It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the weights for these spaces are nonincreasing, the first few variables are in a sense more important than the rest. We thus propose to copy the points of a rank-1 lattice rule a n...

We consider the problem of finding the closest lattice point to a vector in n-dimensional Euclidean space when each component of the vector is available at a distinct node in a network. Our objectives are (i) minimize the communication cost and (ii) obtain the error probability. The approximate closest lattice point considered here is the one obtained using the nearest-plane (Babai) algorithm. ...

Point-to-point vacuum correlation functions for spatially separated hadron currents are calculated in quenched lattice QCD on a 16 × 24 lattice with 6/g = 5.7. The lattice data are analyzed in terms of dispersion relations, which enable us to extract physical information from small distances where asymptotic freedom is apparent to large distances where the hadronic resonances dominate. In the p...

We consider the design of asymmetric multiple description lattice quantizers that cover the entire spectrum of the distortion profile, ranging from symmetric or balanced to successively refinable. We present a solution to a labeling problem, which is an important part of the construction, along with a general design procedure. This procedure is illustrated using the Z2 lattice. The asymptotic p...

We review the development of Monte Carlo algorithms for the simulation of the Ising model with local dynamics. The multi lattice coding algorithm for the pure and for the site-disordered Ising model is described in detail. Application of these algorithms on fast vector computers have led to new progress concerning the critical dynamics of the pure Ising model leading to the critical exponent z ...

We present results for the coupling of the light vector mesons to the tensor current, relative to the standard vector meson decay constants. From an O(a)-improved lattice study, performed at three values of the lattice spacing in the quenched approximation, our final values (in the continuum limit), in the MS scheme at μ = 2 GeV, are: fT ρ /fρ = 0.72(2)( +2 −0), f T K∗/fK∗ = 0.74(2), f T φ /fφ ...

Two methods to overcome the problems with large vector quantization (VQ) codebooks are lattice VQ (LVQ) and product codes. The approach described in this paper takes advantage of both methods by applying residual VQ with LVQ at all stages. Using LVQ in conjunction with entropy coding is strongly motivated by the fact that entropy constrained but structurally unconstrained VQ design leads to mor...