Before revision:  Also, our theory suggests a simple strategy for producing  defect-free patterns.
After revision:  We show that outside this range of parameters, in particular for low cis-coupling, a novel kind of pattern is produced, where high Delta cells have high Notch as well. It also suggests that the biological system is only weakly first order, so that an additional mechanism is required to generate the observed defect-free patterns. We construct a simple strategy for producing defect-free patterns.