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##### DM-41 - Fuzzy logic
• Describe how linear functions are used to fuzzify input data (i.e., mapping domain values to linguistic variables)
• Support or refute the statement by Lotfi Zadeh, that “As complexity rises, precise statements lose meaning and meaningful statements lose precision,” as it relates to GIS&T
• Explain why fuzzy logic, rather then Boolean algebra models, can be useful for representing real world boundaries between different tree species
##### DM-28 - Topological relationships
• Define various terms used to describe topological relationships, such as disjoint, overlap, within, and intersect
• List the possible topological relationships between entities in space (e.g., 9-intersection) and time
• Use methods that analyze topological relationships
• Recognize the contributions of topology (the branch of mathematics) to the study of geographic relationships
• Describe geographic phenomena in terms of their topological relationships in space and time to other phenomena
##### DM-15 - The network model
• Define the following terms pertaining to a network: Loops, multiple edges, the degree of a vertex, walk, trail, path, cycle, fundamental cycle
• List definitions of networks that apply to specific applications or industries
• Create an adjacency table from a sample network
• Explain how a graph can be written as an adjacency matrix and how this can be used to calculate topological shortest paths in the graph
• Create an incidence matrix from a sample network
• Explain how a graph (network) may be directed or undirected
• Demonstrate how attributes of networks can be used to represent cost, time, distance, or many other measures
• Demonstrate how the star (or forward star) data structure, which is often employed when digitally storing network information, violates relational normal form, but allows for much faster search and retrieval in network databases
• Discuss some of the difficulties of applying the standard process-pattern concept to lines and networks
• Demonstrate how a network is a connected set of edges and vertices
##### DM-87 - Raster resampling
• Evaluate methods used by contemporary GIS software to resample raster data on-the-fly during display
• Select appropriate interpolation techniques to resample particular types of values in raster data (e.g., nominal using nearest neighbor)
• Resample multiple raster data sets to a single resolution to enable overlay
• Resample raster data sets (e.g., terrain, satellite imagery) to a resolution appropriate for a map of a particular scale
• Discuss the consequences of increasing and decreasing resolution
• Define “metadata” in the context of the geospatial data set
• Use a metadata utility to create a geospatial metadata document for a digital database you created
• Formulate metadata for a graphic output that would be distributed to the general public
• Formulate metadata for a geostatistical analysis that would be released to an experienced audience
• Compose data integrity statements for a geostatistical or spatial analysis to be included in graphic output
• Identify software tools available to support metadata creation
• Interpret the elements of an existing metadata document
• Explain why metadata production should be integrated into the data production and database development workflows, rather than treated as an ancillary activity
• Outline the elements of the U.S. geospatial metadata standard
• Explain the ways in which metadata increases the value of geospatial data
##### DM-14 - Classic vector data models
• Illustrate the GBF/DIME data model
• Describe a Freeman-Huffman chain code
• Describe the relationship of Freeman-Huffman chain codes to the raster model
• Discuss the impact of early prototype data models (e.g., POLYVRT and GBF/DIME) on contemporary vector formats
• Describe the relationship between the GBF/DIME and TIGER structures, the rationale for their design, and their intended primary uses, paying particular attention to the role of graph theory in establishing the difference between GBF/DIME and TIGER files
• Explain what makes POLYVRT a hierarchical vector data model
##### DM-09 - The hexagonal model
• Illustrate the hexagonal model
• Explain the limitations of the grid model compared to the hexagonal model
• Exemplify the uses (past and potential) of the hexagonal model
##### DM-58 - Content standards
• Differentiate between a controlled vocabulary and an ontology
• Describe a domain ontology or vocabulary (i.e., land use classification systems, surveyor codes, data dictionaries, place names, or benthic habitat classification system)
• Describe how a domain ontology or vocabulary facilitates data sharing
• Define “thesaurus” as it pertains to geospatial metadata
• Describe the primary focus of the following content standards: FGDC, Dublin Core Metadata Initiative, and ISO 19115
• Differentiate between a content standard and a profile
• Describe some of the profiles created for the Content Standard for Digital Geospatial Metadata (CSDGM)