Approximate Conditional Distributions of Distances between Nodes in a Two-Dimensional Sensor Network
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Random restricted matching and lower bounds for combinatorial optimization
Journal of Combinatorial Optimization
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By a ''box integral'' we mean here an expectation where r@? runs over the unit n-cube, with q@? and s fixed, explicitly:@!"0^1...@!"0^1((r"1-q"1)^2+...+(r"n-q"n)^2)^s^/^2dr"1...dr"n.The study of box integrals leads one naturally into several disparate fields of analysis. While previous studies have focused upon symbolic evaluation and asymptotic analysis of special cases (notably s=1), we work herein more generally-in interdisciplinary fashion-developing results such as: (1) analytic continuation (in complex s), (2) relevant combinatorial identities, (3) rapidly converging series, (4) statistical inferences, (5) connections to mathematical physics, and (6) extreme-precision quadrature techniques appropriate for these integrals. These intuitions and results open up avenues of experimental mathematics, with a view to new conjectures and theorems on integrals of this type.