De nitive work on permutation testing by Willem van Zwet his students and collaborators has given us a rich collection of tools for probability and statistics We have come upon a series of variationsâ€¦ (More)

A parallel prefix circuit has n inputs x1, x2, . . . , xn, and computes the n outputs yi = xi â€¢ xiâˆ’1 â€¢ Â· Â· Â·â€¢x1, 1 â‰¤ i â‰¤ n, in parallel, where â€¢ is an arbitrary binary associative operator. Snirâ€¦ (More)

We study the number of configurations in the East model of statistical physics. This may be pictured as sites in a line. The site at zero is always occupied. The site at i > 0 can only be changed ifâ€¦ (More)

Let a1 < a2 < . . . < as be gives integers and let [n] denote the set {1, 2, . . . , n}. In this note we investigate the size of minimum subsets of [n] which intersect every set in [n] of the formâ€¦ (More)

My math 301 Term paper will be concerned with exploring the Collatz conjecture. I will discuss the importance and interest of this conjecture; what progress has been made on this problem and who madeâ€¦ (More)

P rime numbers are the atoms of our mathematical universe. Euclid showed that there are infinitely many primes, but the subtleties of their distribution continue to fascinate mathematicians. Lettingâ€¦ (More)

We report a novel, real-time fluorogenic kinase assay. The peptide substrates are synthesized with a fluorescent dye and a hydrocarbon tail. The substrate self-assembles into micelles, increasing theâ€¦ (More)

Data/algorithmic representations of 3D floorplans for integrated circuits is an essential problem in the study of 3D VLSI circuits. Given a fixed number of rectangular blocks and their volume, 3Dâ€¦ (More)