1) If A is your set of n items, For (a1, a2) in AxA and a date t in R, att(a1, a2, t) in R gives the attraction (>0) or repulsion (<0) between a1 and a2 at date t.
Build a vector V in AxA that spans all possible (a1, a2) with a1 and a2 both in A. V = (v1, ..., vn*n).
Now for each t in R, you...