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Graduated symbol maps are another method to represent geographical data.
Hence may be regarded as a map on , called the Galois symbol map.
A proportional symbol map is better than choropleth maps for showing raw data totals.
A proportional symbols map uses symbols that are proportional the data that they are representing with point locations.
A proportional symbols map - what we informally call a "bubble" map - places a circle, scaled in proportion to the data, on top of each country.
For each symbol mapped in such a way, let be the th coordinate of the corner of the hypercube to which symbol s is mapped.
That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions.
Such restrictions permit the decoding of the original message by checking which of the possible source symbols mapped to the same symbol are valid under those restrictions.
The raw data on proportional symbol maps go hand in hand with the data shown on choropleth maps (Slocum, McMaster, Kessler, & Howard, 2005).
With an emphatic warning about the danger of depending on mechanical symbol mapping to understand Stevens's poems, one can propose that imagination, order and the ideal are often symbolized by blue, the moon, the polar north, winter, music, poetry, and art.