In our simulations, we achieve color violations of 1.7% when using 39 reporters and 10.5% when restricting the solution to only 3 reporters
Results, An Optimal-Coloring Algorithm for Other Tissues and Model Organisms, paragraph 3; Figures 7D and 7E; Methods S2 Figure 1
On the neighbors of ms2-neuropal-color-violations (dandiset head atlas, 192 neurons, 543 Brain Atlas reporters with distinct patterns over them), the best of 10,000 runs at sparsity 100 has a mean shortfall of 1.71 to 1.72% (27 to 30 reporters kept), inside 1.7 +/- 0.17; the best run keeping exactly 39 reporters (189 to 205 runs) has 1.83 to 1.86%, also inside. These values differ in the second decimal between machines with the same seeds; the ranges are those of the runs made for this attempt. The sparsity for 3 reporters is not given, and the criterion's reading, the sparsity whose solutions use 3 reporters, fits 1500, 2000 and 3000 of the scan, where most runs keep 3 reporters (95, 94 and 89 of 100). With the criterion's 7,500 runs the best 3-reporter value is 6.95% at 1500 (7,106 runs with 3 reporters) and 8.38% at 2000 (7,020 runs), below 9.45 to 11.55, and 9.90% at 3000 (6,253 runs, none below 9.45%), inside it (optimal_coloring_sparsity.ipynb); at 1000 the best of 1,000 runs (561 with 3 reporters) is 7.83%. The 39-reporter value is inside the tolerance under every reading. The outcome would be partially reproduced at 1500 and 2000 and reproduced at 3000, and no sparsity is better supported than the others, so the claim is blocked with every result shown, by the rule this attempt applies to fig6de-asj-ric-stimulus-specific. The first record gave partially reproduced at 1500; the change was proposed after round 2 and agreed in round 3. The 3-reporter solutions take few values (5th percentile 9.90% at 1500), so the best of fewer runs lands in the tolerance, in 95% of random subsets of 10 runs, 66% of 100 and 1% of 1,000. On the paper's own adjacency in data.mat (235 neurons, 654 unique reporters as the paper states, 1,000 runs each) the best is 1.74 to 1.81% at sparsity 100 (1.99 to 2.03% for exactly 39 reporters) and 8.71% for 3 reporters. The Methods share, a variant, is 13.65% and 20.84% for the two best head-atlas solutions. What the answer changed. The amended criterion takes the code's mean shortfall as the measure, in place of the Methods share. The first run had blocked this claim (not_runnable) because scipy cannot read the MATLAB table holding the reporters; the author-answers run read it with mat-io and ported the solver. A question is recorded for a reader on whether the 3-reporter value is the best of 7,500 runs of this one setting, as the criterion reads it, or of the part of the paper's 7,500 simulations that had this setting (Methods S2 Figure 1 and Figure 6 legends), since with fewer runs the best falls in the tolerance.
How the test differed from the paper’s method
- Head atlas only (192 neurons); the paper used 235 head and tail neurons. The paper's own adjacency is run as a reference with 1,000 runs per setting, not 10,000 and 7,500.
- optimal_color_solver.m ported to Python and run on many random starts at once; starts are drawn with numpy, not MATLAB's rand, and the loop over neighbors uses squared distances over the nonzero entries of A, which gives the code's updates up to rounding.
- Three intensities taken as the margin of 1/3, from Methods S2 section 4.2 ("1/3 as our minimum color margin (corresponding to discriminating 3 levels of color intensity)"); 300 iterations from optimal_color_parameters.m and Methods S2 section 4.2 ("300 iterations in total").
- The solution kept from a set of runs is the one with the fewest violations, from the Methods S2 Figure 1 legend ("chosen as those with the minimal color violations, among 10,000 simulations"); each solution's colors and kept reporters follow find_optimal_colors.m (Otsu threshold on X, colors scaled by each channel's maximum).
- The sparsity for 3 reporters is not given by the paper; it was chosen as the value of a scan (250, 500, 1000, 1500, 2000, 3000; 100 runs each) whose runs most often keep 3 reporters, as the criterion reads it. Sparsities 2000 and 3000 were also run with 7,500 runs each, and 1000 with 1,000 runs, in optimal_coloring_sparsity.ipynb, a notebook of its own to keep each within its time limit.