S1 Fig: Correlation between GCD and travel cost (maximum, minimum, and symmetric).S2 Fig. Koryakov’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right)S3 Fig. Alekseev’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right)S4 Fig. Schulze’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right)S5 Fig. Filatov & Daniel’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right)S6 Fig. Gudava’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right)S7 Fig. Mudrak’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right)S8 Fig. Flat topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right)S9 Fig. Results for 77 villages (imputed trees)S10 Fig. Kendall’s W for the correlation of each phylogeny with geography, using travel cost (compare withFig 6)S11 Fig. Distributions of Kendall’s W for permuted topologies (1,000 permutations), using travel cost. Dashed lines represent the mean of the distribution, and red full lines represent the observed value for the topology, as red bars in S9 Fig. Compare withFig 7.S12 Fig: Distributions of Kendall’s W for re-sampled village sets (1,000 permutations), using travel costs. Dashed lines represent the mean of the distribution, and red full lines represent the observed value for the topology, as red bars in S9 Fig. Compare withFig 8.S1 Table. List of all villages and languagesS1 File. Comparison of geographic distances (travel cost vs. great circle distance)S2 File. Discussion on imputed treesS3 File. Code 0-data-cleaning.RS4 File. Code 1-leastcostpath.RS5 File. Code 2-phylogenies.RS6 File. Code 3-correlations.R S1 Fig: Correlation between GCD and travel cost (maximum, minimum, and symmetric). S2 Fig. Koryakov’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right) S3 Fig. Alekseev’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right) S4 Fig. Schulze’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right) S5 Fig. Filatov & Daniel’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right) S6 Fig. Gudava’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right) S7 Fig. Mudrak’s topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right) S8 Fig. Flat topology: imputed tree with 77 villages (left) and simplified tree with 8 languages (right) S9 Fig. Results for 77 villages (imputed trees) S10 Fig. Kendall’s W for the correlation of each phylogeny with geography, using travel cost (compare withFig 6) S11 Fig. Distributions of Kendall’s W for permuted topologies (1,000 permutations), using travel cost. Dashed lines represent the mean of the distribution, and red full lines represent the observed value for the topology, as red bars in S9 Fig. Compare withFig 7. S12 Fig: Distributions of Kendall’s W for re-sampled village sets (1,000 permutations), using travel costs. Dashed lines represent the mean of the distribution, and red full lines represent the observed value for the topology, as red bars in S9 Fig. Compare withFig 8. S1 Table. List of all villages and languages S1 File. Comparison of geographic distances (travel cost vs. great circle distance) S2 File. Discussion on imputed trees S3 File. Code 0-data-cleaning.R S4 File. Code 1-leastcostpath.R S5 File. Code 2-phylogenies.R S6 File. Code 3-correlations.R (ZIP)

We proposed a new methodology for reducing multiple types of rasterization errors to simultaneously preserve the spatial properties of area, shape, and topology in polygon-to-raster conversion. By reassigning cells of the rasterized outcome, the method first compensates for the loss in shape properties. Topological changes are then corrected by comparing the topological relations of raster regions and their corresponding polygons. Finally, the areas between pairs of neighboring regions are coordinated to maintain area properties.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The geographic data are built from the Technical Information Management System (TIMS). TIMS consists of two separate databases: an attribute database and a spatial database. The attribute information for offshore activities is stored in the TIMS database. The spatial database is a combination of the ARC/INFO and FINDER databases and contains all the coordinates and topology information for geographic features. The attribute and spatial databases are interconnected through the use of common data elements in both databases, thereby creating the spatial datasets. The data in the mapping files are made up of straight-line segments. If an arc existed in the original data, it has been replaced with a series of straight lines that approximate the arc. The Gulf of America OCS Region stores all its mapping data in longitude and latitude format. All coordinates are in NAD 27. Data can be obtained in three types of digital formats: INTERACTIVE MAP: The ArcGIS web maps are an interactive display of geographic information, containing a basemap, a set of data layers (many of which include interactive pop-up windows with information about the data), an extent, navigation tools to pan and zoom, and additional tools for geospatial analysis. SHP: A Shapefile is a digital vector (non-topological) storage format for storing geometric location and associated attribute information. Shapefiles can support point, line, and area features with attributes held in a dBASE format file. GEODATABASE: An ArcGIS geodatabase is a collection of geographic datasets of various types held in a common file system folder, a Microsoft Access database, or a multiuser relational DBMS (such as Oracle, Microsoft SQL Server, PostgreSQL, Informix, or IBM DB2). The geodatabase is the native data structure for ArcGIS and is the primary data format used for editing and data management.

description: Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then, be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.; abstract: Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then, be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

Comparison between the extracted components and the class they were matched to, for the case . Missing nodes are nodes (students) that are known to be in the class but do not belong to the components that was matched to that class.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

description: Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile. The Economic Census topological faces shapefile is similar to the current shapefile, except that the face boundaries match the vintage of the 2012 Economic Census and the attributes include the Economic Census geographic areas.; abstract: Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile. The Economic Census topological faces shapefile is similar to the current shapefile, except that the face boundaries match the vintage of the 2012 Economic Census and the attributes include the Economic Census geographic areas.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for almost all geographic areas for which the Census Bureau tabulates data for both the 2010 Census and Census 2000. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

The TIGER/Line shapefiles and related database files (.dbf) are an extract of selected geographic and cartographic information from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). The MTDB represents a seamless national file with no overlaps or gaps between parts, however, each TIGER/Line shapefile is designed to stand alone as an independent data set, or they can be combined to cover the entire nation. Face refers to the areal (polygon) topological primitives that make up MTDB. A face is bounded by one or more edges; its boundary includes only the edges that separate it from other faces, not any interior edges contained within the area of the face. The Topological Faces Shapefile contains the attributes of each topological primitive face. Each face has a unique topological face identifier (TFID) value. Each face in the shapefile includes the key geographic area codes for all geographic areas for which the Census Bureau tabulates data for both the 2020 Census and the annual estimates and surveys. The geometries of each of these geographic areas can then be built by dissolving the face geometries on the appropriate key geographic area codes in the Topological Faces Shapefile.

Matrix obtained through NTF containing the number of students in each community projected over the different classes.