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Open quantum systems refer to systems that are affected by interaction with the environment. The effects of these unwanted interactions, called \emph{quantum noise}, are studied using dynamical maps. We study the geometry of these maps in this work. We review the canonical representations of dynamical maps such as reduced dynamics, $\mathcal{A}$ and $\mathcal{B}$ forms and operator sum representation. We develop a framework for simplifying the action of dynamical maps in terms of their action on the coherence vector associated with the density matrix. We use the framework to describe the geometry of depolarization, dephasing and dissipation in the domain of complete positivity. We give a geometric picture of how two-, three- and four-level systems are affected by these common forms of quantum noises. We show useful similarities between two- and four-level depolarizing maps and give a generalization for $n$-qubits. We also derive important results that restrict dephasing and dissipation. / text

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Geographical Information Systems (GIS) play an important role in environmental management solutions, and they are being used with increasing frequency in environmental studies. The use of GIS technology in environmental studies provides a better way to manage, analyze, display and share the information. In this thesis, I automated a process for constructing GIS maps of odor complaints and inspections that have been used to study odor complaints in the vicinity of three landfills in Jefferson Parish. I provided an application that integrates daily environmental observation and monitoring data into a GIS and publishes the resulting maps through the Internet. The user's interaction with the web-based maps does not require any GIS expertise. A Webapplication was also implemented for managing the list of the constructed maps. The maps are deleted or updated through the manager application, a friendly interface application that does not require users to have any GIS technology knowledge.

Learning maps have been used to represent student knowledge for many years. These maps are usually hand made by experts in a given domain. However, these hand-made maps have not been found to be predictive of student performance. Several methods have been proposed to find bet-ter fitting learning maps. These methods include the Learning Factors Analysis (LFA) model and the Rule-space method. In this thesis we report on the application of one of the proposed operations in the LFA method to a small section of a skill graph and develop a greedy search algorithm for finding better fitting models for this graph. Additionally an investigation of the factors that influence the search for better data fitting models using the proposed algorithm is reported. We also present an empirical study in which PLACEments, an adaptive testing system that employs a skill graph, is modified to test the strength of prerequisite skill links in a given learning map and propose a method for refining learning maps based on those findings. It was found that the proposed greedy search algorithm performs as well as an original skill graph but with a smaller set of skills in the graph. Additionally it was found that, among other factors, the number of unnecessary skills, the number of items in the graph, and the guess and slip rates of the items tagged with skills in the graph have an impact on the search. Further, the size of the evaluation data set impacts the search. The more data there is for the search, the more predictive the learned skill graph. Additionally, PLACEments, an adaptive testing feature of ASSISTments, has been found to be useful for refining skill graphs by detecting the strengths of prerequisite links between skills in a graph.