A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

The Church Music Program: The Effect of Moving from Performance-based to Education-based Emphasis in a Church Music Program

This research project sought to answer the primary research question: What occurs when the music program in a church changes its emphasis from performance to education? This qualitative study of a church choir included participant observation of Wednesday evening and Sunday morning rehearsals over a 12 week period, individual interviews, group interviews, written responses, and written and visual assessment of musical skills. The goal was a rich description of the participants and emerging themes resulting from the shift in emphasis. Analysis of data occurred through inductive processing. Data was initially coded and then the codes were categorized into sub-themes, and finally into major themes. Early analysis of the data began with reflection in a researcher journal. Following the completion of the study the journal was entered into a word processor, as were transcriptions of videotaped rehearsals, and written reflections from the participants. After all data had been reviewed repeatedly and entered into the word processor, it was coded, reexamined, and finally categorized into sub-themes and themes. After coding and identification of major themes and sub-themes the finding were challenged by looking for disconfirming evidence. Finally, after the completion of the analysis stage, member checks were conducted. The results of the analysis of data revealed themes that could be associated either with the choir or the director. The key themes primarily associated with the choir were: Response to the change in rehearsal format; Attitude toward learning; Appropriateness of community learning model; and, Member's perceptions of the results of the program. The key themes associated with the director were identified as: Conductor assuming the role of educator; Conductor recognizing the choir as learners; Conductor treating rehearsals as a time for teaching and learning; and, Conductor's perception of the effectiveness of the change in focus. The study concluded that a change in focus from performance to education did not noticeably improve the sound of the choir after twelve-weeks. There were however, indications that improvements were being made by the individual members. Further study of the effects over a longer period of time is recommended.

Derivation of Change from Sequences of Snapshots

Current research in the domain of geographic information science considers possibilities of including another dimension, time, which is generally missing to this point. Users interested in changes have few functions available to compare datasets of spatial configurations at different points in time. Such a comparison of spatial configurations requires large amounts of manual labor. An automatic derivation of changes would decrease amounts of manual labor. The thesis introduces a set of methods that allows for an automatic derivation of changes. These methods analyze identity and topological states of objects in snapshots and derive types of change for the specific configuration of data. The set of change types that can be computed by the methods presented includes continuous changes such as growing, shrinking, and moving of objects. For these continuous changes identity remains unchanged, while topological relations might be altered over time. Also discrete changes such as merging and splitting where both identity and topology are affected can be derived. Evaluation of the methods using a prototype application with simple examples suggests that the methods compute uniquely and correctly the type of change that applied in spatial scenarios captured in two snapshots.