Thank you for your comments. In reply to your comment about accessibility, I did modify my earlier reply to you with a remark stating that I would be happy to share the text of that original publication with anyone who contacts me ( buhlmann@umn.edu ). I stated in my earlier reply that the three different data sets that are fitted simultaneously represent different spectral features. For those who dig deep and look at that publication, they will see that these spectral features refer to NMR spectroscopy (nuclear magnetic resonance spectroscopy). For those not familiar with this technique, let me give an example that is different but would follow a similar logic. Imagine a purple compound reacted in a chemical reaction to give a green product. Three different data sets would be the intensity of absorption of red and blue light of the reacting compound, and the intensity of absorption of green light of the product. Averaging the different data sets would not make any sense, but as all three data sets represent the same reaction, the same set of ODEs. And why is it preferable to solve the ODEs and not just make a fit with any function that gives a nice fit. The reaction constant, kzero, cannot be obtained from a fit with any function that gives a nice fit. It can only be obtained from using a physically meaningful model, as one gets it from solving the ODEs. That reaction constant, kzero, is a very useful parameter as it can be used to predict the speed of reaction of experiments that have not been performed, for example with different concentrations of the reacting compound. Hope that helps.

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