Garlaschi, Stefano (2016) Rank-based Markov chains and self-organized critical for written communication. [Laurea triennale]
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In the thesis I study regular statistical patterns in human written communication through modeling and data. I report the analysis of several databases comprised of hundred of users of email, paper mail and sms and show that after a re-clocking through activity of each user, universality emerges in that the response times of each user follow a -3/2 power-law statistics across all the media and databases. Such regularities can be explained by a simple model based on a markovian queue driven by priority. At the end, I analyze the model from a mathematical perspective using techniques from stochastic processes to unveil the mechanism that produce a power-law tail for execution times for the tasks in the queue. The mechanism at work here, can be found also in other models within the framework of Self-organized criticality. These models with their applications are also briefly illustrated in the thesis. To complete the thesis work I read papers from the recent literature on the subject and reproduce data analysis and computations.
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