We show that s-term DNF formulas can be learned under the uniform distribution in quasi-polynomial time with statistical queries of tolerance Ω(ε/s). The tolerance improves on the known tolerance Ω(ε/s) and is optimal with respect to its dependence on the error parameter ε. We further consider the related model of learning with proper distance queries and show that DNF formulas can be learned u...

A flow of electrically conducting fluid in the presence of a steady magnetic field has a tendency to become quasi two-dimensional, i.e. uniform in the direction of the magnetic field, except in thin so-called Hartmann boundary layers. The condition for this tendency is that of a strong magnetic field, corresponding to large values of the dimensionless Hartmann number (Ha >> 1). This is analogou...

Two-uniform frames and their use for the coding of vectors are the main subject of this paper. These frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest possible error when up to two frame coefficients are set to zero. Here, we consider various numerical measures for the reconstruction error associated with a frame when an arbitrary number...

Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantumclassical comparisons is limited by the non-uniqueness of the particular represen...

Two-uniform frames and their use for the coding of vectors are the main subject of this paper. These frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest possible error when up to two frame coefficients are set to zero. Here, we consider various numerical measures for the reconstruction error associated with a frame when an arbitrary number...

Two-uniform frames and their use for the coding of vectors are the main subject of this paper. These frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest possible error when up to two frame coefficients are set to zero. Here, we consider various numerical measures for the reconstruction error associated with a frame when an arbitrary number...

Two-uniform frames and their use for the coding of vectors are the main subject of this paper. These frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest possible error when up to two frame coefficients are set to zero. Here, we consider various numerical measures for the reconstruction error associated with a frame when an arbitrary number...

Abstract: Unlike a uniformity, a quasi-uniformity is not determined by its quasiuniform covers. However, a classical construction, due to Fletcher, which assigns a transitive quasi-uniformity to each family of interior-preserving open covers, allows to describe all transitive quasi-uniformities on the topological spaces in terms of those families of covers. In this paper we develop a pointfree ...

We give a characterization of the simple, and of the subdirectly irreducible boolean algebras with operators (including modal algebras), in terms of the dual descriptive frame. These characterizations involve a special binary quasi-reachability relation on the dual structure; we call a point u a quasi-root of the dual structure if every ultrafilter is quasireachable from u. We prove that a bool...

In this article, we consider an implicit iterative scheme for two asymptotically quasi-I-nonexpansive mappingsS1, S2 and two asymptotically quasi-nonexpansive mapping I1, I2 in Banach space. We obtain convergence results for considered iteration to common fixed point of two asymptotically quasi-I-nonexpansive mappings, asymptotically quasi-nonexpansive mapping and equilibrium problem in frame w...