  We build upon the recent papers by Weinstein and Yu (FOCS'16), Larsen
(FOCS'12), and Clifford et al. (FOCS'15) to present a general framework that
gives amortized lower bounds on the update and query times of dynamic data
structures. Using our framework, we present two concrete results.
  (1) For the dynamic polynomial evaluation problem, where the polynomial is
defined over a finite field of size $n^{1+\Omega(1)}$ and has degree $n$, any
dynamic data structure must either have an amortized update time of
$\Omega((\lg n/\lg \lg n)^2)$ or an amortized query time of $\Omega((\lg n/\lg
\lg n)^2)$.
  (2) For the dynamic online matrix vector multiplication problem, where we get
an $n \times n$ matrix whose entires are drawn from a finite field of size
$n^{\Theta(1)}$, any dynamic data structure must either have an amortized
update time of $\Omega((\lg n/\lg \lg n)^2)$ or an amortized query time of
$\Omega(n \cdot (\lg n/\lg \lg n)^2)$.
  For these two problems, the previous works by Larsen (FOCS'12) and Clifford
et al. (FOCS'15) gave the same lower bounds, but only for worst case update and
query times. Our bounds match the highest unconditional lower bounds known till
date for any dynamic problem in the cell-probe model.
