Dynamic matrix rank with partial lookahead

of a matrix M under changes to its entries. For an nxn matrix M, we
show an amortized upper bound of O(n^{w-1}) arithmetic operations per
change for this problem, where w < 2.376 is the exponent for matrix
multiplication, under the assumption that there is a lookahead of up
to \Theta(n) locations. That is, we know up to the next \Theta(n)
locations (i1,j1),(i2,j2),... whose entries are going to change, in
advance; however we do not know the new entries in these locations in
advance. We get the new entries in these locations in a dynamic
manner.