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TODO list for SiReNetA tutorials and examples

General

  • TODO: Replace eigenvalue with largest norm by largest real component (?)
  • IDEA: Divide all notebooks into four categories:
    • Tutorials. Basic, getting familiar.
    • Use Cases. Discuss more in detail specific points, "how to" style and good/bad practices.
    • Focus points. Discuss more in detail specific points. Deeper analysis, help understand some problem/point better.
    • Repro. Reproduce paper figures and results.
  • TODO: Add a README.md file to the folder of the tutorial notebooks (?)

Documentation, tutorial explanations, etc.

(Temptative) list of documents (.md files) that we should have.

  1. (DONE) 1. What is sireneta? Overall description of what is Stimulus-Response Network Analysis.
  2. Canonical models. Summary of the (for now) five canonical models. Their equations and illustrations of the time-series for some simple graph (e.g., the N8 graph in the Chaos paper).
  3. Main summary of what the 3D Rij(t) pair-wise response tensor is, how to interpret and how to reduce along different axes to obtain node-wise and global responses, and the time-integrated responses. Show a good diagram of a 3D Rij(t) tensor and its different possible projections. This goes a bit in line with the Tutorial NB #2.

Tutorial Notebooks

Temptative list and content of the Tutorials:

  1. Getting Started : A quick overview of what Stimulus-Response Network Analysis is.
    1. Installing and getting information on the library.
    2. First example: use a simple, small graph to illustrate a typical analysis workflow.
  2. Fundamentals : Fundamentals of Stimulus-Response Network Analysis.
    1. Understanding the stimulus-responses at all levels (pairs-wise, node-wise and network level).
    2. Illustration and interpretation of pair-wise responses.
    3. Examples: directed and undirected chains.
    • MG: I wouldn't talk about TTP in this notebook, leave it for notebook #5
    1. MG: I would move this to notebook #6 Validity in weighted networks.
    2. TODO: Add a figure visualizing how the 3D tensor can be reduced along different axes giving different measures and infos: over time, row-wise, column-wise, etc.
  3. Canonical models : Overview of the five canonical models. Use one simple graph ('TestNet_N8.txt'?) Q: Should we actually have one (short) notebook per canonical model?
    1. Start this Notebook showing how typical graph metrics can be associated to the discrete cascade.
    2. For all the five models, plot the time-series and the responses. This way, we would plot, for each model and a couple of test networks:
    • trajectories of individual nodes.
    • pair-wise, node-wise and global responses.
  4. Compare networks : MG: see suggestions in notebook
    • show how response change with network size and density for a random net
    • normalization for 3 types of nets (random, scale-free, lattice)
  5. Extracting spatio-temporal metrics out of R(t) to compute distances:
    • time-to-peak / time-to-threshold distances. MG: global-responses is already in notebook #3
    • Comparison of TTP for leaky-cascade and the continuous diffusion (as used in Arnaudon's paper).
  6. WeightedNetworks.ipynb : Illustrate that we can naturally deal with weighted nets. How changing the weights alters the "topology" of the interactions. Input / output responses, help proper interpretation. (?) MG: focus on weighted nets, as we already present directed binary network in notebook #2
  7. ??? Extracting more metrics out of R(t) :
    • Self responses (returnability).

Specific examples

Besides the basic tutorials, we can extend the content adding "Use Cases" and "Focus Points" to answer specific questions, specific uses or treat some points in more detail.

Q: Should these go together into the "Tutorial_Notebooks/" folder, or should they have their own? ** MG: tutorials should present the basics and some key use cases**

  • USE CASE: ComparingNetworks.ipynb : More tutorial-like notebook than the reproduction of Figure 3 in the Chaos (2024) paper.
  • USE CASE: Renormalization for the LeakyCascade and the ContinuousDiffusion models. Show what the non-normalised and the intrinsic responses mean. Then, how they are related to the regressed version of the responses.
  • USE CASE: regress or not for measures
  • USE CASE: Defining distance as time, detailed explanations.
    • Theoretical predictions of Matt.
    • Revise Arnaudon's proposal.
    • What to do if responses do not converge? Time to threshold ?
  • FOCUS POINT: A detailed explanation of the eigenvalues of A and of the Jacobian J for different models.
  • FOCUS POINT: A detailed explanation of how classical graph metrics arise from the discrete cascade.
  • FOCUS POINT(s): Q: Dedicate one specific NB for each canonical model?

Reproduce paper figures

  • Probably, we should have a specific folder for this.
  • A notebook to reproduce results of Fig. 2 in the Chaos (2024) paper.
  • (DONE) A notebook to reproduce results of Fig. 3 in the Chaos (2024) paper.
  • (DONE) A notebook to reproduce results of Fig. 4 in the Chaos (2024) paper.