Recipe/Discussions/Bohn
Some thoughts about this article
2 - their aim is the calculate the percentage of all ingredients in a food product. This requires that one knows the total weight of the ingredients that went in.
2 - do they imply to use the energy as well. It is mentioned as part of the Big7. As this is dependent on the other nutrients, it will not offer new information.
2 - fig 1 one of the constraints is a bit strange (X1 > () > x6). Is that intentional?
2 - The German Nutrient Database (Bundeslebensmittelschlüssel) is used. Might be useful for us.
2.2 - they use the subingredients as well, but do not detail how that impacts the equations. They record the percentages as well. What do they mean by noncompositional ingredients?
2.4 - For me there is an error in the formula (5) or the description thereof. They indicate that x denotes the unknown proportion of ingredients. But the question is the proportion of what? The final product or the ingredients that went into the product? They state that no need to specifically consider product weight or volume. Which seems to indicate that they see the proportion per initial product. Anyway it is not clear enough, and becomes more confusing later.
2.4 - Later they state that the proportions of all ingredients need to sum up to 1, respectively and 100%. This implies that their proportions are based on the initial product (prior to processing). Thus their formula is wrong as it needs proportionality factor related to the weight. See also this.
2.4 - The discussion of (under/over)determined linear equations is correct for totally free equations. In the case of a recipe with constraints on nonnegativity and ordering, this is no longer relevant. Also the fact that they're maybe linearly dependent ingredients, makes it impossible to say beforehand what set of equations one has.
2.4 - The optimisation problem they solve (eq. 9) includes a tolerance in the measured values. Not sure why this is needed. And what kind of effect does this have on optimisation problem. I wonder whether this will put a bias on dominant ingredients that determine the nutrients. Anyway they should show the effect of this added component. Remember smaller is better.
2.4 limSolve sounds interesting, need to experiment with it.
2.4 In eq 10 they add water is an unseen element. In fact this is a solution to their error in the formula. Not sure whether this always will be a solution
- Fit fails, why;
- Missing discussion on the errors:
- Usefulness of measurement errors;