On configurations concerning cardinal characteristics at regular cardinals

We study the consistency and consistency strength of various configurations concerning the cardinal characteristics at uncountable regular cardinals. Motivated by a theorem of Raghavan-Shelah who proved that, we explore in the first part of the paper the consistency of inequalities comparing with and. In the second part of the paper we study variations of the extender-based Radin forcing to establish several consistency results concerning from hyper-measurability assumptions, results which were previously known to be consistent only from supercompactness assumptions. In doing so, we answer questions from [1], [15] and [7], and improve the large cardinal strength assumptions for results from [10] and [3].