Sharp Bounds for Mutual Covering

Sharp Bounds on the PI Spectral Radius

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

Sharp bounds for harmonic numbers

In the paper, we collect some inequalities and establish a sharp double inequality for bounding the n-th harmonic number.

Sharp bounds for population recovery

The population recovery problem is a basic problem in noisy unsupervised learning that has attracted significant research attention in recent years [WY12, DRWY12, MS13, BIMP13, LZ15, DST16]. A number of different variants of this problem have been studied, often under assumptions on the unknown distribution (such as that it has restricted support size). In this work we study the sample complexi...

Lower Bounds for Covering Problems

Volume Bounds for Shadow Covering

For n ≥ 2 a construction is given for a large family of compact convex sets K and L in Rn such that the orthogonal projection Lu onto the subspace u⊥ contains a translate of the corresponding projection Ku for every direction u, while the volumes of K and L satisfy Vn(K) > Vn(L). It is subsequently shown that, if the orthogonal projection Lu onto the subspace u⊥ contains a translate of Ku for e...