We study the pure exploration problem subject to a matroid constraint (Best-Basis) in a stochastic multi-armed bandit game. In a Best-Basis instance, we are given n stochastic arms with unknown reward distributions, as well as a matroid M over the arms. Let the weight of an arm be the mean of its reward distribution. Our goal is to identify a basis of M with the maximum total weight, using as f...

Field theories with a S 2-valued unit vector field living on S 3 × IR space-time are investigated. The corresponding eikonal equation, which is known to provide an integrable sector for various sigma models in different spaces, is solved giving static as well as time-dependent multiply knotted configurations on S 3 with arbitrary values of the Hopf index. Using these results, we then find a set...

hen given a set of properties or conditions (say, three) that are claimed to be equivalent, the claim e s can be verified by supplying what we call a circle of proofs. In the case in point, one proves th econd property or condition from the first, the third from the second, and the first from the third. If r s the proof that 1 implies 2 does not rely on 3, then we say that the proof is pure wit...

A proper short exact sequence 0! A!f B! C ! 0 ð*Þ in the category of locally compact abelian groups is said to be t-pure if fðAÞ is a topologically pure subgroup of B, that is, if