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.

Isolation and Characterization of a Microorganism from Groundwater that Reduces Arsenate

This is an investigation into the microbially mediated processes involved in the transformation of arsenic. With the recent change in the Federal Maximum Contaminant Level for arsenic in drinking water, an increasing amount of resources are being devoted to understanding the mechanisms involved in the movement of arsenic. Arsenic in drinking water typically comes from natural sources, but the triggers that result in increased release of arsenic from parent material are poorly understood. Knowledge of these processes is necessary in order to make sound engineering decisions regarding drinking water management practices. Recent years have brought forth the idea that bacteria play a significant role in arsenic cycling. Groundwater is a major source of potable water in this and many other countries. To date, no reports have been made indicating the presence and activity of arsenate reducing bacteria in groundwater settings, which may increase dissolved arsenic concentrations. This research was designed to address this question and has shown that these bacteria are present in Maine groundwater. Two Maine wells were sampled in order to culture resident bacteria that are capable of dissimilatory arsenate reduction. Samples were collected using anaerobic techniques fiom wells in Northport and Green Lake. These samples were amended with specific compounds to enrich the resident population of arsenate utilizing bacteria. These cultures were monitored over time to establish rates of arsenate reduction. Cultures fiom both sites exhibited arsenate reduction in initial enrichment cultures. Isolates obtained fiom the Green Lake enrichments, however, did not reduce arsenate. This indicates either that a symbiotic relationship was required for the observed arsenate reduction or that fast-growing fermentative organisms that could survive in high arsenate media were picked in the isolation procedure. The Northport cultures exhibited continued arsenate reduction after isolation and successive transfers into fiesh media. The cultured bacteria reduced the majority of 1 a arsenate solutions in less than one week, accompanied by a corresponding oxidation of lactate. The 16s rRNA fiom the isolate was arnplifled and sequenced. The results of the DNA sequence analysis indicate that the rRNA sequence of the bacteria isolated at the Northport site is unique. This means that this strain of bacteria has not been reported before. It is in the same taxonomic subgroup as two previously described arsenate respirers. The implications of this study are significant. The fact that resident bacteria are capable of reducing arsenate has implications for water management practices. Reduction of arsenate to arsenite increases the mobility of the compound, as well as the toxicity. An understanding of the activity of these types of organisms is necessary in order to understand the contribution they are making to arsenic concentrations in drinking water. The next step in this work would be to quantitj the actual loading of dissolved arsenic present in aquifers because of these organisms.