Paradigm and behavioral results.

(A) Schematic illustration of the F2 and F2B1 conditions. (B) Illustration of one trial sequence. On each trial, the first visual stimulus presented below the fixation, either accompanied by an auditory beep or without it (the sound icon in the figure is not part of the actual experiment). After a variable ISI, the second visual stimulus was presented. Participants were required to report whether they perceived one or two flashes. Participants were more likely to report perceiving one flash with a short ISI (30 ms) and two flashes with a long ISI (100 ms). Perception became bistable during trials where the ISI matched fusion threshold, individually determined for each participant, resulting in approximately equal proportions of 1-flash and 2-flash reports. (C) Psychometric curves represent the best fit of the average probability of perceiving the two flashes plotted as a function of different ISIs in the F2 and F2B1 conditions. Error bars represent ±1 SEM. (D) Fusion threshold ISIs derived from the psychophysical procedure for each condition. (E) Percentage of 1-flash and 2-flash percepts for the bistable trials in the F2 and F2B1 conditions of the main EEG experiment. ***p < 0.001.

The relationship between decreased post-stimulus IAFs and perceptual precision.

(A) Upper panel: the power spectrum obtained from all bistable trials (from −600 to 600 ms relative to the onset of the first flash) in F2 and F2B1 conditions, collapsed across all electrodes in all participants, clearly revealed a distinct peak in the alpha band. The gray shading represents ±1 within-subjects SEM. The light gray rectangle represents the chosen alpha frequency band (8-13Hz). Lower panel: Topography of absolute alpha-band power (8-13Hz) recorded from 64-channel EEG, averaged over F2 and F2B1 conditions, showed a clear occipital scalp distribution. Black dots indicated the chosen posterior channels. (B) IAFs for F2 and F2B1 bistable trials averaged over the occipital channels. The within-subject findings of the IAFs revealed that the post-stimulus alpha frequency of F2B1 decreased more than that of F2. (C) The between-subject correlation was conducted to examine the relationship between the post-stimulus IAFs difference of F2B1 and F2 in the main EEG experiment and the threshold ISIs difference of F2B1 and F2 in the psychophysical pretest. 95% confidence intervals around the linear fit line are shown by the dashed line. (D) The result is identical to (B), but for explicit short ISI trials. (E) The result is identical to (B), but for explicit long ISI trials.

Relationship between the instantaneous alpha frequency (IAF) and perception.

(A) IAFs over time were averaged over posterior channels (shown in Fig 2a) for different perceptual outcomes in the F2 condition. Shaded areas show ±1 within-subjects SEM. Significant time epochs are indicated with black lines (p < 0.05; permutation test; cluster corrected). (B) Similar to a, but for F2B1 condition. (C) IAFs during the time of interest (−600 to 600 ms) were averaged separately for F2 and F2B1 conditions with different perceptual outcomes. The error bars represent ±1 SEM. ∗∗p < 0.01. ∗∗∗p < 0.001.

Prestimulus alpha phase difference between 1-flash and 2-flash trials.

(A) Time-frequency representation of p values (for occipital regions), computed as a proportion of surrogate phase opposition values (distribution of phase opposition values expected under null hypothesis) that exceeded empirically observed phase opposition values for the F2B1 (upper panel) and F2 conditions (lower panel), respectively. The outlined area indicates significant effects corrected for multiple comparisons using cluster-based correction. The white square indicates the time-frequency point with strongest POS effect in the F2B1 condition. (B) The circular histograms of mean phase angles (at 10.28 Hz; −300 ms) at the occipital channel Oz during 1-flash and 2-flash trials across participants for the F2B1 (upper panel) and F2 conditions (lower panel), respectively. The horizontal black line indicates the number of participants with the mean phase angle in each bin. The direction of the arrows corresponds to the mean phase angle across participants, and the length of the arrows indicates the extent of phases clustering around the mean. (C) Statistical analysis of the differential phase effects between F2B1 and F2 condition within the entire prestimulus period (−600∼0ms) and alpha-band range (8∼13 Hz). The red line indicates the observed mean POS difference between F2B1 and F2 within this cluster. The gray bars represent the surrogate distribution of mean POS difference expected by chance for this cluster, estimated from shuffled data. Dashed black line indicates the 95th percentile value of the surrogate distribution. (D) The relationship between the proportion of two-flash percepts and pre-stimulus phase (at 10.28 Hz; −300 ms) at the occipital channel Oz. Single trials were categorized into 9 phase bins, centered on the preferred phase bin with the highest proportion of 2-flash percepts for each participant (the central bin is removed due to artificial shifting). The error bars represent ±1 SEM.

Results of tACS experiment.

(A) Psychometric curves show the average probability of perceiving two flashes as a function of different ISIs, under three tACS conditions: 13 Hz, sham, and 8 Hz, in the F2 condition. (B) Similar to (A), but for the F2B1 condition. (C) Fusion threshold ISIs from the three tACS sessions in both F2 and F2B1 conditions. Error bars represent ±1 SEM. *p < 0.05.

Hypothesized phase-resetting model of perceptual processing.

(A) The perceptual outcomes depend on the temporal alignment of two stimuli and the phase at which the second flash occurs. When the second flash coincides with good phases, around the peak of the oscillation, effective processing occurs, and the perceptual outcomes are determined based on whether they fall within the same temporal window defined by the alpha cycle. In cases where the two visual stimuli fall in different temporal windows, the 2-flash percept is reported. The introduction of auditory stimuli concurrently with visual stimuli induces phase resetting, elongating the temporal window. Consequently, the second flash, originally falling in different temporal windows, aligns with the first flash, resulting in a 1-flash percept. Conversely, when the second flash aligns with bad phases, around the trough of the oscillation, effective processing is hindered, leading to ambiguity in 1-flash and 2-flash percepts, irrespective of their temporal alignment. (B) Upper panel: The frequency of the alpha rhythm is anticipated to modulate perceptual outcomes, with higher alpha frequencies correlating with an increased proportion of 2-flash percepts. Lower panel: The phase of the alpha rhythm is expected to dictate perceptual clarity. In instances where the second flash falls in bad phases (e.g., [−π, −1/2π] and [1/2π, π]), perceptual clarity is low, making it challenging to distinguish between 1-flash and 2-flash percepts. Conversely, when the second flash aligns with good phases (e.g., [−1/2π, 1/2π]), perceptual clarity is high, and the perception of 1-flash or 2-flash depends on whether the two stimuli fall within the same alpha cycle or not.

Simulation results.

(A) Psychophysical results. Psychometric curves depict the best-fit average probability of perceiving two flashes plotted against different ISIs in simulated F2 and F2B1 conditions. (B) IAFs for simulated F2 and F2B1 trials. (C) IAFs, averaged during the time of interest (−600 to 600 ms), separately for simulated F2 and F2B1 trials with different perceptual outcomes. Error bars represent ±1 within-trials SEM. (D) Statistical analysis of the differential phase effects between F2B1 and F2 condition at stimulus onset (0 ms), prior to the auditory input-induced phase-resetting. The red line indicates the mean POS difference between simulated F2B1 and F2 trials. Dashed black line indicates the 95th percentile value of the surrogate distribution. (E) Phase distribution at the onset of flash 2 (ISI = 50 ms; following the phase-resetting effect). (F) Subjective perceptual sensitivity in distinguishing between 1-flash and 2-flash percepts for simulated F2 and F2B1 trials.