Lower bounds for Auslander's representation dimension

Lower Bounds for Representation Growth

This article examines lower bounds for the representation growth of finitely generated (particularly profinite and pro-p) groups. It also considers the related question of understanding the maximal multiplicities of character degrees in finite groups, and in particular simple groups.

Some Lower Bounds for Estrada Index

Upper bounds for noetherian dimension of all injective modules with Krull dimension

‎In this paper we give an upper bound for Noetherian dimension of all injective modules with Krull dimension on arbitrary rings‎. ‎In particular‎, ‎we also give an upper bound for Noetherian dimension of all Artinian modules on Noetherian duo rings.

Lower Bounds for Evolution Strategies Using VC-Dimension

We derive lower bounds for comparison-based or selection-based algorithms, improving existing results in the continuous setting, and extending them to non-trivial results in the discrete case. We introduce for that the use of the VC-dimension of the level sets of the fitness functions; results are then obtained through the use of Sauer’s lemma. In the special case of optmization of the sphere f...

Lower Bounds for Local Versions of Dimension Reductions

We consider the problem of embedding vectors from an arbitrary Euclidean space into a low dimensional Euclidean space, while preserving up to a small distortion, a subset of the distances. In particular, preserving only the distance of each vector to a small number of its nearest neighbors. We show that even when the subset of distances we wish to preserve is very small, the problem does not be...