Period and toroidal knot mosaics

Knot mosaic theory was introduced by Lomonaco and Kauffman in the paper on `Quantum knots and mosaics' to give a precise and workable definition of quantum knots, intended to represent an actual physical quantum system. A knot (m,n)-mosaic is an $m \! \times \! n$ matrix whose entries are eleven mosaic tiles, representing a knot or a link by adjoining properly. In this paper we introduce two variants of knot mosaics: period knot mosaics and toroidal knot mosaics, which are common features in physics and mathematics. We present an algorithm producing the exact enumeration of period knot (m,n)-mosaics for any positive integers m and n, toroidal knot (m,n)-mosaics for co-prime integers m and n, and furthermore toroidal knot (p,p)-mosaics for a prime number p. We also analyze the asymptotics of the growth rates of their cardinality

Pulsed Laser Deposition of Rocksalt Magnetic Binary Oxides

Here we systematically explore the use of pulsed laser deposition technique (PLD) to grow three basic oxides that have rocksalt structure but different chemical stability in the ambient atmosphere: NiO (stable), MnO (metastable) and EuO (unstable). By tuning laser fluence, an epitaxial single-phase nickel oxide thin-film growth can be achieved in a wide range of temperatures from 10 to 750 {\deg}C. At the lowest growth temperature, the out-of-plane strain raises to 1.5%, which is five times bigger than that in a NiO film grown at 750 {\deg}C. MnO thin films that had long-range ordered were successfully deposited on the MgO substrates after appropriate tuning of deposition parameters. The growth of MnO phase was strongly influenced by substrate temperature and laser fluence. EuO films with satisfactory quality were deposited by PLD after oxygen availability had been minimized. Synthesis of EuO thin films at rather low growth temperature prevented thermally-driven lattice relaxation and allowed growth of strained films. Overall, PLD was a quick and reliable method to grow binary oxides with rocksalt structure in high quality that can satisfy requirements for applications and for basic research

Performance of SSE and AVX Instruction Sets

SSE (streaming SIMD extensions) and AVX (advanced vector extensions) are SIMD (single instruction multiple data streams) instruction sets supported by recent CPUs manufactured in Intel and AMD. This SIMD programming allows parallel processing by multiple cores in a single CPU. Basic arithmetic and data transfer operations such as sum, multiplication and square root can be processed simultaneously. Although popular compilers such as GNU compilers and Intel compilers provide automatic SIMD optimization options, one can obtain better performance by a manual SIMD programming with proper optimization: data packing, data reuse and asynchronous data transfer. In particular, linear algebraic operations of vectors and matrices can be easily optimized by the SIMD programming. Typical calculations in lattice gauge theory are composed of linear algebraic operations of gauge link matrices and fermion vectors, and so can adopt the manual SIMD programming to improve the performance.Comment: 7 pages, 5 figures, 4 tables, Contribution to proceedings of the 30th International Symposium on Lattice Field Theory (Lattice 2012), June 24-29, 201