  We perform a new global analysis of spin-dependent parton distribution
functions with the inclusion of Ioffe time pseudo-distributions computed in
lattice QCD (LQCD), which are directly sensitive to the gluon helicity
distribution, $\Delta g$. These lattice data have an analogous relationship to
parton distributions as do experimental cross sections, and can be readily
included in global analyses. We focus in particular on the constraining
capability of current LQCD data on the sign of $\Delta g$ at intermediate
parton momentum fractions $x$, which was recently brought into question by
analysis of data in the absence of parton positivity constraints. We find that
present LQCD data cannot discriminate between positive and negative $\Delta g$
solutions, although significant changes in the solutions for both the gluon and
quark sectors are observed.
