Neighbourhoods in dynamic digraphs

Neurotopology group homepage

April 2021

Figures 3, 14: Results of classification experiments. Left: Classification accuracy with respect to 50 top value vertices by selection parameter. Right: Classification accuracy with respect to 50 bottom value vertices by selection parameter.

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Supplementary figure 1: Left: Classification accuracy with respect to 50 top value vertices by selection parameter. Center: Percentage of feature value entries that are non-zero. Right: Comparison of left and center plot values, with a linear fit trendline.

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Figures 4, 16: Classification of eight random signals on an Erdos-Renyi random digraph on 1000 vertices and connection probabilities of 8%, 1% and 0.5% and selection of 10 and 20 tribes, modelled on a NEST simulator. Selection parameters are the same as in the main example and feature parameter is always tribe size. Graph G means the BBP graph and its performance with respect to tribe size as feature parameter is given for comparison.

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Figures 5, 13: Comparison of the classification performance of 50 randomlyselected tribes to the performance of tribes selected by graph invariants with respect to several feature parameters. Error bars indicate range over 20 iterations. Labelled error bars indicate best performing selection parameter.

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Figure 6: Classification results by binary vectors using only the chiefs of each of the top and bottom 50 tribes for each parameter. For comparison, the performance for each selection parameter classified by the highest performing feature parameter is included.

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Figure 7: Classification by subgraphs of the same vertex count as the tribes selected by the specified selection parameters. The results of classification by the highest performing feature parameters are above each of the columns.

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Figure 8: Classification by “fake tribes”: Original classification with respect to best performing feature parameter is given for comparison.

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Figure 9: Classification of shuffled binary dynamics functions andcomparison to the top results for the original dynamics.

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Figures 12, 15: Distribution of parameter values across the entire Blue Brain Project microcircuit. The numbers on the right are minimum to maximum values. The values on thex-axis are the relative parameter values, rescaled from 0 to 1.

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Supplementary figure 2: Distribution of parameter values overlaid with individual parameter values of top 50 tribes, when sorting by the best performing selection parameter (Chung Laplacian spectral radius).

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Comparison of values related to spectra. For each vertex, the eigenvalues of the adjacency graph of its tribe are computed. Since the eigenvalues may be complex, the modulus of all eigenvalues is taken, sorted, and only unique values are kept. Three parameters are then extracted:

  • low: (blue) smallest nonzero value
  • high: (red) difference of two largest value
  • radius: (yellow) largest value
See the tab "Links" for specific parameters and code used to generate these graphs.



Supplementary figure 3: Spectral values of Blue Brain microcircuit.

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Supplementary figure 4: Spectral values of 500-vertex Erdos-Renyi graphs with different probabilities.

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Supplementary figure 5: Spectral values of block graphs with different generating values. Each graph has 3 blocks, 100 vertices per block.

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Supplementary figure 6: Spectral values of 500-vertex Barabassi-Albert graphs with different numbers of edges added at each step. Edges are oriented randomly.

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Supplementary figure 7: Spectral values of 500-vertex directed scale-free graphs with different generating values.

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Supplementary figure 8: Spectral values of some real world graphs from the KONECT database.

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Correlation and comparison of tribe paramaters. The parameters have some overlap with the parameters presented in the paper. The visualization and files are included as a tool for inspection and discovery. Correctness of values is not guaranteed. Last updated February 26, 2020. Included files:

Visualization of 7 neuron tribes in the Blue Brain microcircuit. Shown are position, average voltage, and relative voltage of each tribe within the larger circuit. Download the video as MP4, OGG, WebM, uncompressed MP4.