Research has shown that cognitive load affects overall Iowa Gambling Task (IGT) performance, but it is unknown whether such load impacts the selection of the individual decks that correspond to gains or losses. Here, participants performed the IGT either in a full attention condition or while engaged in a number monitoring task to divide attention. Results showed that the full attention group w...

In the straight-line program model, it is known that computing all partial derivatives of a single polynomial induces only a constant increase in complexity, using the reverse derivation mode. We show that no such result holds for shifts, divided differences, q-shifts or q-divided differences.

We give non-symmetric versions of the Cauchy kernel and Littlewood’s kernels, corresponding to the types An, Bn, Cn and Dn, of the classical groups. We show that these new kernels are diagonal in the basis of two families of key polynomials (one of them being Demazure characters) obtained as images of dominant monomials under isobaric divided differences. We define scalar products such that the...

Over the past half-century, democratic constitutional design has undergone a sea change. After the Second World War, newly independent countries tended simply to copy the basic constitutional rules of their former colonial masters, without seriously considering alternatives. Today, constitution writers choose more deliberately among a wide array of constitutional models, with various advantages...

The Newtonian divided-di¤erence operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations. Conditions are given for similar relations to hold in a skew group ring. Interesting extensions of the nil...