Contents

Outline

Figure Panels

  • Show the data

    • What do the neurons look like? Plot the neurons in space, maybe show a few examples, etc.

    • What does the graph look like? Can plot adjacencies as well as some kind of graph layout possibly.

    • [x] Some simple descripive statistics (# nodes, # edges, # synapses, degrees, weights, etc.)

      • Table: number of nodes, number of edges, number of synapses

      • Panel of edge weight distribution

      • Panel of in vs out degree with marginals

    • (Maybe) something describing the different edge types

  • A priori SBM-family model comparison and selection

    • We have some A priori information:

      • left/right hemisphere

      • ipsilateral, contralateral, bilateral

      • loose cell types

        • sensory/motor/interneuron

        • other rough categories

    • We can fit a priori SBMs using all of the above. Some of them can even be nested (e.g. by left/right and then by ipsi/contra/bi)

    • For each, calculate the number of free parameters.

    • Do some kind of model selection/comparison and try to select the best one

    • Left/right hemisphere blockmodel (question: how does this relate to the above, even within a model class of 2 block SBMs there are a ton of different ways to parameterize)

      • maybe framed less as a test, more as part of the model selection question

      • testing for homophillic/assortative, the different SBM block probability hypotheses

      • Could do the above with the different 4 color graphs as well

    • have lots of tools to evaluate.

      • with the DC stuff we don’t quite know how to do it. with SBM jovo thinks we do know how.

    • point of this figure is lets evaluate how good our models are

  • A posteriori modeling

    • point of this one is what can we learn about the structure of the data that we dont have a priori

    • Hierarchical SBM estimation

      • should we revisit how this is estimated?

      • we never tried initializing with a prior

      • could use the best a priori as init for a posteriori

    • Leiden hierarchical SBM estimation, how are these different/not different (do we want this?)

      • this is just another way of fitting an SBM, with different constraints.

    • Comparison of model complexity (dDCSBM, SBM, RDPG-d, etc.)

    • Follow up with brain images labeling the neurons

    • Want to justify by looking at the neurobiology

  • Ok, so maybe we should include vertex attributes

    • Embedding with node covariates for example

    • Maybe we just show?

    • Figure out how to evaluate?

  • (maybe) multigraph model selection

  • Graph matching methods figure (I don’t think these results from Youngser/Carey ever went to a paper anywhere? so I assume CEP would be okay with them here? And we should be able to replicate/improve in python now.)

    • Show some examples of pairs in space.

    • Show results of vanilla GM, GM with some notion of similarity (maybe NBLAST and or spec sim?), GM with multigraph, GM with multigraph + similarity.

    • (Maybe) Seeded graph matching with the known pairs as seeds? I actually use this in my work… so it is useful.

    • Some interesting inference about pairedness? Would be nice to show what this can be used for, or demonstrate which parts are more/less bilaterally similar?

    • Maybe something about testing for homotypic connections?

  • Bilateral symmetry/testing

    • How similar are the SBM models?

      • chi square test?

    • How similar are the RDPG models (nonpar/semipar)?

      • maybe select best model and compare left right on those

    • Can we say anything about the correlation under these different models?

    • Testing homotopic affinity (by edge type)

  • Directedness: testing for whether the graph or specific parts of it are meaningfully directed. (Do we know how to do this?)

  • Feedforwardness: describing (and hopefully modeling) a feedforward pathway through the network, expanding to include multinetwork models.

    • Some description of the chain predicted by signal flow or cascades or graph match flow etc.

    • Comparisons of the flows for different network types (e.g. AA, AD, etc.)

    • Testing for feedforwardness with spring rank model

    • maybe goes in Cambridge paper?

Code

  • Flow/hierarchy/ranking into graspologic

  • Improve the estimation code to make it easier to fit to data in a useful way, examine the models, etc. (as necessary)

  • Adjacency with dendrogram for hierarchical clustering that is not complete

    • I have code, not pretty, probably not generalizable yet

  • Tests from statistical connectomics into graspologic

    • We should talk to Eric/decide what we actually want first

  • Bar dendrogram plotting in general

Welcome Introduction