DANDI:000483

we found a similar percentage heading neurons as in the experiments without controlled rotation, comprising 14.2% (452/3179 neurons) of the total number of cells recorded (n = 16 recordings over 5 mice

Results, Neurons in the RSC represent heading in the absence of physical head movements, paragraph 3; Figure 1G

With the centred fit, 485 of 3179 ROIs (15.26%) pass, within 14.2 +- 1.42% and 452 +- 45; by mouse 8.9 to 25.2%, by recording 2.2 to 33.0%. With the fit as the code calls it, without centring, 345 (10.85%), outside the tolerance. With stricter reliability thresholds (KS p < 0.01, d > 1.2) the centred count is 393 (12.36%). The test is liberal. Its reliability step runs a KS test on 1000 split-half correlations of the same trials, as the paper's code does (ControlledRotation.calculateHeadDirection), and synthetic untuned cells pass the whole test at 4.7% (centred) and 1.7% (uncentred); real cells with each trial shifted once pass at 5.19% (selection-shuffled-control). The count matches the paper's, but about a third of the selected cells could pass by chance.

How the test differed from the paper’s method

• Inferred spikes are computed here from the raw ROI fluorescence (OASIS AR(1), Python port) without the neuropil correction of the Methods (eq. 1), as the files hold no neuropil trace, dF/F or spikes.
• The selection test (code ControlledRotation.calculateHeadDirection) and its Gaussian fits are reimplemented in numpy (bounded Levenberg-Marquardt in place of MATLAB fit).
• Assumption. The code fits the trial-mean curve as it is, with the peak location bounded to pi/2 +- pi/6, so only cells whose peak lies near one heading can pass; its center_flag option, used by its 'fit' preferred direction, first shifts the peak to bin 15. The Methods do not say. The centred fit is adopted because with the uncentred one 93.6% of the selected cells lie in one quadrant, which contradicts the tiling of Figure 1H; both readings are shown, and they give different outcomes.

showing that heading-responsive cells tile the entire circumference of the chamber, even when the cue card is outside of the visual field of the mouse; though we note there is a moderate overrepresentation of responses when the cue is centered in front of the mouse near 0°

Results, Neurons in the RSC represent heading in the absence of physical head movements, paragraph 3; Figure 1H

Tiling holds. The 485 cross-validated preferred headings (centred fit) fill all 60 bins of 6 degrees, and the four quadrants hold 18.1 to 40.0%. The overrepresentation cannot be judged. The files give heading relative to "cage door dead north" and do not say where the cue is. Within 45 degrees of the dataset's 0 lie 24.7% (not above 25%). The densest 90-degree window, centred at -102 degrees, holds 40.4% (Rayleigh p = 2e-05), and the densest heading differs between mice (in 30-degree bins SKKS090 peaks at +60 to +120 and SKKS091 at +60 to +90). Were the cue at dataset heading -90, the share near it would be 40.0%; nothing in the files says so. The code's uncentred fit puts 93.6% of its cells near -90 because its bounds hold the Gaussian's peak at dataset headings -120 to -60, which says nothing about the cue.

How the test differed from the paper’s method

• Rests on the centred fit of fig1g-rotation-heading-fraction.
• The position of the cue in the dataset's heading frame is not in the files, so heading 0 of the claim could not be located.

When repeating these procedures using pre-shuffled data, no cells passed these criteria, suggesting that the number of heading selective cells is accurate, and not due to chance

Methods, Analysis of calcium data, paragraph 4

With each trial shifted once by its own random amount before the whole test, as the Methods' "pre-shuffled data" and the criterion's "before the test" say, 165 of 3179 ROIs (5.19%) pass, above the criterion's 1% limit; 478 pass the reliability step. Run as the commented calculateHeadDirection_shuff of Cue.m does it (the trials re-shifted in every iteration), 0 of 3179 pass under both fits, but under that reading the "real" and null split-half correlations come from the same distribution, so no cell can pass whatever the data. Synthetic untuned cells pass at 4.7% (fig1g). Which reading the claims file intends is asked in questions/000483.yaml.

How the test differed from the paper’s method

• Assumption. The trials are shifted once before the test (the variant of the first run). The criterion names both "before the test" and the commented code, which shifts them afresh in every iteration; only the first can show whether the count is due to chance. Both are shown.
• Spikes computed without neuropil correction, and the test reimplemented, as for fig1g-rotation-heading-fraction.

matched ROIs on average have the same heading preference with respect to wall pattern across conditions ... (V32 = 14.1, p = 2.5 × 10−4, V-test for nonuniformity against 0°

Results, Heading cells exhibit similar preferred directions during rotation of the animal or the environment; Figure 2E, F

What the paper reports

• V-test for nonuniformity against 0 degrees, V32 = 14.1, p = 2.5 × 10⁻⁴ (n = 32 (the subscript of V, read as the number of matched cells), 5 recordings over 4 mice)

The criterion's test passes only under assumptions. Cells selective in both conditions, peak preference, chamber-rotation (CR) heading mirrored, the 5 pairs whose stored headings run in opposite directions, give V = 34.6, n = 228, p = 5.9e-04 ('fit' preference V = 36.0, p = 3.8e-04; cells selective in CR V = 47.7, p = 7.3e-05). 4 of 24 readings give p < 0.05 with V > 0. With all 7 pairs none does, and with the headings as stored every V is negative. Neither the mirroring nor the choice of 5 pairs can be checked against the data. The V is not the paper's 14.1 (n = 32), and no reading has n near 32. Matched ROIs do not keep their preference better than random pairs: pairing ROIs at random over the 5 pairs gives a larger V (mean 46.2, 95th percentile 57.6), and within every pair the real V lies inside its own random-pairing null (share of 1000 random pairings at or above it 0.222 to 0.998; SKKS116, the one pair with a large V, 58.9 against a null mean of 56.8). Head-rotation files have more selective cells (52 to 83% against 8 to 65%) and more activity (0.095 to 3.19 spikes/s against 0.063 to 0.114) than their CR partners, so heading-locked artefacts of derotation are not excluded. A 6-frame clock offset would move preferences by 4 to 8 degrees (head rotation) or 12 degrees (six of the CR files); the clock check of single_cue.ipynb peaks at -6 frames in one of four files, so the timing is not established. The seventh CR file, 210526 SKKS112-PlatformRotation-002, barely rotates (median step 0.12 degree per frame against about 2 in the others; 10 trials against 26).

How the test differed from the paper’s method

• Assumption. The stored headings of 5 of the 7 pairs run in opposite directions in the two conditions, while the paper says the cue moves across the visual field in the same direction in both (Figure 2B legend), so the CR heading is mirrored to put both in the frame of the wall pattern. The files do not say how either heading is defined.
• Assumption. The dataset holds 7 pairs over 5 mice; the paper reports 5 over 4, which matches the 5 opposite-direction pairs. Both sets are shown.
• Cells selected with the centred fit of fig1g-rotation-heading-fraction; spikes without neuropil correction.

changing contexts caused the population of heading cells to coherently remap, as indicated by low Δ phase offsets (V66 = 25.6, p = 4.9 × 10−6

Results, Changing visual cues elicits coherent remapping in RSC neurons; Figure 3C

What the paper reports

• V-test for nonuniformity against 0 degrees, V66 = 25.6, p = 4.9 × 10⁻⁶ (n = 66 (the subscript of V, read as the number of neurons), 12 recordings over 4 mice)

All 8 readings give V > 0 with p < 0.05. Cells selective in both contexts, peak preference, expected offset (i), give V = 47.0, n = 85 over 9 recording pairs, p = 2.8e-13, against V = 25.6 with n = 66 in the paper; no reading gives a V within the tolerance (38.4 to 233.5). Pairing neurons at random gives a V of 36.2 on average (95th percentile 45.7, 1000 draws); 2.6% of random pairings reach the real V, so it lies only just above the null. 8 of the 9 pairs with 3 or more cells have V > 0. The SKKS091 2021-05-04 pair, whose files are both named context 1, has fewer than 3 cells selective in both and enters only the readings with cells selective in either.

How the test differed from the paper’s method

• Cells selected with the centred fit of fig1g-rotation-heading-fraction; spikes without neuropil correction.
• The medians of the Methods are taken as circular medians (a standard choice for angles).
• The 12 remapping pairs are the two files of each mouse and day; one pair (SKKS091, 2021-05-04) is named 1-001 and 1-002 and is taken as a pair.

In the light-on condition, ADN axons show a unimodal tuning curve, whereas visual cortical axons show a bimodal tuning curve

Results, The ADN and visual cortex send distinct information to RSC, paragraph 2; Figure 4D, E

Under reading (b), all 1084 ADN and 247 visual axons, the mean aligned light-on curve has a flip score of -0.207 (ADN) and 1.875 (visual), and single visual axons score higher (means 0.506 and -0.109, KS p = 1.6e-24). Under reading (a), selective axons, the visual mean curve is bimodal (1.814) and single axons differ (KS p = 1.7e-21), but the ADN mean curve has a flip score of 0.277 with the centred fit and 1.132 with the code fit, above 0. One ADN mouse (SKKS092) has a mean flip score above 0 under reading (a) (0.48, 0.423) and about 0 under (b) (-0.001).

How the test differed from the paper’s method

• Axon traces are inferred spikes from the raw fluorescence, with no neuropil correction; the paper used Suite2P traces and excluded duplicate axons (r > 0.5), and the files give ROIs as they are.
• Light and dark segments are the code's hard-coded ones (Separator.m); the files do not mark them.

In the light-off condition, ADN axons maintain their response for several trials, whereas visual cortical axons lose their tuning

Results, The ADN and visual cortex send distinct information to RSC, paragraph 2; Figure 4D, E legends

Visual axons lose their tuning in light-off (mean light-off curve 5 to 11% of the light-on range, under half). The ADN part fails. Over all axons (reading b) the per-recording fraction selective in light-off is not significantly higher for ADN than for visual axons (medians 0.050 and 0.015, Mann-Whitney p = 0.35); pooled, 93 of 1084 against 11 of 247 (Fisher p = 0.035, the variant). Among selective axons (reading a) the share also selective in light-off has medians 0.134 and 0.000 (Mann-Whitney p = 0.15, 14 and 7 recordings); pooled 39 of 135 against 5 of 106 (Fisher p = 5.4e-07). The ADN mean light-off curve keeps 72 to 86% of the light-on range, but its peak lies 24 degrees (reading a, centred fit) or 30 degrees (reading b) from the light-on peak, beyond 18 degrees; with the code fit it lies at 18 degrees.

How the test differed from the paper’s method

• Light-off curves take the circular shift of the mean light-on curve; the code's aligner (leaveOneOutAligner) is not public.
• As for fig4-axons-light-on-shape.

The light-off peak in these alignment cells was always at the same location as one of the two peaks in the light-on condition

Results, A functional class of RSC neurons coregisters visual and heading signals, paragraph 2; Figure 5E

The criterion's V-test passes for the 1150 alignment-like cells (V = 743.5, p < 1e-300), but taking the nearer of two peaks 180 degrees apart folds offsets into +-90 and gives a large V by itself: uniform light-off peaks give V = 669.5 on average (V/n 0.582 against 0.646), and light-off peaks paired at random with other alignment-like cells give 707.2 (95th percentile 728.4, 1000 draws). The real V exceeds the random pairing (share at or above it 0.002), a small coregistration. Only 29.2% of offsets lie within 18 degrees, against 26.2% under random pairing, with a median offset of 36 degrees, so "always" is not supported. In the heading-like and landmark-like classes the V does not exceed random pairing (shares at or above it 0.677 and 0.230). The class is not the paper's alignment class (fig5-class-proportions).

How the test differed from the paper’s method

• Tested on the classes found here, which differ from the paper's.
• The V is compared with a random-pairing null and a uniform-peak null, which the criterion does not ask for, because the nearer-peak offset biases the V-test towards 0.

Heading cells showed no significant difference in flip score across conditions (F1,662 = 0.18, p = 0.67

Results, A functional class of RSC neurons coregisters visual and heading signals, paragraph 3; Figure 5F

What the paper reports

• F-test (mixed-effects model), F(1,662) = 0.18, p = 0.67 (n = heading cells (332, from the degrees of freedom))

The criterion is met on a class that is not the paper's. The 202 heading-like cells have flip scores 0.378 in light-on and 0.279 in light-off, F(1,402) = 2.2, p = 0.141 (mixed model with mouse as random intercept); with the outlier step p = 0.138, with a random intercept per cell p = 0.116. The class has 202 cells where the paper's degrees of freedom imply 332, and its light-on archetype is bimodal (a2/a1 0.70), so it is only the least bimodal of three bimodal classes. In the first round's development, with a different selection seed, the class held 380 cells and the light effect was significant (not run here).

How the test differed from the paper’s method

• statsmodels MixedLM (REML), F as the squared z of the light effect, in place of MATLAB fitlme.
• Tested on the classes found here, which differ from the paper's.

both landmark (F1,1042 = 1062.5, p = 3.1 × 10−161) and alignment (F1,816 = 209.5, p = 2.0 × 10−42) cells have significantly lower flip scores in the light-off than the light-on condition

Results, A functional class of RSC neurons coregisters visual and heading signals, paragraph 3; Figure 5G, H

What the paper reports

• landmark cells, light-off against light-on flip score: F-test (mixed-effects model), F(1,1042) = 1062.5, p = 3.1 × 10⁻¹⁶¹ (n = landmark cells (522, from the degrees of freedom))
• alignment cells, light-off against light-on flip score: F-test (mixed-effects model), F(1,816) = 209.5, p = 2 × 10⁻⁴² (n = alignment cells (409, from the degrees of freedom))

The criterion is met on classes that are not the paper's. Flip scores fall in light-off for landmark-like cells (0.478 to -0.239, F(1,132) = 44.3, p = 2.8e-11, n = 67) and alignment-like cells (0.365 to 0.014, F(1,2298) = 135.4, p = 2.7e-31, n = 1150), against F(1,1042) = 1062.5 and F(1,816) = 209.5 in the paper.

How the test differed from the paper’s method

• As for fig5f-heading-flip-unchanged.

finding that ADN axons and visual axons are mostly restricted to the boundaries of the heading and landmark clusters, respectively (Fig. 5I), although there is some overlap with the alignment cluster boundary

Results, A functional class of RSC neurons coregisters visual and heading signals, paragraph 4; Figure 5I

The criterion is met, but the ellipses do not separate the axon groups. Under reading (a), 88.1% of ADN axons lie inside the heading-class 95% ellipse and 83.0% of visual axons inside the landmark-class ellipse; under (b), 72.4% and 55.5%. The alignment-class ellipse holds 84.3 to 96.2% of both axon groups, the heading ellipse holds 81.0 to 92.5% of visual axons (more than the landmark ellipse), and the LDA assigns 85.2 to 98.0% of axons to the alignment class. The classes come from fig5-class-proportions, which is not reproduced.

How the test differed from the paper’s method

• Tested on the classes found here, which differ from the paper's.
• The 95% ellipse is read as the 95% region of a bivariate normal fitted to the class's LDA points, as the claims file says.

We found that the data were optimally clustered into three functional classes ... although we note that the responses span a continuum

Results, A functional class of RSC neurons coregisters visual and heading signals, paragraph 1; Figure 5B; Methods, Clustering of RSC soma responses

The silhouette value is highest at k = 2 under both readings of the criterion. Selective cells (1419) give 0.272, 0.019 and 0.032 for k = 2, 3 and 4, and all cells (11329) give 0.190, 0.120 and -0.052, so neither has a local maximum at 3. The reviewer-code variant, each curve centred on its own peak, has one for selective cells (0.114, 0.393, 0.004) but not for all cells (0.260, -0.015, 0.016); the criterion reports the variant and decides on readings (a) and (b).

How the test differed from the paper’s method

• Spikes without neuropil correction; cells selected with the centred fit; light-off curves aligned with the shift of the mean light-on curve (leaveOneOutAligner not public).
• GaussianMixture of scikit-learn (full covariance, 20 initialisations, 1000 iterations) in place of MATLAB's fitgmdist; the silhouette is computed on the hard assignments.
• One 1950-frame recording (2021-01-18, SKKS088 DualCue-002) has no light-on trial and is left out.

Of the total number of tuned cells (12.1 ± 1.1%), landmark cells made up the plurality of cells (33 ± 3.5%), followed by alignment cells (28 ± 1.9%, mean ± s.e.m.), and heading (22 ± 2.3%) cells

Results, A functional class of RSC neurons coregisters visual and heading signals, paragraph 3; Figure 5C to E

12.10% of somata are tuned (mean over recordings, s.e.m. 1.44; pooled 12.53%, over mice 11.51%), within 12.1 +- 1.1. The class shares do not match. Over recordings with no outlier step, landmark-like cells are 7.6%, alignment-like 78.9% and heading-like 13.5%; with the chi-square outlier step (58 cells to the null cluster) 7.4, 75.3 and 13.3%. Every reading orders them alignment > heading > landmark. The counts are 67 landmark, 1150 alignment and 202 heading, against 522, 409 and 332 from the paper's degrees of freedom. All three light-on archetypes are bimodal (a2/a1 0.70 to 0.80), so no class is a unimodal heading class. measured gives reading (b) with average (i).

How the test differed from the paper’s method

• Classes are named by a rule on the archetypes (heading, the least bimodal light-on archetype; landmark, the weaker light-off archetype of the other two), as the paper names them by their curves without a rule.
• As for fig5-three-classes.

These responses persisted regardless of rotation direction (Figure S5, p = 0.0094, bootstrapped KS-test, n = 4 recordings over 2 mice)

Results, A functional class of RSC neurons coregisters visual and heading signals, paragraph 1; Figure S5

What the paper reports

• bootstrapped KS-test, p = 0.0094 (n = 4 recordings over 2 mice)

Reading (b) passes. For the 407 cells selective in the four files that rotate both ways, each cell's clockwise and counterclockwise tuning curves correlate more (median 0.210) than randomly paired cells (0.118), bootstrapped KS p = 0.002. Reading (a), differences in preferred heading, gives p = 0.16 (median 24 against 30 degrees). The pass is fragile. The pooled random pairs cross files, and by mouse, with random pairs from the same mouse, (b) passes for SKKS125 only (p = 0.044; SKKS126 0.119, SKKS127 0.699); over all active cells neither reading passes (p = 0.512 and 0.543). The statement's light and dark responses are not separated, as the files do not mark the light condition, so the "diversity" part is not tested beyond tuning stability.

How the test differed from the paper’s method

• Figure S5 was not read; what is compared follows the claims file's readings.
• The dataset's 4 recordings in both directions are over 3 mice, where the paper reports 2; all 4 are used.
• In each bootstrap iteration both samples are drawn with replacement and the random pairing is drawn afresh (a standard choice); dual-cue preferred headings are compared modulo 180 degrees.
• Spikes without neuropil correction; cells selected with the centred fit.

or whether or not the animal was in control of the arena (Figure S6, 0.031, bootstrapped KS-test, n = 7 recordings over 3 mice)

Results, A functional class of RSC neurons coregisters visual and heading signals, paragraph 1; Figure S6

What the paper reports

• bootstrapped KS-test, p = 0.031 (n = 7 recordings over 3 mice)

Without the pair whose animal-controlled file visits 6 of 60 heading bins (SKKS125, 2022-07-21), neither reading passes: n = 269, (a) p = 0.973, (b) p = 0.9 (median correlation 0.093 against 0.086 at random), and no pair passes on its own (p 0.781 to 1). With it, reading (b) passes over all 5 pairs (n = 381, median 0.027 against -0.011, p = 0.026; (a) p = 0.889), but its 112 cells (29% of n) have animal-controlled tuning curves that are 0 in 54 of 60 bins, and the pooled random pairs cross pairs of files.

How the test differed from the paper’s method

• Figure S6 was not read; what is compared follows the claims file's readings.
• The dataset holds 5 pairs over 4 mice, where the paper reports 7 recordings over 3; all 5 are used. Tuning in the animal-controlled file is built from all turning frames (more than 0.5 degree per frame), as these files have few full rotations.
• As for figs5-rotation-direction.
• Assumption. Pairs whose animal-controlled file visits fewer than half of the 60 heading bins are left out (one pair, 6 of 60 bins), as their tuning curves are mostly the 0 that bin_tuning gives an unvisited bin. The result with it is shown.

We found that the visual contributions to tuning were retained in visual cue only rotation, but the loss of proprioceptive and somatosensory information strongly degraded the heading cell responses

Results, A functional class of RSC neurons coregisters visual and heading signals, paragraph 4; Figure 5J, K

The two visual-cue-only recordings (Suspended, SKKS125 2022-08-10 with 446 ROIs and SKKS127 2022-08-11 with 691 ROIs, 15050 frames each) share their number of ROIs with no other file of their mouse (the others have 213 to 670), and no matching of ROIs is given, so the matched neurons of Figure 5K cannot be found in another file. Inside each file the 1250-frame blocks alternate between the two directions of rotation at about 2 degrees per frame and the last block is still; nothing in the heading or the mean fluorescence marks some blocks as standard rotation, and light-on and light-off are not marked (directions.ipynb).

As expected based on their tuning curves, heading cells did not exhibit a preponderance of 180° errors, suggesting they do not represent visual information directly

Results, Contributions of distinct classes to representation of heading, paragraphs 1 and 2; Figure 6B

Under the Bayes decoder, 12.0% (dF/F) and 13.6% (spikes) of the landmark-like decoder's light-on errors lie within 18 degrees of 180, above 0.10, and 7.0% and 9.1% of the heading-like decoder's, no more than 0.10. The result is fragile: without shared frames it holds for dF/F ((a'') landmark 0.135, heading 0.078) but not for spikes (heading 0.137), and under the trial split and the HeadingDecoder it fails (heading-like 0.104 to 0.157); those readings decode at 0.13 to 0.26, and all their groups have 0.104 to 0.202. The classes are not the paper's.

How the test differed from the paper’s method

• Assumption. The decoder readings give different outcomes; the naive Bayes decoder is adopted, as the Methods name Bayesian decoding (Etter et al. 2020), resample each trial to 200 bins and split even and odd time points for training and testing (Methods, Decoding RSC somatic activity), which reading (a) follows, and the claims file puts the Methods first. Every reading is shown, with two Bayes variants in which no test bin shares a frame with a training bin: (a') even trials to train and odd trials to test, (a'') the paper's split of even and odd time points on 100 heading bins that each hold the nearest frame, without interpolation. Both give lower accuracies (all tuned cells, light-on, 0.239 to 0.532 against 0.708 and 0.712), so the accuracies of reading (a) depend heavily on test bins sharing frames with training bins, as the paper's own procedure does.
• The classes are those of somata.ipynb (fig5-class-proportions, not reproduced), rebuilt in decoding.ipynb with the same files, seeds and code; they differ from the paper's.
• Pseudopopulations from the 25 7550-frame recordings with 5 trials on each side of all three light-to-dark transitions (15 trials a side; 1331 of 1419 tuned cells); the 1950-frame recordings are left out. Trials are resampled to 200 bins on heading in place of time, so bins line up across recordings.
• The naive Bayes decoder is written here after Etter et al. (2020): activity binarized (spikes above 0; dF/F above the mean plus 2 SD, a standard choice), 60 states of 6 degrees, a +1/+2 prior, trained on even and tested on odd bins of the trials resampled to 200 bins, as the Methods split even and odd time points after resampling. The HeadingDecoder (github.com/ucsb-goard-lab/HeadingDecoder at ca9842e) is reimplemented in numpy with leave-one-trial-out tuning weights. It decodes synthetic cells at 0.908 to 0.999, and these data at 0.202 and 0.215 for all tuned cells in light-on, twice chance and close to the naive Bayes decoder trained and tested on different trials (0.239 and 0.255). The synthetic test shows the algorithm as written works; a difference from the lab's code in some detail cannot be excluded.
• Chance is measured with each decoder by decoding with each cell's test activity circularly shifted along the trial: 0.101 to 0.102, the 0.10 reading of the claims file.

Since their decoder performance is lower than the population in the light-on condition, heading cells alone may be insufficient for ... providing an optimal representation of instantaneous heading

Results, Contributions of distinct classes to representation of heading, paragraph 2; Figure 6B, right (the text cites "Fig. 6C, right", but the class comparison is the right panel of Figure 6B by its legend); Table S1

Under every decoder and input reading, the 95% interval of light-on accuracy for heading-like cells lies below that of all tuned cells (Bayes dF/F 0.429 [0.399, 0.457] against 0.708 [0.665, 0.747]; spikes 0.415 [0.390, 0.441] against 0.712 [0.678, 0.746]; Bayes without shared frames 0.158 to 0.328 against 0.239 to 0.532; HeadingDecoder 0.130 and 0.146 against 0.202 and 0.215), reading (a); heading-like cells decode worse in 99.8 to 100% of iterations. Reading (b), a mixed model with recording or mouse as random intercept, cannot be formed, as each pseudopopulation trial pools cells of many recordings and mice. The heading-like class is not the paper's.

How the test differed from the paper’s method

• The classes are those of somata.ipynb (fig5-class-proportions, not reproduced), rebuilt in decoding.ipynb with the same files, seeds and code; they differ from the paper's.
• Pseudopopulations from the 25 7550-frame recordings with 5 trials on each side of all three light-to-dark transitions (15 trials a side; 1331 of 1419 tuned cells); the 1950-frame recordings are left out. Trials are resampled to 200 bins on heading in place of time, so bins line up across recordings.
• The naive Bayes decoder is written here after Etter et al. (2020): activity binarized (spikes above 0; dF/F above the mean plus 2 SD, a standard choice), 60 states of 6 degrees, a +1/+2 prior, trained on even and tested on odd bins of the trials resampled to 200 bins, as the Methods split even and odd time points after resampling. The HeadingDecoder (github.com/ucsb-goard-lab/HeadingDecoder at ca9842e) is reimplemented in numpy with leave-one-trial-out tuning weights. It decodes synthetic cells at 0.908 to 0.999, and these data at 0.202 and 0.215 for all tuned cells in light-on, twice chance and close to the naive Bayes decoder trained and tested on different trials (0.239 and 0.255). The synthetic test shows the algorithm as written works; a difference from the lab's code in some detail cannot be excluded.
• Chance is measured with each decoder by decoding with each cell's test activity circularly shifted along the trial: 0.101 to 0.102, the 0.10 reading of the claims file.
• Two Bayes variants in which no test bin shares a frame with a training bin are shown as further readings: (a') even trials to train and odd trials to test; (a'') the paper's split of even and odd time points on 100 heading bins that each hold the nearest frame.

When transitioning from light-on to light-off, there is a drop in the performance of the decoder, although the performance remains above chance ... (mean decoder accuracy = 0.44, 95% CI = [0.34, 0.54], p = 7.6 × 10−3

Results, Contributions of distinct classes to representation of heading, paragraph 1; Figure 6A, bottom

What the paper reports

• bootstrapped t-test, p = 0.0076 (n = 1000 bootstrapped samples)
• bootstrap confidence interval, 95% CI 0.34 to 0.54

Under the Bayes decoder light-off accuracy drops and stays above chance: 0.569 [0.525, 0.612] (dF/F) and 0.572 [0.535, 0.608] (spikes), both intervals above 0.18 and 0.10, light-off lower with p = 0.016 and p < 0.001 (paired; unpaired 0.061 and 0.002). The mean is outside 0.44 +- 0.10 under reading (a), so the criterion is not met in full. Without shared frames (a''), dF/F gives 0.406 [0.361, 0.452], within the tolerance and above both chance levels, but the drop is not significant (paired p = 0.105); spikes give 0.206 [0.177, 0.233]. The trial split (a') gives 0.167 and 0.140. The HeadingDecoder gives 0.137 [0.101, 0.178] and 0.144 [0.112, 0.176], above 0.10 and below 0.18, with no significant drop (p 0.231 to 0.361).

How the test differed from the paper’s method

• Assumption. The decoder readings give different outcomes; the naive Bayes decoder is adopted, as the Methods name Bayesian decoding (Etter et al. 2020), resample each trial to 200 bins and split even and odd time points for training and testing (Methods, Decoding RSC somatic activity), which reading (a) follows, and the claims file puts the Methods first. Every reading is shown, with two Bayes variants in which no test bin shares a frame with a training bin: (a') even trials to train and odd trials to test, (a'') the paper's split of even and odd time points on 100 heading bins that each hold the nearest frame, without interpolation. Both give lower accuracies (all tuned cells, light-on, 0.239 to 0.532 against 0.708 and 0.712), so the accuracies of reading (a) depend heavily on test bins sharing frames with training bins, as the paper's own procedure does.
• The classes are those of somata.ipynb (fig5-class-proportions, not reproduced), rebuilt in decoding.ipynb with the same files, seeds and code; they differ from the paper's.
• Pseudopopulations from the 25 7550-frame recordings with 5 trials on each side of all three light-to-dark transitions (15 trials a side; 1331 of 1419 tuned cells); the 1950-frame recordings are left out. Trials are resampled to 200 bins on heading in place of time, so bins line up across recordings.
• The naive Bayes decoder is written here after Etter et al. (2020): activity binarized (spikes above 0; dF/F above the mean plus 2 SD, a standard choice), 60 states of 6 degrees, a +1/+2 prior, trained on even and tested on odd bins of the trials resampled to 200 bins, as the Methods split even and odd time points after resampling. The HeadingDecoder (github.com/ucsb-goard-lab/HeadingDecoder at ca9842e) is reimplemented in numpy with leave-one-trial-out tuning weights. It decodes synthetic cells at 0.908 to 0.999, and these data at 0.202 and 0.215 for all tuned cells in light-on, twice chance and close to the naive Bayes decoder trained and tested on different trials (0.239 and 0.255). The synthetic test shows the algorithm as written works; a difference from the lab's code in some detail cannot be excluded.
• Chance is measured with each decoder by decoding with each cell's test activity circularly shifted along the trial: 0.101 to 0.102, the 0.10 reading of the claims file.

We found that heading cells were able to accurately decode in both light-on (mean decoder accuracy = 0.61, 95% CI = [0.56, 0.66]) and light-off conditions (mean decoder accuracy = 0.44, 95% CI = [0.36, 0.52]), suggesting that they contribute to the heading signal in both conditions (p = 0.11

Results, Contributions of distinct classes to representation of heading, paragraph 2; Figure 6B, top

What the paper reports

• bootstrapped t-test, p = 0.11 (n = 1000 bootstrapped samples)
• light-on accuracy: bootstrap confidence interval, 95% CI 0.56 to 0.66
• light-off accuracy: bootstrap confidence interval, 95% CI 0.36 to 0.52

Under the Bayes decoder, heading-like cells (179 used) decode above chance in both conditions (dF/F 0.429 and 0.377; spikes 0.415 and 0.341; every interval above 0.18) with no significant difference (p 0.170 to 0.964), as the claim says, but both means are outside 0.61 +- 0.05 and 0.44 +- 0.08 under every reading. Without shared frames the pattern holds at lower accuracy ((a'') dF/F 0.328 and 0.280, both intervals above 0.18, p = 0.806); the trial split and the HeadingDecoder give 0.130 to 0.161 in light-on. The class is not the paper's heading class.

How the test differed from the paper’s method

• Assumption. The decoder readings give different outcomes; the naive Bayes decoder is adopted, as the Methods name Bayesian decoding (Etter et al. 2020), resample each trial to 200 bins and split even and odd time points for training and testing (Methods, Decoding RSC somatic activity), which reading (a) follows, and the claims file puts the Methods first. Every reading is shown, with two Bayes variants in which no test bin shares a frame with a training bin: (a') even trials to train and odd trials to test, (a'') the paper's split of even and odd time points on 100 heading bins that each hold the nearest frame, without interpolation. Both give lower accuracies (all tuned cells, light-on, 0.239 to 0.532 against 0.708 and 0.712), so the accuracies of reading (a) depend heavily on test bins sharing frames with training bins, as the paper's own procedure does.
• The classes are those of somata.ipynb (fig5-class-proportions, not reproduced), rebuilt in decoding.ipynb with the same files, seeds and code; they differ from the paper's.
• Pseudopopulations from the 25 7550-frame recordings with 5 trials on each side of all three light-to-dark transitions (15 trials a side; 1331 of 1419 tuned cells); the 1950-frame recordings are left out. Trials are resampled to 200 bins on heading in place of time, so bins line up across recordings.
• The naive Bayes decoder is written here after Etter et al. (2020): activity binarized (spikes above 0; dF/F above the mean plus 2 SD, a standard choice), 60 states of 6 degrees, a +1/+2 prior, trained on even and tested on odd bins of the trials resampled to 200 bins, as the Methods split even and odd time points after resampling. The HeadingDecoder (github.com/ucsb-goard-lab/HeadingDecoder at ca9842e) is reimplemented in numpy with leave-one-trial-out tuning weights. It decodes synthetic cells at 0.908 to 0.999, and these data at 0.202 and 0.215 for all tuned cells in light-on, twice chance and close to the naive Bayes decoder trained and tested on different trials (0.239 and 0.255). The synthetic test shows the algorithm as written works; a difference from the lab's code in some detail cannot be excluded.
• Chance is measured with each decoder by decoding with each cell's test activity circularly shifted along the trial: 0.101 to 0.102, the 0.10 reading of the claims file.

landmark cells have very high decoder performance in the light-on condition (mean decoder accuracy = 0.80, 95% CI = [0.75, 0.84]), with an overrepresentation of decoder errors at 180°, which immediately plummets to chance levels in the light-off condition (mean decoder accuracy = 0.20, 95% CI = [0.14, 0.27]; p = 8.0 × 10−4

Results, Contributions of distinct classes to representation of heading, paragraph 2; Figure 6B, middle

What the paper reports

• bootstrapped t-test, p = 8 × 10⁻⁴ (n = 1000 bootstrapped samples)
• light-on accuracy: bootstrap confidence interval, 95% CI 0.75 to 0.84
• light-off accuracy: bootstrap confidence interval, 95% CI 0.14 to 0.27

Under the Bayes decoder, landmark-like cells (50 used, sampled 332 with replacement) fall towards chance in light-off (dF/F 0.207 [0.192, 0.220]; spikes 0.187 [0.175, 0.199]), within 0.20 +- 0.07, with p < 0.001 for the drop, but their light-on accuracy (0.396 and 0.383) is half the paper's 0.80, so the criterion is not met. The spikes light-off interval includes 0.18 and the dF/F interval excludes it; neither includes 0.10. Every other reading also gives a significant drop (p 0.014 or less) with light-on accuracy 0.201 to 0.352. The class is not the paper's.

How the test differed from the paper’s method

• Assumption. The decoder readings give different outcomes; the naive Bayes decoder is adopted, as the Methods name Bayesian decoding (Etter et al. 2020), resample each trial to 200 bins and split even and odd time points for training and testing (Methods, Decoding RSC somatic activity), which reading (a) follows, and the claims file puts the Methods first. Every reading is shown, with two Bayes variants in which no test bin shares a frame with a training bin: (a') even trials to train and odd trials to test, (a'') the paper's split of even and odd time points on 100 heading bins that each hold the nearest frame, without interpolation. Both give lower accuracies (all tuned cells, light-on, 0.239 to 0.532 against 0.708 and 0.712), so the accuracies of reading (a) depend heavily on test bins sharing frames with training bins, as the paper's own procedure does.
• The classes are those of somata.ipynb (fig5-class-proportions, not reproduced), rebuilt in decoding.ipynb with the same files, seeds and code; they differ from the paper's.
• Pseudopopulations from the 25 7550-frame recordings with 5 trials on each side of all three light-to-dark transitions (15 trials a side; 1331 of 1419 tuned cells); the 1950-frame recordings are left out. Trials are resampled to 200 bins on heading in place of time, so bins line up across recordings.
• The naive Bayes decoder is written here after Etter et al. (2020): activity binarized (spikes above 0; dF/F above the mean plus 2 SD, a standard choice), 60 states of 6 degrees, a +1/+2 prior, trained on even and tested on odd bins of the trials resampled to 200 bins, as the Methods split even and odd time points after resampling. The HeadingDecoder (github.com/ucsb-goard-lab/HeadingDecoder at ca9842e) is reimplemented in numpy with leave-one-trial-out tuning weights. It decodes synthetic cells at 0.908 to 0.999, and these data at 0.202 and 0.215 for all tuned cells in light-on, twice chance and close to the naive Bayes decoder trained and tested on different trials (0.239 and 0.255). The synthetic test shows the algorithm as written works; a difference from the lab's code in some detail cannot be excluded.
• Chance is measured with each decoder by decoding with each cell's test activity circularly shifted along the trial: 0.101 to 0.102, the 0.10 reading of the claims file.

When sampling across all the classes, the heading network shows remarkable accuracy, even in the presence of symmetric visual cues (mean decoder accuracy = 0.82, 95% CI = [0.78, 0.86]

Results, Contributions of distinct classes to representation of heading, paragraph 1; Figure 6A

What the paper reports

• bootstrap confidence interval, 95% CI 0.78 to 0.86 (n = 1000 bootstrap samples of 332 neurons)

No decoder reading gives a light-on mean within 0.82 +- 0.04. The naive Bayes decoder gives 0.708 [0.665, 0.747] (dF/F) and 0.712 [0.678, 0.746] (spikes); the Bayes variants without shared frames 0.239 to 0.532; the HeadingDecoder 0.202 and 0.215. Chance is 0.10 (0.101 to 0.102 with each decoder). measured gives dF/F with the Bayes decoder, the first reading.

How the test differed from the paper’s method

• The classes are those of somata.ipynb (fig5-class-proportions, not reproduced), rebuilt in decoding.ipynb with the same files, seeds and code; they differ from the paper's.
• Pseudopopulations from the 25 7550-frame recordings with 5 trials on each side of all three light-to-dark transitions (15 trials a side; 1331 of 1419 tuned cells); the 1950-frame recordings are left out. Trials are resampled to 200 bins on heading in place of time, so bins line up across recordings.
• The naive Bayes decoder is written here after Etter et al. (2020): activity binarized (spikes above 0; dF/F above the mean plus 2 SD, a standard choice), 60 states of 6 degrees, a +1/+2 prior, trained on even and tested on odd bins of the trials resampled to 200 bins, as the Methods split even and odd time points after resampling. The HeadingDecoder (github.com/ucsb-goard-lab/HeadingDecoder at ca9842e) is reimplemented in numpy with leave-one-trial-out tuning weights. It decodes synthetic cells at 0.908 to 0.999, and these data at 0.202 and 0.215 for all tuned cells in light-on, twice chance and close to the naive Bayes decoder trained and tested on different trials (0.239 and 0.255). The synthetic test shows the algorithm as written works; a difference from the lab's code in some detail cannot be excluded.
• Chance is measured with each decoder by decoding with each cell's test activity circularly shifted along the trial: 0.101 to 0.102, the 0.10 reading of the claims file.
• Two Bayes variants in which no test bin shares a frame with a training bin are shown as further readings: (a') even trials to train and odd trials to test; (a'') the paper's split of even and odd time points on 100 heading bins that each hold the nearest frame.

alignment cells show decoder performance that is between that of heading and landmark cells, taking advantage of improved decoding from the visual cues in the light-on condition (mean decoder accuracy = 0.71, 95% CI = [0.66, 0.76]), but retaining fairly accurate heading in the light-off condition (mean decoder accuracy = 0.51, 95% CI = [0.43, 0.59], p = 0.54

Results, Contributions of distinct classes to representation of heading, paragraph 2; Figure 6B, bottom

What the paper reports

• bootstrapped t-test, p = 0.54 (n = 1000 bootstrapped samples)
• light-on accuracy: bootstrap confidence interval, 95% CI 0.66 to 0.76
• light-off accuracy: bootstrap confidence interval, 95% CI 0.43 to 0.59

Under the Bayes decoder both means of alignment-like cells are within tolerance (dF/F 0.720 and 0.580; spikes 0.711 and 0.581), with light-off intervals above chance, but their light-on accuracy is the highest of the three classes, not between heading-like (0.429, 0.415) and landmark-like (0.396, 0.383) cells, and light-off is lower, by the paired test significantly (p = 0.011 and 0.001; unpaired 0.053 and 0.001), which the criterion counts against the claim under the reading that matches the values. No other reading puts both means within tolerance (light-on 0.203 to 0.548). The class is not the paper's.

How the test differed from the paper’s method

• The classes are those of somata.ipynb (fig5-class-proportions, not reproduced), rebuilt in decoding.ipynb with the same files, seeds and code; they differ from the paper's.
• Pseudopopulations from the 25 7550-frame recordings with 5 trials on each side of all three light-to-dark transitions (15 trials a side; 1331 of 1419 tuned cells); the 1950-frame recordings are left out. Trials are resampled to 200 bins on heading in place of time, so bins line up across recordings.
• The naive Bayes decoder is written here after Etter et al. (2020): activity binarized (spikes above 0; dF/F above the mean plus 2 SD, a standard choice), 60 states of 6 degrees, a +1/+2 prior, trained on even and tested on odd bins of the trials resampled to 200 bins, as the Methods split even and odd time points after resampling. The HeadingDecoder (github.com/ucsb-goard-lab/HeadingDecoder at ca9842e) is reimplemented in numpy with leave-one-trial-out tuning weights. It decodes synthetic cells at 0.908 to 0.999, and these data at 0.202 and 0.215 for all tuned cells in light-on, twice chance and close to the naive Bayes decoder trained and tested on different trials (0.239 and 0.255). The synthetic test shows the algorithm as written works; a difference from the lab's code in some detail cannot be excluded.
• Chance is measured with each decoder by decoding with each cell's test activity circularly shifted along the trial: 0.101 to 0.102, the 0.10 reading of the claims file.
• Two Bayes variants in which no test bin shares a frame with a training bin are shown as further readings: (a') even trials to train and odd trials to test; (a'') the paper's split of even and odd time points on 100 heading bins that each hold the nearest frame.