Wavefront and caustic surfaces of refractive laser beam shaper
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
We study the composition of random permutations drawn from a small family of O(n3) simple permutations on (0, 1)n. Specifically, we ask how many randomly selected simple permutations need be composed to yield a permutation that is close to k-wise independent. We improve on the results of Cowers (Combin Probab Comput 5 (1996) 119-130) and Hoory et al. (Presented at 31st ICALP 2004) and show that it suffices to compose min(O(n3k 2), Õ(n2k2)) random permutations from this family for any n ≥ 3 and k ≤ 2n - 2. The Õ notation suppresses a poly logarithmic factor in k and n. © 2007 Wiley Periodicals, Inc.
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
John A. Hoffnagle, William D. Hinsberg, et al.
Microlithography 2003
Chai Wah Wu
Linear Algebra and Its Applications
Vladimir Yanovski, Israel A. Wagner, et al.
Ann. Math. Artif. Intell.