Making a plan for a paper
This is how I think about it. What works for you may be different. Just like orienteering, there are two main steps: finding out where you are and then determining what you need to do next.
Key statements and evidence (i.e., plots and figures)
Each paper is made up of a few key logical statements, supported by evidence. The evidence typically comes in the form of either data or mathematical proof.
Let’s go through the paper from reading ( https://arxiv.org/abs/2009.13556 ) In that exercise we identified some key statements:
- The objective function $O[\Psi] = E[\Psi] + \sum_i^N \lambda_i |S_i|^2$ has the N+1’th excited state as its minimum if $\lambda_i > E_N-E_i$.
- A method optimizing the objective function $O[\Psi]$ enables optimization of orbitals, determinant coefficients, and Jastrow parameters.
- A CASCI-J wave function agrees with full CI for H2, using this method.
- DMC on a CASCI-J wave function, with all parameters optimized agrees with CC3 within around 0.24 eV for benzene. For fixed parameters the difference is 0.35 eV.
Now let’s think about what evidence supports each of those statements:
- There is a proof of this statement in Section II A.
- This is shown in figures showing that the optimized orbitals are lower in energy than not optimized orbitals.
- Figure 3 shows exactly this by plotting energy versus bond length, with color indicating the method used.
- Tables II and III.
To plan your paper, you should try to match up logical statements to evidence in a similar way. Note that if you look at the paper closely, there are more logical statements and more evidence than just the four I’ve listed here. During the writing of the paper, typically we try many versions of statements and evidence pairs before we settle on the final ones. During the course of writing probably on the order of ~100 or so were generated, but we only considered 5-10 at a time.
Understand what you know now
Idea generation: statement/evidence pairs
In this phase, just try to write down statements and evidence that would be required to show the statements. For evidence, usually it comes in the form of a plot. Write down the x- and y-axes of the plot, and what quantities are being plotted. Try to make the statements as atomic as possible; it’s totally ok (and useful) to plot different views of the same data. I think it’s usually best to aim for around 5-10 statement/evidence pairs at a time.
Now look at your statements. Are some of them redundant? Try to figure out the minimal set of statement/evidence pairs that still amount to the same thing logically. Don’t try to combine two statements that are saying different things, but do try to combine statements that are saying the same thing in slightly different ways.
Forming a heirarchy of statements
Now look at your statements. Which are more important than others, and to whom? Think about who might be interested in which statements. You might not be sure about some of them. That’s ok, but it does mean that you may not want to emphasize that particular statement. For example, from above:
- The proof is mainly interesting to method developers.
- That orbital optimization matters for excited states is mainly interesting to people seeking to apply the method to other systems.
Find the key statements
Now we want to figure out what the project is about. Are there any statements contained in your list that you think summarize the work best? Or maybe is there a meta-statement? If you had two sentences to describe the work, what would you say?
Make a plan to finish the paper
Now go through the evidence required for your revised statement list. Making the plan is very simple; just figure out what you need to do to finish the plots and proofs, and make a plan for doing that!