Physical Sciences and Mathematics | Open Access Articles

A Multiple Linear Regression Analysis On Mathematics Placement At The University Of Tennessee, Knoxville, Steven K. Moore Dec 2004

A Multiple Linear Regression Analysis On Mathematics Placement At The University Of Tennessee, Knoxville, Steven K. Moore

Masters Theses

This paper looks at solving the least squares problem and then using that theory to solve a simple multiple regression analysis for placing students into mathematics courses at the University of Tennessee, Knoxville.

The first chapter is an introduction and a basic outline of the problem. Chapter 2 outlines the theory behind solving an actual least squares problem for both the general case and for the particular case of nonsingular matrices. Chapter 3 discusses assumptions that must be made when running the analysis.

In chapters 4 and 5 computers are discussed and software output is explained. Finally, Chapter 6 gives …

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A Study Of Hidden Markov Model, Yang Liu Aug 2004

A Study Of Hidden Markov Model, Yang Liu

Masters Theses

The purpose of this thesis is fourfold: Introduce the definition of Hidden Markov Model. Present three problems about HMM that must be solved for the model to be useful in real-world application. Cover the solution of the three basic problems; explain some algorithms in detail as well as the mathematical proof. And finally, give some examples to show how these algorithms work.

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Modeling The Cascade Of Reactions In Visual Transduction, Philip Torry Patton Aug 2004

Modeling The Cascade Of Reactions In Visual Transduction, Philip Torry Patton

Masters Theses

Phototransduction in the process by which light energy is transferred to an electrical potential by photoreceptors in the eye. Recently, Hamer et al proposed a mechanism for the cascade of reactions that occurs when a rhodopsin molecule on the surface of a disc in the rod photoreceptor becomes activated. From these reactions, one can derive a system of ordinary differential equations to simulate phototransduction.

These ODEs are solved numerically using forward Euler’s method. The products of this cascade are then used to predict the drop in photocurrent that occurs. A kinetic Monte Carlo simulation with the Gillespie algorithm is implemented …

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Mathematical Representations Of The Architecture Of Graphical User Interfaces, Eric Freeman Mann Aug 2004

Mathematical Representations Of The Architecture Of Graphical User Interfaces, Eric Freeman Mann

Masters Theses

This text is an introduction to mathematical representations of graphical user interfaces, GUIs. Vectors are employed as a means to represent the state of a GUI and the user interaction with a GUI. These representations form a model of the behavior of a GUI over time. The usefulness of the model in testing and developing well-behaved GUIs is discussed and demonstrated by example.

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Fractured Branched Circle Packings On The Plane, James Russell Ashe Aug 2004

Fractured Branched Circle Packings On The Plane, James Russell Ashe

Masters Theses

William Thurston first proposed that real circles could be used to approximate the underlying infinitesimal circles of conformal maps in 1985. Inspired pioneers developed Circle Packing into a very rich and deep field that can be used as a method for constructing discrete conformal maps of surfaces on different types of geometries. Offering the advantages of a computational method that lends itself to experimentation and the easy creation of visual models, Circle Packing has proven itself as valuable new tool in approaching both old and new problems.

In particular, Circle Packing has been used to make discrete analogues of continuous …

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Practical Approach To Incorporating Maple Into The Finite Mathematics Course: 3 Modules And 8 Case Studies, Jonica Helene Craft-Mcbride Jan 2004