Third, imposing additional assumptions on the gas composition can endow the underdetermined inverse problem associated with a non-injective gas sensor with a unique solution. This idea of imposing additional assumptions, consistent with but not imposed by the physics underlying the problem, is a common approach to, given an inverse problems with nonunique solutions, grant it a unique solution . We provided one example in eqn. 17, where we sought the minimumnorm change in the gas composition consistent with the change in the response.