Before illustrating the calculation of the kernel density for multi-dimensional USM hypercube it is useful to illustrate the procedure for the one-dimensional example of a binary sequence such as 'ABABAAA'. The corresponding USM forward coordinates would be [0.3138 0.6569 0.3284 0.6642 0.3321 0.1661 0.0830] and the corresponding kernel density, Equation 2, for all positions in the one-dimensional USM map are shown in Figure 2 for different values of memory length, L, and smoothing, S.