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GNM Tutorials — Next Steps & Full Plan

General Setup

  • Create a dedicated Conda environment that includes:

    • GenerativeNetworkModels (the GNM toolbox)
    • jupyter (so that Quarto can execute Python chunks during render)
    • Plotting libraries (e.g., matplotlib, nilearn, networkx)
    • Any other dependencies needed across all tutorials

  • We will NOT use real data! All brain networks used throughout the tutorials will be generated using the GNM toolbox itself.

Section 1: Brain Networks

Tutorial: Introduction (DONE — Introduction.qmd)

  • Conceptual intro to brain networks, graph theory, and connectivity matrices.
  • Under the hood (without showing the code overtly), we produce two figures:
    1. A 3D brain connectivity plot using nilearn, displaying the GNM default network with default coordinates.
    2. A connectivity matrix of the same data.
  • These figures are embedded as images — the reader sees the visuals but not the code that generated them.

Tutorial: Installation (DONE — Installation.qmd)

  • Install Python, set up Conda environment, pip install GenerativeNetworkModels.
  • Callout box briefly explaining what GNMs are (simple rules to create artificial networks mimicking real brains — full details later).
  • Load the default built-in network using gnm.defaults.get_binary_network().
  • Now we show the script! We reproduce the same connectivity matrix from the Introduction tutorial, but this time the reader sees and runs the code themselves.

Tutorial: Research Question

  • Introduce a general scientific question that will drive the rest of the tutorial series.
  • Scenario: We have 20 brains, and we want to investigate whether brain network organisation changes depending on early life stress.
  • Each brain has an associated early life stress score from a real questionnaire (we need to identify which one — e.g., the Childhood Trauma Questionnaire, CTQ, or the Adverse Childhood Experiences, ACE).
  • Frame the question: Do individuals with higher early life stress show different network properties?
  • This question will be tackled using different approaches across the following tutorials.

Tutorial: Preprocessing

  • Before analysing the networks, we must check the data is usable!
    • Threshold all networks to the same density (so they are comparable).
    • Check: are the networks fully connected? Identify and discard any that are not.
    • Any other quality-control steps.

Tutorial: Topology

  • First approach to the research question: look at topology metrics and see if they correlate with early life stress.
  • Compute network metrics for each of the 20 brains (e.g., clustering coefficient, path length, modularity, degree distribution, betweenness centrality, etc.).
  • Possibly run a PCA on the metrics to show that they naturally cluster into integration vs segregation dimensions.
  • Build regression models in R to test whether topology metrics (or PCA components) correlate with early life stress scores.

Section 2: Generative Models

Tutorial: What is a GNM?

  • We got very weak correlations from topology alone — but there is more we can do!
  • Introduce the idea of Generative Network Models: finding a parsimonious, small set of parameters that captures complex brain topology.
  • Explain what a GNM is conceptually: using simple wiring rules to grow artificial networks that look like real brains.
  • Introduce the two key parameters:
    • eta (η): controls the spatial/distance penalty (how much wiring cost matters).
    • gamma (γ): controls the topological preference (e.g., homophily — connecting to nodes with similar existing connectivity).
  • Explain what each parameter does and how they interact to shape the generated network.

Tutorial: Model Fitting

  • Now that we understand GNMs, we apply them!
  • Perform a binary sweep over the eta-gamma parameter space.
  • Define the energy function (how we measure how close a generated network is to a real one).
  • Identify the lowest energy model (the parameter combination that best reproduces the observed brain network).
  • Interpret the results at group level: what do the best-fitting eta and gamma values tell us about how brains are wired?

Tutorial: Individual Differences

  • Move from group-level to individual-level parameter estimation.
  • Perform a second sweep that is:
    • More focused / fine-grained (narrower parameter range around the group optimum).
    • Run over multiple runs to ensure robust individual estimates.
  • Extract individual-level eta and gamma estimates for each of the 20 brains.
  • Correlate these individual parameter estimates with early life stress scores.
  • Interpret the results: what do individual differences in wiring rules tell us?
  • Speculate on links to cognition: how might differences in eta/gamma relate to cognitive outcomes?