Physical Sciences and Mathematics Commons^™

Biochemical Reactions Instigating Vision – Parameter Sensitivity Analysis, Sophonie Ketcha Tchoua

Masters Theses

The purpose of this work is to investigate the sensitivity of parameters involved in a cascade of biochemical reactions occurring in photoreceptor cells in the retina of the eye. This cascade constitutes the first stage of the elaborate process of vision, by which light captured in a photoreceptor generates an electrical signal. It is this signal that travels to the brain enabling vision.

Sensitivity on parameters was performed on an ODE model of the biochemical cascade using two methods. One method used SimLab, a statistical sensitivity analysis program. We found that there are at most five important parameters out of …

A Note On Hamel Bases, Jeremy S. Higdon

Masters Theses

The purpose of this paper is to discuss certain properties of Hamel bases. In particular, we reprove and generalize a theorem of R. Mabry (Aequations Mathematicae 71 (2006) p. 294-299) on the non-existence of nontrivial Hamel bases closed under multiplication.

Tree-Like Spaces With The Fixed-Point Property, Realized As Inverse Limits Of Special Finite Trees, Jennifer Katherine Aust

Masters Theses

In this paper, we explore some properties of inverse limit sequences on sub-spaces of Euclidean n-space. We address some well-known examples, in particular the example by David Bellamy of the "tree-like" continuum that does not have the fixed-point property. We highlight some spaces with the fixed-point property that are between snake-like continua and Bellamy's example in their level of complexity. Specifically, we prove the fixed-point property for inverse limits of limit sequences on the unit interval and on the n-ad (in two configurations), and for inverse limits that can be mapped via a continuous function with small point pre-images to …