This work shows that the following problems are equivalent, both in theory and in practice: • median filtering : given an n-element vector, compute the sliding window median with window size k, • piecewise sorting : given an n-element vector, divide it in n/k blocks of length k and sort each block. By prior work, median filtering is known to be at least as hard as piecewise sorting: with a sing...

299 Community Policing in America: Changing the Nature, Structure, and Function of the Police

BACKGROUND The paired box 6 (PAX6) gene is considered as a master gene for eye development. Linkage of myopia to the PAX6 region on chromosome 11p13 was shown in several studies, but the results for association between myopia and PAX6 were inconsistent so far. METHODOLOGY/PRINCIPAL FINDINGS We genotyped 16 single nucleotide polymorphisms (SNPs) in the PAX6 gene and its regulatory regions in a...

In this paper, we present new blind signature schemes based on the factorization problem. They are the first blind signature schemes proved secure relatively to factorization. By security, we mean that no “one-more forgery” is possible even under a parallel attack. In other terms, a user that receives k electronic coins cannot manufacture k + 1. Those security definitions have been introduced b...

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A parallelotope is a polytope whose translation copies fill space without gaps and intersections by interior points. Voronoi conjectured that each parallelotope is an affine image of the Dirichlet domain of a lattice, which is a Voronoi polytope. We give several properties of a parallelotope and prove that each of them is equivalent to it is an affine image of a Voronoi polytope.

Mutation testing is a software testing technique that is considered to be very powerful, but is very expensive to apply. One open problem in mutation testing is how to automatically detect equivalent mutant programs. Currently, equivalent mutants are detected by hand, which makes it a very expensive and time-consuming process, and restricts the use of mutation testing. This paper presents a tec...

We prove that the set of properties describable by a uniform sequence of rst-order sentences using at most k + 1 distinct variables is exactly equal to the set of properties checkable by a Turing machine in DSPACEn k ] (where n is the size of the universe). This set is also equal to the set of properties describable using an iterative deenition for a nite set of relations of arity k. This is a ...

We show that a quantum system possessing an exact antilinear symmetry, in particular PT -symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian Hamiltonian with exact PT -symmetry to a Hermitian Hamiltonian. We apply our general results to PT symmetry in finite-dimensions and give the explicit form of the...