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EDIT: I was told by my supervisor to implement the algorithm first and then look back over the question because "biologists' papers do not always contain the information that is necessary to reproduce their calculations". That is to say that I will come back to this question at some point when I've had an epiphany.

I've just started my mathematics thesis on Topological Data Analysis last week and I was given a question to resolve for next week:

"What are the 3-dimensional subspaces to which the projections are made in figure A? Are they really subspaces or are they quotient spaces?"

I am actually not sure how to proceed to resolve this question. I've skimmed over the paper and I didn't spot anything helpful, except for the figure description:

"leads to nine distinct clusters in a two-dimensional state space inferred by generalized regression modelling"

  1. Why do they talk about a two-dimensional state space. The question mentions a three-dimensional space. j.c.: "The three lines you call axes actually arise from the branching analysis performed by the software Monocle 2. Relevant documentation"
  2. Using some method we project an n-dimensional space to a 2 (or 3)-dimensional space. What does he mean by "subspaces/quotient spaces to which the projections are made" How would I check this?
  3. Do I need to find out how the branching analysis or Generalized Regression Modelling works? By G.R.M. do they mean this: Generalized linear model?

It would be great if someone could assist me with this problem, or maybe make the question more understandable.

kjetil b halvorsen
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rlamesch
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  • Do you have an advisor in your department (maybe the person who posed the question) who could give you some hints? –  Jul 08 '19 at 08:16
  • Yes, my supervisor who gave me the question. I just wanted to wait before asking him, just because I'm supposed to show that I'm able to work independently. I will get in touch with him, if I don't figure out more on my own or with the help of the internet. –  Jul 08 '19 at 08:24
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    If your advisor doesn't want you to ask him the answer, then he probably doesn't want you to ask the internet the answer. –  Jul 09 '19 at 08:35
  • I am not really asking the internet for the answer nor would I ask him for the answer. I'm asking for assistance of how to proceed. The PhD student I went to today told me the question wasn't exactly clear and I should ask for more details, which I did. However my supervisor is currently travelling and hasn't responded to me e-mail yet. It's always possible someone has any helpful hints, otherwise I'll just have to wait until he responds or until my next meeting. –  Jul 09 '19 at 08:48
  • Thanks a lot. Yes, I got confused with the axes, just because the question talks about a 3-dimensional subspace. –  Jul 10 '19 at 13:27

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