142,703 research outputs found
A deterministic approximation algorithm for computing the permanent of a 0, 1 matrix
We consider the problem of computing the permanent of a n by n matrix. For a class of matrices corresponding to constant degree expanders we construct a deterministic polynomial time approximation algorithm to within a multiplicative factor ( 1 + ∈)[superscript η] for arbitrary∈ > 0. This is an improvement over the best known approximation factor e[superscript η] obtained in Linial, Samorodnitsky and Wigderson (2000), though the latter result was established for arbitrary non-negative matrices. Our results use a recently developed deterministic approximation algorithm for counting partial matchings of a graph (Bayati, Gamarnik, Katz, Nair and Tetali (2007)) and Jerrum–Vazirani method (Jerrum and Vazirani (1996)) of approximating permanent by near perfect matchings
Andreev reflection and the semiclassical Bogoliubov-de Gennes Hamiltonian: Resonant states
International audienceWe present a semi-classical analysis of the opening of superchannels in gated mesoscopic SNS junctions. For perfect junctions (i.e. hard-wall potential), this was considered by [ChLeBl] in the framework of scattering matrices. Here we allow for imperfections in the junction, so that the complex order parameter continues as a smooth function, which is a constant in the superconducting banks, and vanishes rapidly inside the lead. We obtain quantization rules for resonant Andreev states near energy E close to the Fermi level, including the determination of the resonance width
Cut-and-paste of quadriculated disks and arithmetic properties of the adjacency matrix
We define cut-and-paste, a construction which, given a quadriculated disk
obtains a disjoint union of quadriculated disks of smaller total area. We
provide two examples of the use of this procedure as a recursive step. Tilings
of a disk receive a parity: we construct a perfect or near-perfect
matching of tilings of opposite parities. Let be the black-to-white
adjacency matrix: we factor , where and are
lower and upper triangular matrices, is obtained from a larger
identity matrix by removing rows and columns and all entries of ,
and are equal to 0, 1 or -1.Comment: 20 pages, 17 figure
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