We present a probabilistic polynomial-time reduction from the lattice Bounded Distance Decoding (BDD) problem with parameter 1/( √ 2 · γ) to the unique Shortest Vector Problem (uSVP) with parameter γ for any γ > 1 that is polynomial in the lattice dimension n. It improves the BDD to uSVP reductions of [Lyubashevsky and Micciancio, CRYPTO, 2009] and [Liu, Wang, Xu and Zheng, Inf. Process. Lett.,...

In the present paper we show how to speed up lattice parameter searches for Monte Carlo and quasi–Monte Carlo node sets. The classical measure for such parameter searches is the spectral test which is based on a calculation of the shortest nonzero vector in a lattice. Instead of the shortest vector we apply an approximation given by the LLL algorithm for lattice basis reduction. We empirically ...

We use an optimised hopping parameter expansion for the free energy (linear δ-expansion) to study the phase transitions at finite temperature and finite charge density in a global U(1) scalar Higgs sector on the lattice at large lattice couplings. We are able to plot out phase diagrams in lattice parameter space and find that the standard second-order phase transition with temperature at zero c...

‘Lattice parameters determined from the synchrotron X-ray diffraction scans of the cubic 200 and tetragonal 220/004 Bragg peaks. Fits to the cubic lattice parameter (black solid line) and the average tetragonal lattice parameter (= 2atet + ctet)/3 (blue solid line), were used to determine the linear coefficients of thermal expansion of 1.95 × 10−4 K−1 (cubic) and 2.66 × 10−4 K−1 (tetragonal). T...

Figure S1: X-ray powder diffraction pattern of the iron oxide nanospheres sample. X-ray Powder diffraction (XRPD) was measured on a conventional in-house powder diffractometer using Cu Kα radiation. Rietveld refinement yields cubic lattice parameters of 8.362(2) Å for the nanospheres and 8.348(1) Å for the nanocubes, which are both close to the cubic spinel lattice parameter of maghemite. The r...

This study investigates the effect of material parameters of the Gurson-Tvergaard-Needleman (GTN) model on the failure prediction of cellular structures. The effect of elastic modulus, calibration parameter of GTN model, isotropic hardening, fracture strain, and strut diameter on the load-displacement curve of a lattice structure fabricated by Selective Laser Melting (SLM) has been studied by u...