│ ├── links/0/<i.j.k> # intra-level link rows (delta=0)

│ ├── links/+1/<i.j.k> # optional: fine→coarse pyramid edges │ │ # (only when cross_level_storage != "none")

9.2 Downsampling Strategies

This unprecedented scale

Edge-wise Properties

ig. 2

ASE and LSE each captured a different, but still true, truth about the underlying network. { requestKernel: true, binderOptions: { repo: "binder-examples/jupyter-stacks-datascience", ref: "master", }, codeMirrorConfig: { theme: "abcdef", mode: "python" }, kernelOptions: { kernelName: "python3", path: "./representations/ch6" }, predefinedOutput: true } kernelName = 'python3'

Discriminability Plot¶

Fig. 9

Fig. 4 Th

𝐻𝑘𝑙0:𝑏𝑙𝑒𝑓𝑡,𝑘𝑙=𝑏𝑟𝑖𝑔ℎ𝑡,𝑘𝑙,𝐻𝑘𝑙𝐴:𝑏𝑙𝑒𝑓𝑡,𝑘𝑙≠𝑏𝑟𝑖𝑔ℎ𝑡,𝑘𝑙

Plot the number of edges for each lateral type with 99% confidence intervals¶

Plot the network split out by left/right¶

Plot neurons and connectivity¶

Test for bilateral symmetry - latent distribution test¶

Plot the 2-sample test p-values by varying dimension¶

Look at what the components mean in the probability space¶

nan

G = G.to_undirected()

From these plots, we can tell that the degree distribution remains relatively static across age.

def vis_degree_dist(dd, max_degree, ages, dd_name):

vis_degree_dist(stats.in_degree, stats.graph_origin, stats.sex, "In Degree")

vis_stat(stats.density, "Density", use_log=False)

ax.xaxis.set_ticklabels(syntypes, rotation=45)

def vis_stat(stat, stat_name, use_log=True):

Again the lowest -BIC for each developmental stage is set to 0, allowing for easy comparison.

The lowest -BIC is set to 0, since the scale doesn’t really matter here.

Drosophila Hemibrain Connectome

We can’t visualize this connectome using grapological layouts becuase it is too large! We can still get the basic stats though:

C. Elegans

Elegens

1707

for i in range(len(layouts)):

data = {'Number of Nodes': [], 'Number of Edges': [], 'Density': [], 'Max Out Degree': [], 'Max In Degree': []} num_nodes = len(connectome.nodes) data['Number of Nodes'].append(num_nodes) num_edges = len(connectome.edges) data['Number of Edges'].append(num_edges) data['Density'].append(num_edges / (num_nodes * (num_nodes - 1))) data['Max Out Degree'].append(max(connectome.out_degree, key=lambda x: x[1])[1]) data['Max In Degree'].append(max(connectome.in_degree, key=lambda x: x[1])[1]) df = pd.DataFrame.from_dict(data) df.index = ['Ciona Intestinalis',] df.head()

connectome.to_undirected()

side_map = {'L': '#FF0000', 'DL': '#B22222', 'VL': '#F08080', 'R': '#0000FF', 'DR': '#00008B', 'VR': '#87CEEB', 'DM': '#800080', 'D': '#800080', 'VM': '#BA55D3', None: '#A9A9A9'}

Now we generate a 2-dimmensional node layout using Graspologic’s layout_tnse.

Generalized Random Dot Product Graph (GRDPG)¶

Recreate fig 4 from FAQ Paper¶

Plot the adjacency matrices sorted by fit partition¶

label

Matching objective function: 6229.611251407659 # collapse dataset2_intra_matched = dataset2_intra[perm_inds][:, perm_inds][: len(dataset1_ids)] dataset2_meta_matched = dataset2_meta.iloc[perm_inds][: len(dataset1_ids)]

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.)

Create a color palette by department/institute

heatmap(A[[vtx_perm]] [:,vtx_perm])

Plot the alignment for d=7 dimensions¶

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.)

Figure Panels

A priori modeling

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

A posteriori modeling

(Do we know how to do this?)

Discriminability

Neuron 16977881 has more than one soma, removing

Neuron 15571194 has more than one soma, removing

Discriminability plotted as a function of stage 1 and stage 2 dimension