Coordinatisation by binding groups and unidimensionality in simple theories

In a simple theory with elimination of finitary hyperimaginaries if tp(a) is real and analysable over a definable set Q, then there exists a finite sequence (a_i |i ≤ n*) ⊆ dcl^eq(a) with a _n* = a such that for every i ≤ n*, if p_i = tp(a_i/{a_j |j < i}) then Aut(p_i/Q) is type-definable with its action on p_i^C. A unidimensional simple theory eliminates the quantifier ∃^∞ and either interprets (in C^eq) an infinite type-definable group or has the property that ACL(Q) = C for every infinite definable set Q.