We prove a sampling discretization theorem for the square norm of functions from finite dimensional subspace satisfying Nikol'skii's inequality with an upper bound on number points order dimension subspace.

In this paper we summerize recent results on a posteriori error estimation and adaptivity for space-time finite element discretizations of parabolic optimization problems. The provided error estimates assess the discretization error with respect to a given quantity of interest and separate the influences of different parts of the discretization (time, space, and control discretization). This al...

Many algorithms in decision tree learning have not been designed to handle numerically-valued attributes very well. Therefore, discretization of the continuous feature space has to be carried out. In this article we introduce the concept of cost-sensitive discretization as a preprocessing step to induction of a classifier and as an elaboration of the error-based discretization method to obtain ...

In order to perform numerical simulations of the Kardar-Parisi-Zhang (KPZ) equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf-Cole transformation applied to a diffusion equation (with multiplicative noise) is shown here to strongly restrict the arbitrariness in the choice of spatial disc...

Abstract This paper presents a novel fiber-based muscle model for the forward dynamics of musculoskeletal system. While bones are represented by rigid bodies, muscles taken into account means one-dimensional cables that obey laws continuum mechanics. In contrast to standard force elements such as Hill-type model, this approach is close real physiology and also avoids issue wobbling masses. On o...