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We prove that the set of first k vertices of a Hamming graph in reverse-lexicographic order constitutes an extremal set minimizing the dimension-normalized edge-boundary over all k-vertex subsets of the graph. This generalizes a result of Lindsey and can be used to prove a tight lower bound for the isoperimetric number and the bisection width of arrays. 1.… (More)

The application of nonparametric probability density function estimation for the purpose of data analysis is well established. More recently, such methods have been applied to fluid flow calculations since the density of the fluid plays a crucial role in determining the flow. Furthermore, when the calculations involve directional or axial data, the domain… (More)

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