We have performed precision measurements of the double-spin virtual-photon
asymmetry $A_1$ on the neutron in the deep inelastic scattering regime, using
an open-geometry, large-acceptance spectrometer. Our data cover a wide
kinematic range $0.277 \leq x \leq 0.548$ at an average $Q^2$ value of
3.078~(GeV/c)$^2$, doubling the available high-precision neutron data in this
$x$ range. We have combined our results with world data on proton targets to
extract the ratio of polarized-to-unpolarized parton distribution functions for
up quarks and for down quarks in the same kinematic range. Our data are
consistent with a previous observation of an $A_1^n$ zero crossing near
$x=0.5$. We find no evidence of a transition to a positive slope in $(\Delta d
+ \Delta \bar{d})/(d + \bar{d})$ up to $x=0.548$.
