Endogenous circadian clock regulation is essential to normal rhythmicity, particularly the timing of hormone release in the brain. In the context of mammalian reproduction, a surge of a specific hormone, gonadotrophin-releasing hormone (GnRH), initiates a surge of luteinizing hormone (LH) from the pituitary gland, which is required for ovulation in...
This thesis consists of extensions of results on a perpetual American swaption problem. Companies routinely plan to swap uncertain benefits with uncertain costs in the future for their own benefits. Our work explores the choice of timing policies associated with the swap in the form of an optimal stopping problem....
Preservation of rare plant species often requires establishment of new populations. Survivorship surveys are the most common method of post-introduction monitoring. However, they provide an incomplete picture of establishment success. This study is an attempt to develop a model for determining establishment success by determining the factors affecting recruitment in...
This thesis studies connections between disorder type in tree polymers and the branching random walk and presents an application to swarm site-selection. Chapter two extends results on tree polymers in the infinite volume limit to critical strong disorder. Almost sure (a.s.) convergence in the infinite volume limit is obtained for...
Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive...
Endogenous circadian clock regulation is essential to normal rhythmicity, particularly the timing of hormone release in the brain. In the context of mammalian reproduction, a surge of a specific hormone, gonadotrophin-releasing hormone (GnRH), initiates a surge of luteinizing hormone (LH) from the pituitary gland, which is required for ovulation in...
We examine a discrete-time quantum walk with two-step memory for a particle on a one-
dimensional infinite space. The walk is defined with a four-state memory space analogous to the
two-state coin space commonly used in discrete time quantum walks, and a method is presented
for calculating the time evolution...