  We study the homology structure of spaces having an action of the
\emph{framed disks} operad. In particular, we compute the relations between
Kudo-Araki operations and generalized Batalin-Vilkovisky operators. As an
application, we complete the computations of the modulo 2 homology of $\Omega^2
S^3$ as a Batalin-Vilkovisky algebra, and give some evidence for a classical
conjecture about the modulo 2 Hurewicz homomorphism of the infinite loop space
of the sphere spectrum.
