Sylvester to Mariaelena Boglione

1. The covariance matrix does not include the systematic uncertainties. It is very hard to properly incorporate them without going to a very complex formalism, as the correlation between the different bins of the systematic uncertainties is unknown. For this reason we provide the integrated multiplicities with *re-evaluated* systematic uncertainties.

Now as my advise as to what to do: in general the systematics are at least the same size as the systematic uncertainty, and often quite a bit larger. Because of this, the extra "precision" with the _statistical_ covariance matrix is negligible. I believe it makes most sense to just use the standard statistical+systematic uncertainty.

2. The given covariance matrix is an estimator (both experimental AND numerical ) of the "true" statistical covariance matrix. The actual formula to propagate the uncertainty of the measured yields (SIDIS *and* DIS) through the unfolding (cov_unf = S^-1*diag(sigma_meas)*(S^-1)^T with S the smearing matrix as defined in the paper), and then through the mulitpicity calculation, is numerically not trivial.

In the rare case where both the SIDIS and the DIS cross section get very small compared to their uncertainties, the machine uncertainty (even with double precision floats!) of this calculation is not negligible anymore. However, while not esthetically pleasing, these differences occur *below* the significance of the measurement. This means that, when standard rounding of the uncertainties is done (a bit tricky for the covariance matrix), the matrix *does* become nicely symmetric. I also want to stress again this only happens in correlations with ultra-low-statistic corners (where the measurement isn't very significant anyway).