We describe the groups of automorphisms two generated free braided associative algebras with involutive diagonal braidings over a field characteristic ≠2. Depending on form braiding, five different automorphism arise as algebras. This list covers all three that in case quantum planes.

We consider the problem of constructing distribution-free prediction sets for data from two-layer hierarchical distributions. For iid data, can be constructed using method conformal prediction. The validity hinges on exchangeability which does not hold when groups observations come distinct distributions, such as multiple each patient in a medical database. extend methods to setting. develop CD...