better one.

proofmathisbeautiful:

cloois:

The distribution of opening moves in chess has been shown to follow Zipf’s law (a linguistic model of the occurrence of words in written English):

We perform a quantitative analysis of extensive chess databases and showthat the frequencies of opening moves are distributed according to a power law with an exponent that increases linearly with the game depth, whereas the pooled distribution of all opening weights follows Zipf’s law with universal exponent. We propose a simple stochastic process that is able to capture the observed playing statistics and show that the Zipf law arises from the self-similar nature of the game tree of chess. Thus,in the case of hierarchical fragmentation the scaling is truly universal and independent of a particular generating mechanism. Our findings are of relevance in general processes with composite decisions.

also used to detect financial fraud - a person entering random numbers does not really achieve randomness.