where p i and n represent fractional prevalence of the i-th particle type and number of particles, respectively. However, linear equality constraints are not directly supported by most optimization packages 17 due to the difficulty of sampling from slices in higher-dimensional spaces (e.g. a triangle embedded in three dimensions, where a triangle naturally has zero volume). A straightforward solution is to reparameterize a linear equality constraint, albeit with some distortion of the original search space, as a linear inequality constraint as Eq. ( ):