(A) Traces show 500 ms of the instantaneous phase time series of two Kuramoto oscillators (see Materials and methods). When uncoupled (top panels), the mean natural frequencies of the ‘theta’ and … see more
(A,B) Panels show the same as in Figure 1B,C, but for the uncoupled oscillators. Notice roughly uniform Δφnm distributions.
(A) Example white-noise signal (black) along with its theta- (blue) and gamma- (red) filtered components. The corresponding instantaneous phases are also shown. (B) n:m phase-locking levels for 1- … see more
(A) Distribution of the phase difference between two consecutive samples for white noise band-pass filtered at theta (4–12 Hz, top) and slow gamma (30–50 Hz, bottom). Epoch length = 100 s; sampling … see more
(A) Mean Rn:m curves computed for 1 s long white-noise signals filtered into different bands (same color labels as in B; n = 2100). Notice that the narrower the filter bandwidth, the higher the Rn:m … see more
The histograms show the distribution of p-values (bin width = 0.02) for 10000 t-tests of Original Rn:m vs Single Run surrogate values (n = 30 samples per group; epoch length = 1 s). The red dashed … see more
(A) The left panels show mean Rn:m curves and distributions of R1:5 values for original and surrogate (Random Permutation/Single Run) data obtained from the simulation of two coupled Kuramoto … see more
(A) The top traces show a theta sawtooth wave along with its decomposition into a sum of sinusoids at the fundamental (7 Hz) and harmonic (14 Hz, 21 Hz, 28 Hz, 35 Hz, etc) frequencies. The bottom … see more
(A) A theta sawtooth wave along with its theta- (7 Hz) and gamma-filtered (35 Hz) components. Notice that no gamma oscillations exist in the original sawtooth wave, but they spuriously appear when … see more
Shown are the median R1:5 computed between theta and slow gamma for sawtooth waves simulated as in Figure 4C, but of different epoch lengths and peak frequency variability. Dashed area corresponds … see more
(A) n:m phase-locking levels for actual hippocampal LFPs. Compare with Figure 2B. (B) Original and surrogate distributions of Rn:m values for slow (R1:5; left) and middle gamma (R1:8; right) for … see more
(A) The left plots show the mean radial distance (R) computed for gamma phases in different theta phase bins, as described in Sauseng et al. (2009). The lines denote the mean ± SD over all channels … see more
(A) n:m phase-locking levels for actual hippocampal LFPs (same dataset as in Figure 5). Theta phase was estimated by the interpolation method described in Belluscio et al. (2012). (B) Original and … see more
(A) n:m phase-locking levels for actual hippocampal LFPs. (B) Original and surrogate distributions of Rn:m values. Results obtained for three rats recorded in an independent laboratory (see … see more
(Left) Example estimation of the anatomical location of a 16-channel silicon probe by the characteristic depth profile of sharp-wave ripples (inter-electrode distance = 100 μm). (Middle) Original … see more
(Left) Average phase-amplitude comodulograms for three independent components (IC) that maximize coupling between theta phase and the amplitude of slow gamma (top row), middle gamma (middle row) and … see more
(A) Examples of slow-gamma bursts. Top panels show raw LFPs, along with theta- (thick blue line) and slow gamma-filtered (thin red line) signals. The amplitude envelope of slow gamma is also shown … see more
Average Rn:m curves computed for theta- and gamma-filtered hippocampal LFPs. The green curves were obtained using 1 s (top) or 10 s (bottom) continuous epochs of the phase time series, sampled at … see more
(A) Original (green) and surrogate (red) n:m phase-locking levels for actual hippocampal LFPs (same dataset as in Figure 5) filtered at theta and slow gamma (1 s epochs). Different rows show results … see more
Phase-phase plot for theta and slow gamma (average over animals; n = 7 rats). Notice diagonal stripes suggesting phase-phase coupling.
(A) Top, representative LFP epoch exhibiting prominent theta activity (~7 Hz) during REM sleep. Bottom, power spectral density. The inset shows power in dB scale. (B) Phase–phase plots for theta and … see more
Panels show the significance of the phase-phase plots in Figure 7 when compared to the mean and standard deviation of pooled surrogate counts.
(A) Representative example in which theta has peak frequency of 7.1 Hz. The phase-phase plot between theta and slow gamma (30–50 Hz) exhibits five stripes, since the fourth theta harmonic (35.5 Hz) … see more
(A) The middle panels show phase-phase plots for theta and slow gamma computed for different time shifts of the example epoch analyzed in Figure 8A. Notice diagonal stripes in individual surrogate … see more
(A) Representative phase-phase plots computed for white-noise signals. Notice the presence of diagonal stripes for both 100 s (left) and 1200 s (right) epochs. The colormaps underneath show the … see more
(A) Panels show the same as in Figure 9A but for a representative hippocampal LFP. Notice that several bin counts of the 1200 s epoch remain statistically significant after correction for multiple … see more
Examples of phase-phase plots computed for single Time Shift (top) and Random Permutation (bottom) surrogate runs of 100 (left) and 1200 s (right) for the same hippocampal LFP as in Figure 10A. … see more
Phase-phase plots of a white noise (left) and an actual LFP (right) computed using 100 s of total data, but subsampled at 83.3 Hz (we used a subsampling period of 12 ms because the total data length … see more