Neuroscience and Neurobiology Commons^™

Deep Hybrid Modeling Of Neuronal Dynamics Using Generative Adversarial Networks, Soheil Saghafi

Dissertations

Mechanistic modeling and machine learning methods are powerful techniques for approximating biological systems and making accurate predictions from data. However, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. This dissertation constructs Deep Hybrid Models that address these shortcomings by combining deep learning with mechanistic modeling. In particular, this dissertation uses Generative Adversarial Networks (GANs) to provide an inverse mapping of data to mechanistic models and identifies the distributions of mechanistic model parameters coherent to the data.

Chapter 1 provides background information on …

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, …