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Near Extensions and Alignment of Data in R(superscript)n
book

Near Extensions and Alignment of Data in R(superscript)n

by Steven B. Damelin
November 2023
Intermediate to advanced content levelIntermediate to advanced
192 pages
3h 29m
English
Wiley
Content preview from Near Extensions and Alignment of Data in R(superscript)n

19 Equidistribution: Extremal Newtonian-like Configurations, Group Invariant Discrepancy, Finite Fields, Combinatorial Designs, Linear Independent Vectors, Matroids and the Maximum Distance Separable Conjecture

We use the notation mu and nu for measures.

The problem of “distributing well” a large number of points on certain n-dimensional compact sets embedded in double-struck upper R Superscript n plus 1 (see Figures 19.119.6) is an interesting problem with numerous wide applications in diverse areas, for example, harmonic analysis, approximation theory, zeroes of extremal polynomials in all kinds of settings, singular operators, for example, Hilbert transforms, random matrix theory, crystal and molecule structure, electrostatics, special functions, Newtonian energy, extensions, alignment, data science, number theory, manifold learning, clustering, shortest paths, codes and discrepancy, computer vision, signal processing, biology, neuroscience, networks, clustering, optimal transport, and many others. We say the points equidistribute over the set or cover it.

Figure 19.1 , .

Figure 19.2 , .

Figure 19.3 , .

Figure 19.4 Torus, ...

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