ORCID Identifier(s)

https://orcid.org/0000-0002-7839-1959

Graduation Semester and Year

Spring 2025

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Pedro D. Maia

Abstract

Sleep models are vital for understanding sleep dynamics and related disorders, but parameter estimation remains challenging. This thesis presents an automated framework for estimating parameters in sleep models comprising competing neuronal populations, each linked to a sleep stage, and evolving independently of weakly observed inputs. We focus on a system of coupled nonlinear ODEs representing three neuronal populations governing sleep-stage transitions. Using minimal clinical input, we employ a smoothed winner-takes-all strategy within a constrained minimization framework, reformulate the problem in an unconstrained setting via the Lagrangian, and derive the corresponding optimality conditions from state and adjoint equations. A projected nonlinear conjugate gradient scheme is then used to estimate the parameters numerically. Applying this framework to hypnogram data from cannabis users and non-users, we explore significant differences in inferred parameters, linking them to sleep regulation features. Finally, we explore how well sleep characteristics are reflected in these parameters.

Keywords

Sleep Dynamics, Parameter Estimation, Optimization, Dynamical Systems, Neuronal Networks.

Disciplines

Computational Neuroscience | Dynamic Systems | Non-linear Dynamics | Ordinary Differential Equations and Applied Dynamics

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