  Let $k\geq 2$ be an integer. Given a uniform function $f$ - one that
satisfies $\|f\|_{U(k)}<\infty$, there is an associated anti-uniform function
$g$ - one that satisfied $\|g\|_{U(k)}^{*}$. The question is, can one
approximate $g$ with the Gowers-Host-Kra dual function $D_{k}f$ of $f$?
Moreover, given the generalized cubic convolution products
$D_{k}(f_{\alpha}:\alpha\in\tilde{V}_{k})$, what sorts of algebras can they
form? In short, this paper explores possible structures of anti-uniformity on
Euclidean spaces.
