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It looks like I am going to have three articles (if all goes well) that are dealing with quite different fields (psycho-accoustics, time-series analysis and machine learning). I do not have a single clue on how to start writting the introduction for a thesis that should tie these together ... Do you have tips for writting introduction when dealing with "sandwitch"/"stapler" thesis ?

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As a comment says, this really is a question for your supervisor. I'm assuming it was your supervisor's idea to put your three papers together in the thesis, so perhaps they have suggestions on how to make them fit together.

If it was your initiative, check with your supervisor first. They might propose to leave out one of the papers so that the resulting thesis will be more homogeneous (at the expense of being shorter).

My thesis included only some of the publications I did during my PhD, those that were part of a larger project. In the meantime I did other things which have not been included in there.

Otherwise try to find a common denominator to all the papers, no matter how far it is, write a section about it, and then specialize to the topics at hand. I suppose there has to be a common denominator of some sort, but I'm not an expert in your specific field.

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