This paper develops fundamental limits of deep neural network learning by characterizing what is possible if no constraints are imposed on the algorithm and amount training data. Concretely, we consider Kolmogorov-optimal approximation through networks with guiding theme being a relation between complexity function (class) to be approximated approximating in terms connectivity memory requiremen...

in this work we use density functional theory based on the ultra-soft pseudo-potential to calculate thestructural, mechanical and thermal properties of narrow single walled bn, aln and gan nanotubes.the electron-electron interactions were expressed within the local density approximation (lda). wehave also obtained the phonon dispersion and elastic constants of these nanotubes using the densityf...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...