Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are LDPC codes with linear rate and distance n. Their rate is evaluated via Euler characteristic arguments and their distance using Z2-systolic geometry. This construction answers a queston of Zémor [Z], who asked whether homological codes with such parameters could exist ...

UNLABELLED There is a multitude of new techniques that promise to extract predictive information in bioinformatics applications. It has been recognized that a first step for validation of the resulting model fits should rely on proper use of resampling techniques. However, this advice is frequently not followed, potential reasons being difficulty of correct implementation and computational dema...

Sparse grids are tailored to the approximation of smooth high-dimensional functions. On a d-dimensional cube, the number of grid points is N = O(h−1| log h|d−1) with a mesh size parameter h. The so-called combination technique, based on hierarchical decomposition, facilitates the numerical solution of partial differential equations on these grids. Key to the convergence analysis are specific mu...

The relative mean square error in the three-dimensional stress field predicted by classical plate theory is shown to be OQi/L^)2, where h is the plate thickness and Lj. is a mean square measure of the wavelength of the midplane deformation pattern. This improves a recent result of Nordgren who obtained a relative error estimate of 0(h/L*). The improved error estimate, which, like Nordgren's, is...

We examine nonstationary inverse problems in which the time evolution of the unknown quantity is modelled by a stochastic partial differential equation. We consider the problem as a state estimation problem. The time discrete state evolution equation is exact since the solution is given by an analytic semigroup. For the practical reasons the space discretization of the time discrete state estim...

We study full Bayesian procedures for high-dimensional linear regression. adopt data-dependent empirical priors introduced in Martin et al. (Bernoulli 23(3):1822–1847, 2017). In their paper, these have nice posterior contraction properties and are easy to compute. Our paper extend theoretical results the case of unknown error variance . Under proper sparsity assumption, we achieve model selecti...