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SLEEP-WAKE TRANSITION DYNAMICS AND POWER-LAW FITTING WITH AN UPPER BOUND
Olmez, Fatih

2014, Doctor of Philosophy, Ohio State University, Mathematics.
Sleep and wake bout durations, for mammalian species, are known to follow lawful statistical behavior. Experiments have shown that while sleep bout durations are exponentially distributed, the distribution of wake bout durations follow a power-law. Furthermore, in infant rats, wake bout durations are exponentially distributed which turns to a power-law only when the animal develops.
In this dissertation, we analyze the sleep-wake regulatory system as a competitive graph model in order to understand the relation between the degree distributions of the graph and the resulting distribution of the bout durations. For graphs with small average excitatory and inhibitory degrees, simulated sleep and wake bout durations are found to follow power-law distributions but only in finite intervals. For a careful identification of power-law distributions in finite intervals, we developed a robust method for fitting a power-law distribution with an upper bound. This new method is also applied on real sleep and wake bout durations collected from rat experiments, and the numerical analysis showed that sleep bouts are exponentially distributed only in the tail which is preceded by a power-law distributed region in a finite interval.
Janet Best (Advisor)
Edward Overman (Committee Member)
David Sivakoff (Committee Member)
Vincent Billock (Other)
185 p.

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Olmez, F. (2014). SLEEP-WAKE TRANSITION DYNAMICS AND POWER-LAW FITTING WITH AN UPPER BOUND. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Olmez, Fatih. "SLEEP-WAKE TRANSITION DYNAMICS AND POWER-LAW FITTING WITH AN UPPER BOUND." Electronic Thesis or Dissertation. Ohio State University, 2014. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Olmez, Fatih "SLEEP-WAKE TRANSITION DYNAMICS AND POWER-LAW FITTING WITH AN UPPER BOUND." Electronic Thesis or Dissertation. Ohio State University, 2014. https://etd.ohiolink.edu/

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Full text release has been delayed at the author's request until September 23, 2019