Let $Q$ be the Cantor middle third set, and $S$ the unit circle, and let $\tau :Q\rightarrow Q$ be an adding machine (i.e., odometer). Let $X=Q\times S$ be equipped with (a metric equivalent to) the Euclidean metric. We show that there are continuous triangular maps $F_i: X\rightarrow X$, $F_i: (x,y)\mapsto (\tau (x), g_i(x,y))$, $i=1,2$, with the following properties:
(i) Both $(X, F_1)$ and $(X, F_2)$ are minimal systems, without weak mixing factors (i.e., neither of them is semiconjugate to a weak mixing system).
(ii) $(X, F_1)$ is spatio-temporally chaotic but not Li-Yorke sensitive.
(iii) $(X,F_2)$ is Li-Yorke sensitive.
This disproves conjectures of E. Akin and S. Kolyada [Li-Yorke
sensitivity, {\it Nonlinearity} 16 (2003), 1421--1433].