Uncertain locations, symmetry

VIII. SYMMETRY OF POINTS WITH UNCERTAIN LOCATIONS... 

Symmetry of Experimental Points with Uncertain Locations... 

Information obtained from any analytical instrument has a certain degree of uncertainty. In structural chemistry, the uncertainty may be in the location of the atoms, as obtained by, e.g., diffraction methods, due to all known causes (crystal imperfections, thermal motion, etc.). Thus quite often the data is given as a collection of probability distribution functions of point locations. Given points with such uncertain locations, the following questions regarding symmetry are of interest. 

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