◐Partially reproducedResults, second paragraph; Figure 2e,f; Abstract ("accelerated tenfold")
The angular velocity of the internal HD signal, estimated from the temporal profile of pairwise cross-correlograms, is about tenfold faster during SWS than during waking.
The angular velocity of the internal HD signal, either estimated by a Bayesian decoder or from the temporal profile of pairwise cross-correlograms ... was approximately tenfold faster during SWS than during waking (Fig. 2e,f)
Results, second paragraph; Figure 2e,f; Abstract ("accelerated tenfold")
Over 1509 pairs (64 of 1573 dropped for a fit at the edge of the speed range), the median ratio of SWS to waking angular velocity is 8.33 (quartiles 5.91 to 11.31), below 9 to 11; SWS is faster in 1420 pairs (sign test p = 4.1e-309). Median speeds are 36.9 deg/s in waking, 33.5 in REM and 324.4 in SWS. By mouse the ratio is 7.89 to 13.52. The Bayesian decoder variant gives a median of 11.53 over 28 sessions. Under reading (b) the median is 8.02 over 2129 pairs; with pairs whose fits reach R2 of 0.25 or 0.5 in every state, 8.46 (1063 pairs) and 8.56 (748 pairs). Median R2 is 0.84 in waking, 0.55 in REM and 0.78 in SWS. The waking estimates are 0.60 times the measured mean angular speed of the head (median over sessions) and correlate with it at r = 0.20 across 33 sessions. On Poisson surrogates driven by the measured head direction and the waking tuning curves, the estimator returns 0.37 of the true mean speed (median 37.0 deg/s, as on the data, against a true 99.9), and for the same trajectory played ten times faster it gives a median ratio of 4.99 (quartiles 2.76 to 7.02), not 10. Scaled by that compression the data's 8.33 becomes 16.69, so the data are consistent with a speed-up below, at or above tenfold. The estimator shows that SWS is faster but does not determine the fold; how far its bias in SWS matches that of the surrogates is not known.
How the test differed from the paper’s method
- The paper does not say how the expected and observed cross-correlograms are put on one scale; a free scale and offset are fitted here.
- The lag range (4 s) and speed grid are chosen here.
- The expectation over the chi-squared speed distribution is computed exactly from its characteristic function.
- Pairs within and across structures are pooled; the paper shows ADn-ADn and PoS-PoS pairs.