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Cox Processes and Their Use In Mathematical Models of Sleep-Wake Regulation

Dinitz, Thomas, Dinitz
http://rave.ohiolink.edu/etdc/view?acc_num=osu1512083964984545

Abstract Details

2017, Doctor of Philosophy, Ohio State University, Mathematics.
The neural network controlling sleep-wake cycling in mammals is an area of active research. In experimental data we see a large degree of variance in the firing rate for some neurons involved in sleep-wake regulation. However, the role stochasticity plays in determining the behavior of the network is not well understood. Because the stochasticity in the network comes, in large part, from the random spike times of neurons, doubly stochastic processes provide a natural foundation for a model of this network. In this thesis, we analyze an existing model that utilizes doubly stochastic processes and show the existence and uniqueness of an invariant measure. We also work with the simplest form of this model and show it is capable of generating bout distributions as seen in the data. In the second part of this thesis, we use the same mathematical formalism and develop a new model that incorporates a more complete understanding of the network structure and physiological mechanisms involved in sleep-wake regulation. We validate the new model against experimental data, and propose a few testable predictions that could be used to further validate and refine the model.
Janet Best (Advisor)
David Sivakoff (Committee Member)
Chuan Xue (Committee Member)
108 p.
Mathematics

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Citations

  • Dinitz, Dinitz, T. (2017). Cox Processes and Their Use In Mathematical Models of Sleep-Wake Regulation [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1512083964984545

    APA Style (7th edition)

  • Dinitz, Dinitz, Thomas. Cox Processes and Their Use In Mathematical Models of Sleep-Wake Regulation. 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1512083964984545.

    MLA Style (8th edition)

  • Dinitz, Dinitz, Thomas. "Cox Processes and Their Use In Mathematical Models of Sleep-Wake Regulation." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1512083964984545

    Chicago Manual of Style (17th edition)

osu1512083964984545
248
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This open access ETD is published by The Ohio State University and OhioLINK.