Physical Sciences and Mathematics Commons^™

Mathematical Models And Tools To Understand Coupled Circadian Oscillations And Limit Cycling Systems, Guangyuan Liao

Dissertations

The circadian rhythm refers to an internal body process that regulates many body processes including the sleep-wake cycle, digestion and hormone release. The ability of a circadian system to entrain to the 24-hour light-dark cycle is one of the most important properties. There are several scenarios in which circadian oscillators do not directly receive light-dark forcing. Instead they are part of hierarchical systems in which, as \peripheral" oscillators, they are periodically forced by other \central" circadian oscillators that do directly receive light input. Such dynamics are modeled as hierarchical coupled limit cycle systems. Those models usually have a large population, …

Comparison Of Longitudinal Changes In Resting State Functional Magnetic Resonance Imaging Between Alzheimer’S And Healthy Controls, Berk Can Yilmaz

Theses

Resting State Functional Magnetic Resonance Imaging (rs-fMRI) is a technique that is widely used for analyzing brain function using different approaches and methods. This study involves rs-fMRI analysis of Blood Oxygenation Level Dependent (BOLD) signals acquired from Alzheimer’s disease (AD) Patients and Healthy Controls (HC). Each subject in the study had both functional and anatomical images with at least one rs-fMRI scan with their Anatomical (T1) scans. Previous rs-fMRI studies have demonstrated that AD shows differences in Amplitude of Low Frequency (<0.1 Hz) Fluctuations (ALFF), and Regional Homogeneity (ReHo) measures according to HCs.

The aim of the study is to investigate individual and group level differences using ReHo and mALFF related …

Data Assimilation For Conductance-Based Neuronal Models, Matthew Moye

Dissertations

This dissertation illustrates the use of data assimilation algorithms to estimate unobserved variables and unknown parameters of conductance-based neuronal models. Modern data assimilation (DA) techniques are widely used in climate science and weather prediction, but have only recently begun to be applied in neuroscience. The two main classes of DA techniques are sequential methods and variational methods. Throughout this work, twin experiments, where the data is synthetically generated from output of the model, are used to validate use of these techniques for conductance-based models observing only the voltage trace. In Chapter 1, these techniques are described in detail and the …