Dissociated amplitude and phase effects of alpha oscillation in a nested structure of rhythm- and sequence-based temporal expectation

The human brain can utilize various information to form temporal expectation and optimize perceptual performance. Here we show dissociated amplitude and phase effects of pre-stimulus alpha oscillation in a nested structure of rhythm- and sequence-based expectation. A visual stream of rhythmic stimuli was presented in a fixed sequence such that their temporal positions could be predicted by either the low-frequency rhythm, the sequence, or the combination. The behavioral modelling indicated that rhythmic and sequence information additively led to increased accumulation of sensory evidence and alleviated threshold for the perceptual discrimination of the expected stimulus. The electroencephalographical (EEG) results showed that the alpha amplitude was dominated by rhythmic information, with the amplitude fluctuating in the same frequency of the oscillation entrained by the rhythmic information (i.e., phase-amplitude coupling). The alpha phase, however, was affected by both rhythmic and sequence information. Importantly, rhythm-based expectation improved the perceptual performance by decreasing the alpha amplitude, whereas sequence-based expectation did not further decrease the amplitude on top of rhythm-based expectation. Moreover, rhythm-based and sequence-based expectation collaboratively improved the perceptual performance by biasing the alpha oscillation toward the optimal phase. Our findings suggested flexible coordination of multiscale brain oscillations in dealing with a complex environment.

6 as the target, by which the target was also highly predictable while being located at an 158 optimal phase of the neural oscillation entrained by the 2.5 Hz sequence. For S-P+, an extra 159 stimulus after the 2.5 Hz sequence was presented as the target, by which the target was 160 unpredictable while being located at an optimal phase of the neural oscillation entrained by 161 the 2.5 Hz sequence. In the irregular stream, stimuli were presented with varying inter-162 stimulus intervals, but the number of the stimuli preceding the target was matched with each 163 condition in the regular stream.  The 2 × 3 ANOVA revealed that the drift rate was higher in the regular condition (4.41) than 213 in the irregular condition (3.62), F(1, 23) = 21.5, p < 0.001, η p 2 = 0.483 ( Figure 1C, left). The 214 main effect of position was significant, F(2, 46)= 18.9, p < 0.001, η p 2 = 0.451. Pair-wise 215 comparisons showed that the drift rate was higher at S+P+ (4.75) than the drift rates at S+P-216

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The low-frequency neural oscillation entrained by the rhythmic stimuli 267 S+P-, 2.5Hz for S+P+ and S-P+) neural entrainment over the visual cortex. To check this 269 assumption, we calculated the phase-locking value (PLV) for each target position. As shown 270 in Figure 2A, the 1.25 Hz PLV at S+P-, the 2.5 Hz PLV at S+P+ and S-P+ were higher in the 271 regular condition than in the irregular condition (paired-T test, p < 0.05, with cluster-based 272 permutation correction), demonstrating the typical neural entrainment synchronized with the 273 rhythmic stimuli. A data-driven spectral analysis also confirmed the neural entrainment by 274 showing higher amplitudes of the entrained frequencies in the regular condition than in the 275 irregular condition (Supplementary Figure S1). Moreover, the 1.25 Hz phase of S+P-was at 276 an opposite phase (antiphase) of an optimal phase predicted by the 1.25 Hz neural 277 entrainment, as shown by the phase difference (centered mean = 2.94) between S+P-and its 278 preceding position, p < 0.001(Rayleigh Test, radian, Figure 2B left). By contrast, the 2.5 Hz 279 phases of S+P+ and S-P+ were both at an optimal phase predicted by the 2.5 Hz neural 280 entrainment. The phases were the same, as shown by the phase difference (centered mean = -281 0.04) between these two positions, p < 0.001(Rayleigh Test, radian, Figure 2B

Communication between low-frequency entrainment and alpha activity 284
The fluctuation of the alpha activity (8-12Hz) before the target onset showed a typical 285 periodical characteristic in the regular condition relative to the irregular condition for all of 286 the three positions (Supplementary Figure S2). The FFT analysis showed that the strongest 287 fluctuation of the alpha amplitudes was at 1.25Hz for S+P-, regular vs. irregular: t(23) = 5.16, 288 p FDR < 0.001, at 2.5 Hz for S+P+, t(23) = 6.04, p FDR < 0.001, and at 2.5 Hz for S-P+, t(23) = 289 3.84, p FDR = 0.012 ( Figure 2C). These results suggested that the alpha amplitude was 290 modulated by the phase of the low-frequency neural oscillation. To verify this cross-291 frequency coupling, we further calculated phase-amplitude coherence (PAC) between the 292 phase of the low-frequency oscillation and the amplitude of the alpha activity. The PAC z (Z 293 scored PAC value) was stronger in the regular condition than in the irregular condition for all 294 of the three positions: t(23) = 6.54, p < 0.001 at S+P-(1.25 Hz), t(23) =5.02, p < 0.001 at 295 S+P+ (2.5Hz), and t(23) = 6.90, p < 0.001 at S-P+ (2.5 Hz) ( Figure 2D).

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Pre-target alpha amplitude under different structures of temporal expectation 315 For the analysis of alpha amplitude, the evoked component was firstly removed from the data 316 to avoid the confounding effect contributed by phase (see Materials and Methods). As shown 317 in Figure 3A, the amplitude of the pre-stimulus alpha activity over the visual cortex was 318 higher in the regular condition than in the irregular condition at S+P-, with a significant 319 temporal cluster of -400 to -290 ms relative target onset (cluster-based permutation corrected 320 p < 0.001). By contrast, the alpha amplitude was lower in the regular condition than in the 12 significant temporal cluster of -400 to 512ms at S-P+. The reversed pattern of alpha 324 amplitude between S+P-and S+P+/S-P+ conditions suggested that the alpha amplitude was 325 mainly modulated by the phase of the low-frequency oscillation, but was not additionally 326 modulated by the sequence-based expectation. To further test this hypothesis, we compared 327 the amplitude difference between regular and irregular conditions at S+P-with the amplitude 328 difference between irregular and regular conditions (i.e., the reverse of the difference 329 between regular and irregular conditions) at S+P+/S-P+. For each position, the alpha 330 amplitudes were extracted from the significant cluster to calculate the mean difference 331 between regular and irregular conditions ( Figure 3B). To avoid making statistical inferences 332 based on non-significant p values, we performed the Bayes Factor analysis to quantify the 333 likelihood of the null hypothesis against the alternative hypothesis (Keysers, Gazzola, & 334 Wagenmakers, 2020). The results showed that the hypothesis "the deceased amplitude at 335 S+P+ was equivalent to the decreased amplitude at S-P+" was 4.46 times more likely to be 336 true than the alternative hypothesis "the decreased amplitude at S+P+ was different from the 337 decreased amplitude at S-P+". Moreover, the hypothesis "the decreased amplitude at S+P+ 338 was equivalent to the increased amplitude at S+P-" was 3.60 times more likely to be true than 339 the alternative hypothesis "the decreased amplitude at S+P+ was different from the increased 340 amplitude at S+P-". 341

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To assess if and how the amplitude of pre-target alpha activity could be related to the 343 perceptual performance of the target, we tested if the HDDM parameters (drift rate, threshold, 344 and non-decision time) could be predicted by the alpha amplitude. For each position and each 345 HDDM parameter, a regression model that combined with the HDDM was constructed to 346 estimate to which extent the amplitude difference between regular and irregular conditions 347 could predict the difference of the HDDM parameter between regular and irregular 348 conditions. Convergence was achieved for all estimated regression coefficients, R-hats < 1.01. 349 The results of the regression models are shown in Figure 3C. The drift rate could be 350 negatively predicted by the alpha amplitude at S+P+ (mean regression coefficient = -0.082), 351 p (coefficient > 0) = 0.004, with the drift rate increasing linearly as the alpha amplitude was 352 decreased by regularity ( Figure 3C, left). The predictability did not reach significance at S+P-353 13 p = 0.002, which was due to higher predictability at S+P+ (p bonferroni < 0.001) and S-P+ 358 (p bonferroni = 0.012) than at S+P-. No significant difference was observed between S+P+ and 359 S-P+, p bonferroni > 0.999 (see Figure 3D, left). The results of the alpha amplitude and the modelling suggested that the alpha amplitude and 382 its contribution to the perceptual performance were mainly driven by the rhythm-based 383 expectation. Even at S+P+ when both the rhythmic and sequence information availed to form 384 temporal expectation, the alpha amplitude was not additionally modulated by the sequence 385 information on top of the rhythmic information. At S+P-, due to the antiphase of the low-386 frequency oscillation, the alpha amplitude was increased by the rhythmic regularity. The based expectation. Considering that the rhythm-based and the sequence-based expectation 418 may have entangling effects, we compared the alpha phase during the time interval before the 419 target (pre-target alpha phase, regular condition) with the alpha phase prior to the stimulus 420 immediately before the target (pre-pre-target alpha phase, regular condition) for each of the 421 three positions. During these two intervals, the neural entrainment induced by the rhythmic 422 stimuli was locked to the same low-frequency phase so that any observed difference should 423 be attributed to the sequence-based expectation. To consider the different lengths of the two 424 intervals at S+P-, the comparison was performed on the 400ms range that was time-locked to 425 the onset of the stimulus before the two intervals (i.e., the onset of the pre-target stimulus for 426 the pre-target alpha phase, the onset of the pre-pre-target stimulus for pre-pre-target phase). 427 At S+P-, the alpha phases showed significant differences during the time interval of 324 to 428 400 ms relative to the stimulus onset, p < 0.001 (Watson-Williams test, with cluster-based 429 correction) ( Figure 4A). At S+P+, the alpha phases showed significant differences during the 430 time interval of 320 to 382 ms relative to the stimulus onset, p < 0.001 (with cluster-based 431 correction). At S+P+, however, no significant difference in the alpha phase was observed. 432 These results suggested that sequence-based expectation (S+P-, S+P+) of the target changed 433 the pre-target alpha phase. 434

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Then, we tested if the rhythm-based expectation also contributed to the pre-target alpha phase 436 by comparing the phases during the pre-target interval between different conditions. The 437 results showed significant differences in the alpha phase between S+P-and S+P+ during the 438 time interval of -224 to -200 ms relative to the target onset, p < 0.001 (Watson-Williams test, 439 with cluster-based correction) ( Figure 4B). However, no significant difference was observed 440 between S+P-and S-P+, or between S+P+ and S-P+. The difference between S+P-and S+P+ 441 suggested that the pre-target alpha phase was also affected by rhythm-based expectation. 442

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Last but not least, we assessed if and how the alpha phase was biased by the temporal 444 expectation to improve the perceptual performance. We first sorted the data into epochs with 445 a correct response and epochs with an incorrect response, with the expectation that the target 446 onset of the former would be more likely to be localized at an optimal phase than the latter 447 (Samaha et al., 2015). Consistent with this assumption, the epochs with correct responses and 448 the epochs with incorrect responses showed a significant difference in the alpha phase, responses as the optimal phase and calculated the phase distance in terms of the circular 451 distance between the phase at the target onset in each trial and the optimal phase. To avoid 452 the risk of double-dipping, we did not test the difference in phase distance. Instead, we 453 focused on the predictability of the phase distance on the single-trial perceptual performance. 454 455 Similar regression models to the above were conducted to assess to which extent the HDDM 456 parameters could be predicted by the alpha phase. Convergence was achieved for all 457 regression coefficients, R-hats < 1.02. The drift rate could be negatively predicted by the 458 with the drift rate increasing linearly as the alpha phase was closer to the optimal alpha phase, 461 whereas the predictability at S+P-(mean regression coefficient = -0.087) did not reach 462 significance, p (coefficient > 0) = 0.114. The ANOVA on the coefficients showed a main 463 effect of position, F(2, 46) = 30.8, p < 0.001, which was due to higher predictability at S+P+ 464 (p bonferroni < 0.001) and S-P+ (p bonferroni < 0.001) than S+P-, and also higher predictability at 465 S+P+ than S-P+, p bonferroni < 0.001 ( Figure 4E, left). was higher at S+P+ than S+P-(p bonferroni < 0.001) and S-P+ (p bonferroni < 0.001), and was also 474 higher at S-P+ than S+P-, p bonferroni < 0.001 ( Figure 4E, middle). is that a stimulus aligned with the high-excitability phase gains improved perceptual 528 processing, whereas a cost is that a stimulus aligned with the low-excitability is less likely to 529 be efficiently recognized (Lakatos et al., 2008). This prediction was supported by our results 530 that the pre-stimulus alpha amplitude was reduced when the rhythmic stimulus was at an 531 optimal phase of the low-frequency entrainment (i.e., S+P+ and S-P+), and the single-trial 532 perceptual decision-making was critically predicted by the alpha amplitude. However, when 533 the rhythmic stimulus was at an antiphase (i.e., S+P-), the alpha amplitude was otherwise 534 increased, indicating a lowered preparing state for the stimulus. Our results elucidated the 535 mechanism that the rhythmic regularity in the environment affected the perceptual 536 performance through the cross-frequency coupling between the phase of the low-frequency 537 entrainment and the amplitude of pre-stimulus alpha oscillation. that the alpha amplitude was mainly driven by the rhythmic information, whereas the 545 sequence information did not additively modulate the alpha amplitude. This notion is 546 supported by the following evidence: 1) at an optimal phase of the rhythmic stimuli, the was equivalent to the increased alpha amplitude at an antiphase (S+P-) of the rhythmic 550 stimuli; 3) the predictive power of the alpha amplitude on the single-trial perceptual 551 performance was not additionally contributed by the sequence-based expectation (S+P+ vs. 552 S-P+). In contrast, the alpha phase was modulated by both rhythmic and sequence 553 information, leading to synergistic effects in biasing the alpha oscillation toward an optimal 554 phase where the perceptual performance can be optimized. Specifically, on top of the 555 rhythmic information, the addition of sequence information induced a change in the phase of 556 the pre-target alpha oscillation (i.e., at both S+P-and S+P+), whereas such phase change was 557 not observed when the sequence-based expectation was absent (i.e., at S-P+). And, the phase 558 of the pre-target alpha oscillation was also affected by whether the target was at an optimal 559 phase of rhythmic stimuli (i.e., S+P-vs. S+P+). At the single-trial level, the perceptual 560 performance was predicted by the extent to which the phase was close to the optimal phase of 561 the alpha oscillation, and the combination of the rhythmic and sequence information rendered 562 the highest predictive power. 563 564 Although the alpha amplitude was involved only in the rhythm-based expectation here, it 565 should not be generalized into that alpha amplitude was immune to the sequence-based 566 expectation regardless of task context. Instead, the suggestion based on the current findings is 567 that the alpha amplitude and alpha phase were flexibly coordinated to take effect according to 568 the task. The rhythmic processing has been suggested as a default mode of the brain, the high 569 and low excitability of which can be reset on multiple time scales ( and speech segmentation . Our results showed that the dynamic 602 interaction of brain oscillations is not only expressed as the cross-frequency coupling (e.g., 603 the phase-amplitude coupling), but also as the amplitude-phase coordination within a specific 604 frequency range (e.g., the alpha oscillation). Taken together, these findings suggested that the 605 multiscale brain oscillations are flexibly organized to deal with the complex environment and 606 empower adaptive behaviour. 607

Participants 609
A total of 26 right-handed university students participated in this study. One participant was 610 excluded from analysis due to incomplete data caused by technical errors during the 611 experiment, and another participant was excluded from data analysis due to excessive 612 artifacts (50% of total trials) of the EEG signals, resulting in 24 participants (10 females, 613 mean age 20.5 years old). All participants had normal or corrected-to-normal visual acuity 614 and normal color vision and reported no history of psychiatric or neurological disorders.

Stimuli and Apparatus 621
Stimuli were created and presented using Psychtoolbox-3 extension for MATLAB (Brainard, 622 1997). Stimuli were presented on a Display++ monitor (1920*1080 spatial resolution, 120Hz 623 refresh rate) against a gray background (RGB:125, 125, 125). The eye-to-monitor distance 624 was fixed at 70 cm. A chin rest was used to maintain the head position and a constant 625 viewing distance. Responses were collected using a standard keyboard. 135° or 45° relative to the horizontal axis, and the spatial frequency of the Gabor patches was 636 2 cycles/degree of visual angle. The above-mentioned parameters of the stimuli were chosen 637 following a previous study (Rohenkohl, Cravo, Wyart, & Nobre, 2012). Prior to the 638 experiment, a psychophysical test was conducted to estimate the contrast threshold with 75% 22 procedure (Kaernbach, 1991). The contrast that 10 0.1 times of contrast threshold 641 corresponding to 75% accuracy was used in the formal experiment across all conditions. 642 643 Design and procedure 644 There were two types of stimuli stream: the regular stream and the irregular stream. In both 645 streams, each stimulus remained on the screen for 50 ms. Within the regular stream, stimuli 646 were presented at two alternating frequencies (i.e., 1.25 Hz, and 2.5 Hz). The stimulus onset 647 asynchrony (SOA) between successive stimuli changed with a fixed rule: five SOAs of 800 648 ms followed by five SOAs of 400 ms which was then followed by five 800 ms SOAs and so 649 on. Every ten stimuli were grouped into a unit where the long-SOA stimuli were always 650 followed by the short-SOA stimuli. Within the irregular stream, the SOA between each 651 successive two stimuli was randomly chosen from 300 ms, 400 ms, 500 ms, 600 ms, 700 ms, 652 800 ms, and 900 ms. Within the irregular stream, every ten successive stimuli were also 653 grouped into a unit. In each unit, there was a 75% probability that one target stimulus was 654 embedded in the stream while a 25% probability that no target was presented at all (Target 655 absent, filter unit). No target was presented in the very first unit of each trial. In the regular 656 stream, the target was presented at one of the three temporal positions with equal probability 657 (as shown in Figure 1A): 1) the first position of the short-SOA stimuli following the long-658 SOA stimuli, which could be predicted by the stimuli sequence but not predicted by the 659 rhythm (i.e., 1.25Hz) that preceded the position (S-P+); 2) the last position of the short-SOA 660 stimuli that followed by the long-SOA stimuli in the next unit, which could be predicted by 661 both the stimuli sequence and the rhythm (i.e., 2.5Hz) that preceded the position (S+P+); 3) 662 an extra position inserted after the last position of the short-SOA stimuli that followed by the 663 long-SOA stimuli, with a short SOA before while a long SOA after this extra position, and 664 this position could be predicted by the rhythm (2.5Hz) but not by the stimuli sequence (S-P+). 665 The three positions within the irregular stream (S'+P'-, S'+P'+, S'-P'+) were matched the 666 positions within the regular stream in the way that the numbers of stimuli between two target 667 stimuli were the same in the two streams, and the SOAs before and after the positions within 668 the irregular stream were consistent with the regular stream. To test if S+P-was at an antiphase of an optimal phase of 1.25Hz entrained neural activity, 747 the difference between the phase of 1.25 Hz at the target onset and the phase of 1.25 Hz at the 748 onset of the preceding stimulus before the target was obtained for each participant. The 749 preceding stimulus was expected to be at an optimal phase of the entrained neural activity at 750 1.25Hz. Rayleigh test was used to test whether the phase difference was uniformly distributed 751 or centered around 180°. For S+P+ and S-P+, the phase difference of 2.5 Hz at the target 752 onset between the two positions was calculated for each participant. The two positions were 753 expected to be at an optimal phase of the entrained neural activity at 2.5 Hz. Rayleigh test 754 was used to test whether the phase difference of 2.5 Hz between S+P+ and S-P+ was 755 uniformly distributed or centered around 0°. 756

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The extraction of alpha amplitude and alpha phase 758 For each of the occipital electrodes, the stimulus-locked data (time range: -4000 to 1500 ms 759 relative to target onset) was filtered (8-12 Hz) using a two-way least-squares FIR filter 760 For each of the three positions, we tested if the alpha phase after the stimulus preceding the 835 target (i.e., pre-target alpha phase) was different from the alpha phase after the stimulus that 836 two positions before the target (i.e., pre-pre-target alpha phase). This phase difference was 837 conducted in the regular conditions provided that the time intervals were random in the 838 irregular condition. For the pre-target alpha phase, the 400 ms interval was time-locked to the 839 onset of the pre-target stimulus; for the pre-pre-target alpha phase, the 400 ms interval was 840 time-locked to the pre-pre-target stimulus (i.e., the stimulus that two positions before the For each participant, "optimal" and "non-optimal" alpha phases were differentiated based on 850 the correctness (correct vs. incorrect) of the behavioural response. For each participant, 851 across all epochs (regardless of condition) with correct responses, the alpha phases at the 852 target onset were averaged as the "optimal" phase; and across all epochs with incorrect 853 responses, the alpha phases at the target onset were averaged as the "non-optimal" phase. 854 Watson-Williams test was used to test the phase difference between correct and incorrect 855 responses. For each epoch, the phase distance was calculated as the difference between the 856 phase at the target onset and the "optimal" phase. The same regression models were fitted to 857 estimate to which extent the HDDM parameters could be predicted by the phase distance.