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Our perception phenomenologically appears continuous over time. Yet, our perceptual performance fluctuates periodically between favorable and less favorable moments (VanRullen and Koch, 2003, VanRullen, 2016). These perceptual cycles have been observed in human and non-human primates at low frequencies (theta, 4-7 Hz; alpha, 8-13 Hz) (Purves et al., 1996; VanRullen et al., 2005, 2006, 2007; Reddy et al., 2011; Landau and Fries, 2012; Fiebelkorn et al., 2013a; Song et al., 2014; Huang et al., 2015; Dugué et al., 2015, 2017; Senoussi et al., 2019; Michel et al., 2022; for review, see Kienitz et al., 2021; Re et al., 2023), and can be induced by flickering visual stimuli (Stefanics et al., 2010; Mathewson et al., 2012; Henry and Obleser, 2012; De Graaf et al., 2013; Henry et al., 2014; Spaak et al., 2014; Ten Oever and Sack, 2015; Kizuk and Mathewson, 2017). Electrophysiological recordings showed that perceptual cycles correlate with brain oscillations, and specifically their phase, at the same frequencies (Valera et al., 1981; Busch et al., 2009; Mathewson et al., 2009; Busch and VanRullen, 2010; Dugué et al., 2011; Fiebelkorn et al., 2013b; Hanslmayr et al., 2013; Samaha et al., 2017; Fakche et al., 2022). Yet, this phase effect accounts for less than 20% of the trialby-trial variability in perceptual performance (Busch et al., 2009; Busch and VanRullen, 2010; Dugué et al., 2011, 2015; Baumgarten et al., 2015; Samaha et al., 2017; Fakche et al., 2022) . Here, we build upon the well-known organization of the visual system and propose to fill this gap by assessing the spatial organization of induced perceptual cycles.

Visual input is topographically decomposed in the visual cortex, i.e., there is a topographic correspondence between the visual space and the cortical space called retinotopy (for review, Wandell and Winawer, 2011). Neural populations in the retinotopic cortex are connected by intra-cortical networks of long-range unmyelinated horizontal axons of up to several millimeters (for review, Chavane et al., 2022). Interestingly, invasive recordings in animals showed that brain activity originating from a specific location in the retinotopic cortex can propagate across the map (e.g., Bringuier et al., 1999; Jancke et al., 2004; Benucci et al., 2007; Muller et al., 2014; Zhang et al., 2012; Yang et al., 2015; Zanos et al., 2015; Townsend et al., 2015; Chemla 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 et al., 2019; Davis et al., 2020). Here, we test the hypothesis that induced perceptual cycles can propagate across the retinotopic visual space presumably due to horizontal connections in the retinotopic visual cortex.

Sokoliuk and VanRullen (2016) showed in a psychophysics experiment that induced 5 and 10 Hz perceptual cycles assessed by detection of a low-contrast target stimulus propagated across the retinotopic visual space. Specifically, a brief target at threshold contrast was presented at three possible distances from a continuously oscillating disk in the periphery of the visual field (inducer). They showed that the optimal behavioral phase (the moment of the oscillating disk leading to the highest performance in target detection) shifted as a function of distance between target and inducer. Here, we used the same psychophysics approach. We additionally recorded EEG to identify the shape of the induced-brain activity, and eye-tracking to ensure successful fixation of the center of the screen, critical for stable retinotopic representation. Other critical changes were made to the design, including the size of the targets, which was adjusted to cortical magnification, so that each stimulus activated the same number of neurons in the retinotopic cortex. Additionally, we parametrized the frequencies by testing four different frequencies in the theta/alpha range (4, 6, 8, and 10 Hz), which was done in each participant (n=17) to ensure robust statistical analyses (in Sokoliuk and VanRullen, n=5 for 5 Hz, n=7 for 10 Hz and n=15 for a 10-Hz replication set). Finally, we added a control experiment to ensure that the results were not due to low-level luminance masking (in Sokoliuk and VanRullen, the control that was used was designed in a way that could have interacted with the attention of the participant).

Our study assessed the propagation of induced perceptual cycles across the retinotopic space. Contrary to the earlier study (Sokoliuk and VanRullen, 2016), our results demonstrate that alpha-induced perceptual cycles, and not theta, traveled across the retinotopic space in human observers at a propagation speed ranging from 0.3 to 0.5 m/s, consistent with the conduction delay of long-range horizontal connections in the visual cortex (Shao and Burkhalter, 1996; Nowak and Bullier, 1996; Girard et al., 2001). 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

Participants 18 participants (9 females, 16 right-handed, mean ± standard deviation (std) age: 26.2 ± 4.1 years) were recruited for the main experiment. One participant was excluded from the analysis because the number of false alarms exceeded the number of targets presented. 15 participants (7 females, 13 right-handed, mean ± sd age: 25.5 ± 3 years) were recruited for the additional control experiment 1 (see Flashing Disk section below), and 15 participants (9 females, mean ± sd age: 26.1 ± 4.3 years) for control experiment 2 (see Broadband Oscillating Disk). The number of participants was decided based on previous studies using flickering visual stimuli to induce perceptual cycles (mean ± sd number of participants from a sample of representative studies: 15.5 ± 9.3; Stefanics et al., 2010 (n=11; n=13); Mathewson et al., 2012 (n=13); Henry and Obleser, 2012 (n=12); Graaf et al., 2013 (n=21, n=18); Henry et al., 2014 (n=17); Spaak et al., 2014 (n=19); ten Oever and Sack, 2015 (n=20); Sokoliuk and VanRullen, 2016 (n=7, n=15, n=5, n=4); Kizuk and Mathewson, 2017 (n=42)). All participants were free from medication affecting the central nervous system, reported no history of psychiatric or neurological disorders, gave their written informed consent and were compensated for their participation. The study was approved by the local French ethics committee Ouest IV (IRB #20.04.16.71057) and followed the Declaration of Helsinki.

Participants (n=17) performed a threshold visual detection task, while a luminance oscillating disk was concurrently presented in the periphery (eccentricity: 7.5°) to modulate perception at the theta and alpha frequency (4, 6, 8 and 10 Hz; EEG simultaneously recorded). Nearthreshold target stimuli appeared at one of three possible eccentricities between a central fixation cross and the disk (Figure 1A; adjusted according to cortical magnification so each target measured 0.8 mm of diameter and were placed 0.8 mm away from each other in the cortex; see Figure 1B). We tested whether (1) the periodic disk stimulation modulates detection performance periodically at each target position, (2) the optimal phase (of highest performance) shifts as a function of distance from the disk suggesting that induced perceptual cycles travel across space (Figure 1C), and (3) the occurrence of such traveling properties depends on the induced frequency. the periphery to induce perceptual cycles at the theta and alpha frequency. Participants were instructed to detect visual targets at threshold (50% detection) at three different positions in the retinotopic space, based on cortical magnification. Disks oscillated for a 30-seconds period during which 6 to 18 targets were presented at random times according to a decreasing probability distribution. Participants pressed the space bar when they detected the target (1-s response window after target onset) B. In the visual cortex, visual targets measured 0.8 mm of diameter and were placed 0.8 mm away from each other. C. Hypothesis: the oscillating disk, presented in the lower right corner, induced a brain activity that traveled across the retinotopic space (note that we concentrate our predictions to the quadrant in which the disk is presented). At an instant t, position 3 is located at the maximum amplitude of the induced brain activity, leading to the highest performance, while position 1 is located at the minimum amplitude. EEG activity was analyzed using frequency decomposition (Fast Fourier Transform, FFT, performed on the time series of each participant and electrode) and Event-Related Potentials (ERPs) measures to ensure that we successfully induced frequency-specific brain activity and to characterize the shape of the evoked response. First, peaks in the spectrum (as measured per SNR, averaged across participants and electrodes) were identified for each induced frequency (4, 6, 8 and 10 Hz; SNR > 1.4) and their first harmonics (8, 12, 16 and 20 Hz; SNR > 1.57), with topographies showing brain activity in the occipital cortex (for simplicity, frequencies were rounded to a whole number; real values are displayed in Figure 2 left side of each panel). Second, ERP analyses showed that the evoked signal is a complex signal composed of the induced frequency and its first harmonic (Figure 2 right side of each panel).

We further computed an FFT on the ERPs of electrode Oz. Peaks were again identified for each induced frequency (4, 6, 8 and 10 Hz; SNR > 2.4) and their first harmonics (8, 12, 16 and 20 Hz; SNR > 4.41; data not shown). Note that both SNR computed on EEG time series and on EEG evoked activity are > 1 for each induced frequency and first harmonic demonstrating that the disk induced frequency-specific brain activity. These complex evoked responses were interpreted as the overlap between the periodic brain response (i.e., inducer) and the neural population response to individual stimuli (i.e., contrast change) at low frequencies, or alternatively, to the nonlinear nature of the visual system, i.e., nonlinear systems produce complex output consisting of the input frequency and multiple harmonics (Heinrich, 2010; Norcia et al., 2015). Together, the EEG analyses confirm that we successfully induced theta/alpha activity in the visual cortex and show that the evoked signal is a complex signal composed of the induced frequency and its first harmonic (Heinrich, 2010; Norcia et al., 2015). cortex. Left side of each panel, Fast Fourier Transform analyses performed on the EEG time series. Right side of each panel, ERP analyses, for induced frequencies of A. 4, B. 6, C. 8 and D. 10 Hz (rounded frequency values). Signal-to-noise ratio (SNR) amplitude averaged across 17 participants and all 62 electrodes, from 2 to 22 Hz. In each panel, a peak in SNR is identified 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 for the induced frequency and its first harmonic. Topographies of the two SNR peaks revealed that we successfully induced brain activity in the visual cortex. Black dot, Electrode Oz. ERP of the Oz electrode computed on one-second epochs (the first-second epoch was removed to each 30-seconds blocks to avoid the EEG transient evoked response; each block represented 29 1-second epochs) averaged across participants (n=17). Solid black line, averaged ERP. Shaded area, standard error of the mean.

Second, we investigated whether detection performance was modulated periodically for each induced frequency and each target position. Targets (from 6 to 18 targets per 30 secondsblocks) can appear at random delays during the periodic disk stimulation (from 1s to 29s from disk onset). Targets were binned according to the phase of the oscillating disk (7 bins/cycle; least number of bins to sample one oscillatory period while allowing a large number of trials per bin to achieve high statistical power). In each bin, detection performance was computed as per hit rate (correct target detection) for each participant, frequency, and target position. Finally, the data were averaged across participants and given the complex shape of the ERP (Figure 2), fit to a complex sine function (the shape of the evoked response was used as proxy for the shape of the behavioral response), separately for each frequency and target position. Detection performance showed a significant oscillatory pattern for each target position and frequency (Monte Carlo on fitted amplitude, Bonferroni corrected across frequencies and positions, p-value threshold < 0.004, corresponding to a Z-score threshold of 2.64, and a Cohen’s d threshold of 1.66; Figure 4), and a clear optimal phase (of highest performance). Note that the fitted amplitude of the induced frequency (distance between the optimal and nonoptimal phase) was significantly higher than the one of the first harmonic (two-tailed t-test on fitted amplitude across all frequencies and positions, p-value < 0.01, Cohen’s d = 0.67, CI = [0.05; 0.1]). A high fitted amplitude indicates that the fitted sine function explains a large portion of the variance in the behavioral performance. The results thus suggest that the oscillatory pattern was mainly driven by the induced frequency across all tested target positions and frequencies. The inducer modulated detection performance periodically, at each target position and at each frequency, with an average amplitude modulation (optimal to non-optimal hit rate difference) of 42.71 ± 3.37 %. The amplitude modulation was further computed for each 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 participant, frequency, and target position (Figure 3). A two-way repeated-measures ANOVA revealed a significant main effect of the frequency (F(3, 48) = 23.85, SS = 0.67, p-value < 0.01, eta² = 59.85), and no main effect of the target position (F(2, 32) = 0.9, SS = 0.01, p-value = with increasing frequency but is constant across target positions. The amplitude modulation allowed to reliably estimate the optimal phase at each frequency and target positions. A complementary analysis showed that behavioral performance was better explained when taking into account the spatial position of the targets. Specifically, we compared the amplitude modulation when detection performance was calculated disregarding target position, with the amplitude modulation calculated independently for each target position and then averaged across positions (two-tailed t-tests Bonferroni corrected for multiple comparisons: 4 Hz, t-stat = -5.84, p-value < 0.01, Cohen’s d = -0.3, CI = [-0.05; -0.02]; 6 Hz, t-stat = -5.45, p-value < 0.01, Cohen’s d = -0.25, CI = [-0.04; -0.02]; 8 Hz, t-stat = -5.35, p-value < 0.01, Cohen’s d = 0.3, CI = [-0.04, -0.01]; 10 Hz, t-stat = -9.1, p-value < 0.01, Cohen’s d = -0.52, CI = [-0.05; 0.03]). The amplitude modulation was significantly stronger when calculated position-byposition, suggesting that taking into account the spatial position of visual targets better explain perceptual performance. Amplitude computed as the difference between the maximum and the minimum hit rate. Dots, individual outlier data. A two-way repeated-measures ANOVA revealed a significant main effect of frequency (F(3, 48) = 23.85, SS = 0.67, p-value < 0.01, eta² = 59.85). Critically, we tested whether (1) perceptual cycles propagate across the retinotopic space, and (2) the occurrence of such traveling properties depends on the induced frequency. Propagation is defined as a shift in the optimal phase between two positions. To assess whether the optimal phase shifted as a function of target position, individual optimal phases were converted in radians based on a one-cycle sine wave fit (see Methods) at the induced frequency (the oscillatory pattern was mainly driven by the induced frequency; see analysis above). A Harrison-Kanji test revealed a significant main effect of the frequency (F(3,48) = 25.13, SS = 14.33, p-value < 0.01), target position (F(2,32) = 3.06, SS = 1.16, p-value = 0.04) and a tendency for the interaction (F(6,96) = 1.99, SS = 2.42, p-value = 0.06). For the post-hoc analyses, we performed Watson-Williams tests against 0, i.e., null difference, on participantby-participant pairwise phase differences, for each pair of positions (positions 1 and 2, 1 and 3, 2 and 3). The results showed a significant phase shift between positions 1 and 2, 1 and 3, and 2 and 3, for both 8 Hz and 10 Hz (Figure 4C,D; Bonferroni corrected across frequencies and positions, p-value < 0.004); and between positions 1 and 2 for 6 Hz. Thus, we did not find a systematic phase shift, i.e., phase shift between each target positions, for 4 and 6 Hz (Figure 4A,B). Together, the results demonstrate that the behavioral optimal phase of alpha perceptual cycles shifted across target positions, suggesting that brain signals traveled across the retinotopic cortical space. In addition, the phase shift cannot be explained by a decreased phase estimation accuracy at low frequencies (see Figure 3, showing that the amplitude modulation is in fact higher at low compared to high induced frequency). Lower graph of each panel, hit rate averaged across participants (n=17), binned as a function of the phase of the oscillating disk, and fitted to a complex sine function. Shaded colored area, 95 confidence intervals. Solid line, sine fit. Dotted line, optimal phase in degrees. The value of the optimal phase in degrees is extracted for fit on data averaged across participants (note 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 that this closely resemble the value obtained from averaging individual optimal phases from top graph). Top graph of each panel, rose plot distribution of the optimal phase across participants. Colored solid line, optimal phase averaged across participants. Gray scale, phase bins of the oscillating disk (90°, white disk). Each bin represents 51.4° of the oscillatory cycle. A. results for induced frequencies of A. 4, B. 6, C. 8 and D. 10 Hz. Performance was significantly modulated periodically at each target position and frequency (Monte Carlo, Bonferroni corrected across target positions and frequencies, p-value threshold < 0.01). The optimal phase shifted between positions 1 and 2, 2 and 3, and 1 and 3 for 8 Hz- and 10 Hzinduced frequencies; and between positions 1 and 2 for 6 Hz-induced frequency (WatsonWilliam test, Bonferroni corrected across target positions and frequencies, p-value threshold < 0.004). There was no significant phase shift for 4 Hz-induced frequencies.

When converting the phase shift observed between target positions into milliseconds (3 ms for 8 Hz, and 5.5 ms for 10 Hz, respectively) and given the cortical distance between two target positions (0.8 mm distance edge-to-edge) as well as the targets’ cortical size (0.8 mm diameter), one can estimate that alpha-induced brain oscillations traveled across the retinotopic space at an averaged propagation speed ranging between 0.3 (1.6 mm / 5.5 ms) and 0.5 m/s (1.6 mm / 3 ms).

Finally, one may ask whether the phase shift observed in behavioral data was due to luminance masking from the disk. We performed two control experiments (15 participants each) to address this potential concern. Participants were instructed to detect visual targets at threshold (50% detection) at one of the same three positions as in the main experiment, while a peripheral disk was simultaneously flashed at one of seven possible levels of luminance (Control Experiment 1: Flashing Disk; same as Sokoliuk and VanRullen, 2016), or while the disk was oscillating in luminance with an arrhythmic broadband frequency profile centered on 10 Hz (Control Experiment 2: Broadband Oscillating Disk). First, for both control experiments, detection performance was calculated for each level of luminance, and a onecycle sine function was fitted to the empirical data (see Luminance binning in Methods). For both control conditions, detection performance showed a significant oscillatory pattern at each target position (Monte Carlo, Bonferroni corrected across positions, p-value threshold of 0.01, corresponding to a Z-score threshold of 2.12, and a Cohen’s d threshold of 1.31, Figure 5A,B) 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 confirming the presence of luminance masking at all three positions. We then compared the individual optimal phase between target positions. There was no significant phase shift in both the Flashing Disk control (F(2, 14) = 1, SS = 345.5, p-value = 0.38, eta² = 6.67) and the Broadband Oscillating Disk control (F(2, 14) = 0, SS = 3.61, p-value = 0.99, eta² = 0), suggesting that the propagation of perceptual cycles observed in the main experiment was not due to masking.

To further investigate whether the maximal luminance of the disk (100 % contrast) could induce a propagation of behavioral masking, targets in the Broadband Oscillating Disk Experiment were binned as a function of the peak luminance (see Luminance peak binning in Methods). Visual performance showed a significant oscillatory modulation for position 1 and 2 (Monte Carlo, Bonferroni corrected across positions, p-value threshold of 0.01, corresponding to a Zscore threshold of 2.12, and a Cohen’s d threshold of 1.31) but not position 3 (p = 0.04, above the Bonferroni corrected p-value threshold) (Figure 5C). Although the fluctuation was not significant at position 3, we still compared the individual optimal phases between target positions. The test did not reveal a significant phase shift (F(2, 14) = 0.7, SS = 590.93, p-value = 0.5, eta² = 4.82). Coherent with the previous result, although the disk maximal luminance masked visual performance of nearby targets, this masking cannot explain the shift of the optimal phase in the main experiment.

We finally investigated whether the arrhythmic, broadband peripheral disk produced the same results as in the main experiment by binning the targets every 100 ms (see Pseudo-phase binning in Methods). Although centered at 10 Hz, the broadband oscillating disk did not periodically modulate detection performance at 10 Hz (Monte Carlo, p-value > 0.44, Figure 5D). This absence of rhythmic modulation was coherent with the EEG analysis on two participants showing that the broadband peripheral disk did not evoke a frequency-specific 10 Hz brain activity (see SNR results on Figure 5E; although it did induce broadband activity around 10 Hz, analysis not shown). In other words, the broadband visual stimulation did not induce narrow band 10 Hz-brain activity, coherent with the behavioral results showing no alpha induced perceptual cycle.

Taken together, the results of both control experiments show that the phase shift observed in the main experiment cannot be merely explained by low-level luminance masking (Figure 5). masking. A. Flashing Disk control: Hit rate for each 13 discrete luminance levels and 3 target positions averaged across participants (n=15) and fitted to a one-cycle sine function. Shaded color area, 95 confidence intervals. Solid line, fit. Dotted line, optimal behavioral phase. Green, position 1. Cyan, position 2. Blue, position 3. B. Broadband Oscillatory Disk control: Hit rate for each 13 luminance bins and 3 target positions averaged across participants (n=15) and fitted to a one-cycle sine function. C. Hit rate for each 7-time bins from the peripheral disk maximal luminance onset, and the 3 target positions averaged across participants (n=15) and fitted to a one-cycle sine function. D. Hit rate for each 7 pseudo-phase bins of 10 Hz rhythmic modulation, and the 3 target positions averaged across participants (n=15) and fitted to a onecycle sine function. E. EEG data of two individual participants. Left side of each panel, SNR amplitude averaged across all 62 electrodes on the Fast Fourier Transform performed on the 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647

EEG time series. Right side, ERP of the PO3 electrode computed on one-second epochs (the first-second epoch was removed to each 30-seconds blocks to avoid the EEG transient evoked response; each block represented 29 1-second epochs).

Using psychophysics and EEG, we showed that visual perception at each target position is modulated periodically at the induced frequency, replicating previous results (Stefanics et al., 2010; Mathewson et al., 2012; Henry and Obleser, 2012; Graaf et al., 2013; Henry et al., 2014; Spaak et al., 2014; ten Oever and Sack, 2015; Kizuk and Mathewson, 2017). Critically, the optimal phase for visual perception systematically shifted between target position. This effect was observed for alpha-induced frequencies (8 Hz and 10 Hz; and cannot be simply explained by a mere luminance masking confound) and not theta, with an average propagation speed ranging from 0.3 to 0.5 m/s. Together, the results support the hypothesis that induced perceptual cycles propagate across the retinotopic visual space presumably due to horizontal connections in the retinotopic visual cortex.

Entrained oscillations or periodic evoked response? Our results showed that perceptual cycles are propagating across the visual retinotopic space, suggesting that the underlying neural activity is propagating as well in the cortical retinotopic space through horizontal axons. We cannot, however, conclude whether this propagating activity corresponds to the propagation of true entrained oscillations or of a succession of evoked responses. Our EEG recordings highlighted that the evoked signal was composed of the induced frequency and its first harmonic, interpreted as the overlap between the periodic brain response (i.e., inducer) and the neural population response to individual stimuli (i.e., contrast change) at low frequencies, or alternatively, to the nonlinear nature of the visual system, i.e., nonlinear systems produce complex output consisting of the input frequency and multiple harmonics (Heinrich, 2010; Norcia et al., 2015). The propagation we observed in this study being frequency band-specific, we argue that the most parsimonious interpretation is to consider entrained brain oscillations. However, and regardless the underlying cortical mechanism, whether entrained oscillations or 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 periodic ERPs, our conclusions remain unchanged, i.e., induced perceptual cycles propagate across the retinotopic space.

Propagation of alpha but not theta perceptual cycles. Attention is the cognitive function that selects relevant information to facilitate its processing while still being able to flexibly redeploy resources to other information if necessary (Carrasco, 2011; Dugué et al., 2018, 2020). Studies have shown that when covert attention (no head/eye movements) is sustained at a given spatial location, information is sampled periodically at the alpha frequency (review: Dugué and VanRullen, 2017; Kienitz et al., 2022). In other words, visual performance fluctuates over time in the alpha band in detection tasks in which the target stimulus appeared always at the same spatial location (Valera et al., 1981; Busch et al., 2009; Mathewson et al., 2009; Busch and VanRullen, 2010; Dugué et al., 2011; Samaha and Postle, 2015; Samaha et al., 2017; Fakche et al., 2022). However, when multiple stimuli are presented, attention rhythmically samples information at the theta frequency (Dugué et al., 2015; Landau et al., 2012; Fiebelkorn et al., 2013a; Song et al., 2014; Huang et al., 2015; Dugué et al., 2019; Merholz et al., 2022; Galas et al., 2023; see also Re et al., 2023; review: VanRullen, 2016; Dugué and VanRullen, 2017; Kienitz et al., 2022; Keitel et al., 2022).

Here, while we did not explicitly manipulate covert attention, participants fixated at the center of the screen and targets appeared in a constrained location suggesting that covert, voluntary spatial attention was sustained on the bottom right quadrant. This manipulation likely recruited alpha sampling, which potentially favored the propagation of alpha-induced perceptual cycles. One can speculate that the propagation of alpha perceptual cycles away from the main attention focus could allow the observer to periodically monitor other nearby locations allowing for flexible attentional reallocation when a target appears. Further studies are necessary to investigate this hypothesis.

Perceptual propagation suggests cortical propagation. Sokoliuk and VanRullen (2016) reasoned that if an induced brain activity propagates across the visual cortex, it should have perceptual consequences across the retinotopic visual space. Using a similar psychophysical 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 paradigm, they found a shift of the behavioral optimal phase as a function of distance from the inducer. Yet, there are two notable differences between their study and the present one. First, they observed that the phase shifted between the visual stimulus the closest to the inducer and more distant ones (no differences between intermediate positions). Yet, postulating brain activity is traveling within the cortex requires showing a phase change across all positions. Here, contrary to Sokoliuk and VanRullen (2016), we found a systematic phase shift across all three positions.

Second, Sokoliuk and VanRullen (2016) observed an optimal phase shift for both inducedfrequencies of 5 Hz (theta) and 10 Hz (alpha), but not 15 Hz. Here, however, we showed a shift for alpha-induced frequencies (8 Hz and 10 Hz), but not theta (4 Hz and 6 Hz). Together, these discrepant results can be explained by a number of critical differences between the two studies. First, the EEG analysis confirmed that the oscillating disk induced frequency-specific brain activity in the occipital cortex. This result was important to validate our rationale postulating that induced perceptual cycles travel across the visual retinotopic space due to the propagation of brain activity across the cortical retinotopic space. Importantly, our EEG results revealed that the oscillating disk produced a complex neural response composed of the induced frequency and its first harmonic, coherent with the nature of the visual system (Heinrich et al., 2010; Norcia et al., 2015; Spaak et al., 2014). Thus, one must fit the behavioral response with a corresponding complex sine function to accurately capture the non-linearity of the neural response. Since the EEG was not recorded in Sokoliuk and VanRullen (2016), the shape of the induced brain signal was unknown. Second, to ensure that the three targets activated the same number neurons in visual regions, hence landing in a similar spatial extent (spatial phase) of the propagating activity, we adjusted the size of each target to cortical magnification. Third, in our study, the same participants (n=17) performed all four frequency conditions thus ensuring equal statistical power and no inter-individual variability (n=5 for 5Hz, n=7 for 10Hz and n=15 for a 10-Hz replication set, and n=4 for 15Hz in Sokoliuk and VanRullen, 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 2016). Finally, we used eye-tracking to ensure stable fixation, critical when investigating retinotopic propagation.

Neural mesoscopic traveling waves, a growing, yet largely understudied field. A traveling wave is the propagation of neural activity over space with a monotonic shift in the peak latency between the origin of the signal and more distal positions (Sato et al., 2012; Muller et al., 2018). Mesoscopic waves travel within individual brain regions (e.g., V1) spanning millimeters (Sato et al., 2012; Muller et al., 2018). Studies using invasive recordings with high spatial and temporal resolution showed non-oscillatory traveling activity in visual cortices of mammals (Bringuier et al., 1999; Jancke et al., 2004; Roland et al., 2006; Lippert et al., 2007; Sharon et al., 2007; Xu et al., 2007; Takagaki et al., 2008; Nauhaus et al., 2009, 2012; Gao et al., 2012; Rekauzke et al., 2016; Slovin et al., 2002; Chen et al., 2006; Sit et al., 2009; Reynaud et al., 2012; Zhang et al., 2012; Yang et al., 2015; Chemla et al., 2019). Much fewer studies have focused on mesoscopic oscillatory traveling waves (spontaneous, entrained or evoked). They showed that delta, theta, alpha, beta and gamma oscillations can propagate within individual visual areas of mammals and turtles (Prechtl et al., 1997, 2000; Sanchez-Vives and McCormick, 2000; Huang et al., 2004; Benucci et al., 2007; Han et al., 2008; Ray and Maunsell, 2011; Maris et al., 2013; Stroh et al., 2013; Muller et al., 2014; Townsend et al., 2015; Zanos et al., 2015; Davis et al., 2020). In humans, only a few studies, using invasive recordings in patients, showed the propagation of theta, alpha, and beta mesoscopic traveling waves (Takahashi et al., 2011; Zhang and Jacobs, 2015; Sreekumar et al., 2021), but only in nonvisual cortical areas. There is no electro-physiological study to date investigating the propagation of low-frequency oscillations in individual human visual areas (see Grabot et al., 2022, for a computational solution).

Finally, if a few studies have investigated the functional role of propagating oscillatory activity at the mesoscopic levels (attention: Maris et al., 2013; memory: Han et al., 2008; motricity: Rubino et al., 2006; Takahashi et al., 2011, 2015; saccadic eye movements: Zanos et al., 2015; visual perception: Besserve et al., 2015; Davis et al., 2020), very little is known about the link between oscillatory activity propagation within individual visual areas and perceptual performance, especially in human. The present study addresses this clear gap in the literature. Speed and spatial extent of mesoscopic traveling waves. Our results show that induced alpha perceptual cycles travel across the retinotopic space at a propagation speed ranging from 0.3 to 0.5 m/s. Such observation is in line with results from the animal literature showing that lowfrequency oscillations propagate within visual areas at a speed ranging from 0.01 to 0.6 m/s (Prechtl et al., 1997, 2000; Sanchez-Vives and McCormick, 2000; Benucci et al., 2007; Han et al., 2008; Ray and Maunsell, 2011; Muller et al., 2014; Zanos et al., 2015; Davis et al., 2020). Additionally, given a phase difference of maximum 40° between target positions, it is unlikely that more than one (spatial) cycle (360°) of oscillatory activity propagates across such a small portion of the visual cortex, in line with previous observations (Zanos et al., 2015; Zhang and Jacobs, 2015).

Finally, given our specific contrast manipulation and the observed propagation of induced perceptual cycles, it is likely that our paradigm preferentially probed alpha traveling waves in area V1 (with small receptive fields).

Conclusion. Using a carefully designed psychophysical paradigm, combined with EEG and eye-tracking, our study demonstrates that induced alpha perceptual cycles travel across the retinotopic visual space in humans, at a propagation speed ranging from 0.3 to 0.5 m/s. These results suggest that brain activity travels across the visual cortex to modulate performance periodically across space and time.

Raw behavioral data and code relative to the main results will be available at https://github.com/CamilleFakche after publication.

Conceptualization, C. F., L. D.; Formal Analysis, C. F.; Funding Acquisition, L. D.; Investigation, C. F.; Methodology, C. F., L. D.; Supervision, L. D.; Validation, L. D.; Visualization, C. F., L. D.; Writing – Original Draft Preparation, C. F.; Writing – Review and Editing, L. D.

useful comments on the manuscript.

We thank Kirsten Petras, Andrea Alamia, Rufin VanRullen and Frédéric Chavane for their This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 852139 – Laura Dugué) and the Agence Nationale de la Recherche (ANR) – Deutsche Forschungsgemeinschaft (DFG) program (grant agreement No J18P08ANR00 – Laura Dugué).

Retrospective analysis of the citations in every article published in this journal from 2010 to 2021 reveals a persistent pattern of gender imbalance: Although the proportions of authorship teams (categorized by estimated gender identification of first author/last author) publishing in the Journal of Cognitive Neuroscience (JoCN) during this period were M(an)/M = .407, W(oman)/M = .32, M/W = .115, and W/W = .159, the comparable proportions for the articles that these authorship teams cited were M/M = .549, W/M = .257, M/W = .109, and W/W = .085 (Postle and Fulvio, JoCN, 34:1, pp. 1–3). Consequently, JoCN encourages all authors to 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 consider gender balance explicitly when selecting which articles to cite and gives them the opportunity to report their article’s gender citation balance. The authors of this article report its proportions of citations by gender category to be as follows: M/M = .642; W/M = .221; M/W = .074; W/W = .063. Berens, P. (2009). CircStat: a MATLAB toolbox for circular statistics. Journal of statistical software, 31, 1-21. https://doi.org/10.18637/jss.v031.i10 Besserve, M., Lowe, S. C., Logothetis, N. K., Schölkopf, B., & Panzeri, S. (2015). Shifts of gamma phase across primary visual cortical sites reflect dynamic stimulus-modulated information transfer. PLoS biology, 13(9), e1002257. https://doi.org/10.1371/journal.pbio.1002257, PubMed: 26394205 Bringuier, V., Chavane, F., Glaeser, L., & Frégnac, Y. (1999). Horizontal propagation of visual activity in the synaptic integration field of area 17 neurons. Science, 283(5402), 695-699. https://doi.org/10.1126/science.283.5402.695, PubMed: 9924031 Busch, N. A., & VanRullen, R. (2010). Spontaneous EEG oscillations reveal periodic sampling of visual attention. Proceedings of the National Academy of Sciences, 107(37), 16048-16053. https://doi.org/10.1073/pnas.1004801107, PubMed: 20805482 Busch, N. A., Dubois, J., & VanRullen, R. (2009). The phase of ongoing EEG oscillations predicts visual perception. Journal of neuroscience, 29(24), 7869-7876. https://doi.org/10.1523/JNEUROSCI.0113-09.2009, PubMed: 19535598 Carrasco, M., & McElree, B. (2001). Covert attention accelerates the rate of visual information processing. Proceedings of the National Academy of Sciences, 98(9), 5363-5367. https://doi.org/10.1073/pnas.081074098, PubMed: 11309485 Chavane, F., Perrinet, L. U., & Rankin, J. (2022). Revisiting horizontal connectivity rules in V1: from like-to-like towards like-to-all. Brain Structure and Function, 227(4), 1279-1295. https://doi.org/10.1007/s00429-022-02455-4, PubMed: 3512252 Chemla, S., Reynaud, A., Di Volo, M., Zerlaut, Y., Perrinet, L., Destexhe, A., & Chavane, F. (2019). Suppressive traveling waves shape representations of illusory motion in primary visual cortex of awake primate. Journal of Neuroscience, 39(22), 4282-4298. https://doi.org/10.1523/JNEUROSCI.2792-18.2019, PubMed: 30886010 Chen, Y., Geisler, W. S., & Seidemann, E. (2006). Optimal decoding of correlated neural population responses in the primate visual cortex. Nature neuroscience, 9(11), 1412-1420. https://doi.org/10.1038/nn1792, PubMed: 17057706 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858

Davis, Z. W., Muller, L., Martinez-Trujillo, J., Sejnowski, T., & Reynolds, J. H. (2020). Spontaneous travelling cortical waves gate perception in behaving primates. Nature, 587(7834), 432-436. https://doi.org/10.1038/s41586-020-2802-y, PubMed: 33029013 De Graaf, T. A., Gross, J., Paterson, G., Rusch, T., Sack, A. T., & Thut, G. (2013). Alpha-band rhythms in visual task performance: phase-locking by rhythmic sensory stimulation. PloS one, 8(3), e60035. https://doi.org/10.1371/journal.pone.0060035, PubMed: 23555873 Dugué, L., Merriam, E. P., Heeger, D. J., & Carrasco, M. (2020). Differential impact of endogenous and exogenous attention on activity in human visual cortex. Scientific reports, 10(1), 21274. https://doi.org/10.1038/s41598-020-78172-x, PubMed: 3327755 Dugué, L., Beck, A. A., Marque, P., & VanRullen, R. (2019). Contribution of FEF to attentional periodicity during visual search: a TMS study. Eneuro, 6(3). https://doi.org/10.1523/ENEURO.0357-18.2019, PubMed: 31175148 Dugué, L., Merriam, E. P., Heeger, D. J., & Carrasco, M. (2018). Specific visual subregions of TPJ mediate reorienting of spatial attention. Cerebral Cortex, 28(7), 2375-2390. https://doi.org/10.1093/cercor/bhx140, PubMed: 28981585 Dugué, L., & VanRullen, R. (2017). Transcranial magnetic stimulation reveals intrinsic perceptual and attentional rhythms. Frontiers in Neuroscience, 11, 154. https://doi.org/10.3389/fnins.2017.00154, PubMed: 28396622 Dugué, L., Marque, P., & VanRullen, R. (2015). Theta oscillations modulate attentional search performance periodically. Journal of cognitive neuroscience, 27(5), 945-958. https://doi.org/10.1162/jocn_a_00755, PubMed: 25390199 Dugué, L., Marque, P., & VanRullen, R. (2011). The phase of ongoing oscillations mediates the causal relation between brain excitation and visual perception. Journal of neuroscience, 31(33), 11889-11893. https://doi.org/10.1523/JNEUROSCI.1161-11.2011, PubMed: 21849549 Fakche, C., VanRullen, R., Marque, P., & Dugué, L. (2022). α phase-amplitude tradeoffs predict visual perception. ENeuro, 9(1). https://doi.org/10.1523/ENEURO.0244-21.2022, PubMed: 35105658 Fiebelkorn, I. C., Saalmann, Y. B., & Kastner, S. (2013a). Rhythmic sampling within and between objects despite sustained attention at a cued location. Current biology, 23(24), 25532558. https://doi.org/10.1016/j.cub.2013.10.063, PubMed: 24316204 Fiebelkorn, I. C., Snyder, A. C., Mercier, M. R., Butler, J. S., Molholm, S., & Foxe, J. J. (2013b). Cortical cross-frequency coupling predicts perceptual outcomes. Neuroimage, 69, 126-137. https://doi.org/10.1016/j.neuroimage.2012.11.021, PubMed: 23186917 Gao, X., Xu, W., Wang, Z., Takagaki, K., Li, B., & Wu, J. Y. (2012). Interactions between two propagating waves in rat visual cortex. Neuroscience, 216, 57-69. https://doi.org/10.1016/j.neuroscience.2012.04.062, PubMed: 22561730 Girard, P., Hupé, J. M., & Bullier, J. (2001). Feedforward and feedback connections between areas V1 and V2 of the monkey have similar rapid conduction velocities. Journal of 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 neurophysiology, 85(3), 1328-1331. https://doi.org/10.1152/jn.2001.85.3.1328, PubMed: 11248002 Grabot, L., Merholz, G., Winawer, J., Heeger, D., & Dugué, L. (2022). Computational modeling of traveling waves using MEG-EEG in human. Journal of Vision, 22(14), 3511-3511. https://doi.org/10.1167/jov.22.14.3511 Han, F., Caporale, N., & Dan, Y. (2008). Reverberation of recent visual experience in spontaneous cortical waves. Neuron, 60(2), 321-327. https://doi.org/10.1016/j.neuron.2008.08.026, PubMed: 18957223 Hanslmayr, S., Volberg, G., Wimber, M., Dalal, S. S., & Greenlee, M. W. (2013). Prestimulus oscillatory phase at 7 Hz gates cortical information flow and visual perception. Current Biology, 23(22), 2273-2278. https://doi.org/10.1016/j.cub.2013.09.020, PubMed: 24184106 Heinrich, S. P. (2010). Some thoughts on the interpretation of steady-state evoked potentials. Documenta Ophthalmologica, 120, 205-214. https://doi.org/10.1007/s10633-0109212-7, PubMed: 20101435 Henry, M. J., Herrmann, B., & Obleser, J. (2014). Entrained neural oscillations in multiple frequency bands comodulate behavior. Proceedings of the National Academy of Sciences, 111(41), 14935-14940. https://doi.org/10.1073/pnas.1408741111, PubMed: 25267634 Henry, M. J., & Obleser, J. (2012). Frequency modulation entrains slow neural oscillations and optimizes human listening behavior. Proceedings of the National Academy of Sciences, 109(49), 20095-20100. https://doi.org/10.1073/pnas.1213390109, PubMed: 23151506 Horton, J. C., & Hoyt, W. F. (1991). The representation of the visual field in human striate cortex: a revision of the classic Holmes map. Archives of ophthalmology, 109(6), 816-824. https://doi.org/10.1001/archopht.1991.01080060080030, PubMed: 2043069 Huang, X., Troy, W. C., Yang, Q., Ma, H., Laing, C. R., Schiff, S. J., & Wu, J. Y. (2004). Spiral waves in disinhibited mammalian neocortex. Journal of Neuroscience, 24(44), 9897-9902. https://doi.org/10.1523/JNEUROSCI.2705-04.2004, PubMed: 15525774 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949

Lippert, M. T., Takagaki, K., Xu, W., Huang, X., & Wu, J. Y. (2007). Methods for voltagesensitive dye imaging of rat cortical activity with high signal-to-noise ratio. Journal of neurophysiology, 98(1), 502-512. https://doi.org/10.1152/jn.01169.2006, PubMed: 17493915 Liu-Shuang, J., Norcia, A. M., & Rossion, B. (2014). An objective index of individual face discrimination in the right occipito-temporal cortex by means of fast periodic oddball stimulation. Neuropsychologia, 52, 57-72. https://doi.org/10.1016/j.neuropsychologia.2013.10.022, PubMed: 24200921 Maris, E., Womelsdorf, T., Desimone, R., & Fries, P. (2013). Rhythmic neuronal synchronization in visual cortex entails spatial phase relation diversity that is modulated by stimulation and attention. Neuroimage, 74, 99-116. https://doi.org/10.1016/j.neuroimage.2013.02.007, PubMed: 23416733 Mathewson, K. E., Prudhomme, C., Fabiani, M., Beck, D. M., Lleras, A., & Gratton, G. (2012). Making waves in the stream of consciousness: entraining oscillations in EEG alpha and fluctuations in visual awareness with rhythmic visual stimulation. Journal of cognitive neuroscience, 24(12), 2321-2333. https://doi.org/10.1162/jocn_a_00288, PubMed: 22905825 Mathewson, K. E., Gratton, G., Fabiani, M., Beck, D. M., & Ro, T. (2009). To see or not to see: prestimulus α phase predicts visual awareness. Journal of Neuroscience, 29(9), 2725-2732. https://doi.org/10.1523/JNEUROSCI.3963-08.2009, PubMed: 19261866 Merholz, G., Grabot, L., VanRullen, R., & Dugué, L. (2022). Periodic attention operates faster during more complex visual search. Scientific Reports, 12(1), 6688. https://doi.org/10.1038/s41598-022-10647-5, PubMed: 35461325 Michel, R., Dugué, L., & Busch, N. A. (2022). Distinct contributions of alpha and theta rhythms to perceptual and attentional sampling. European Journal of Neuroscience, 55(11-12), 30253039. https://doi.org/10.1111/ejn.15154, PubMed: 33609313 Muller, L., Chavane, F., Reynolds, J., & Sejnowski, T. J. (2018). Cortical travelling waves: mechanisms and computational principles. Nature Reviews Neuroscience, 19(5), 255-268. https://doi.org/10.1038/nrn.2018.20, PubMed: 29563572 Muller, L., Reynaud, A., Chavane, F., & Destexhe, A. (2014). The stimulus-evoked population response in visual cortex of awake monkey is a propagating wave. Nature communications, 5(1), 3675. https://doi.org/10.1038/ncomms4675, PubMed: 24770473 Nauhaus, I., Busse, L., Ringach, D. L., & Carandini, M. (2012). Robustness of traveling waves in ongoing activity of visual cortex. Journal of Neuroscience, 32(9), 3088-3094. https://doi.org/10.1523/JNEUROSCI.5827-11.2012, PubMed: 22378881 Nauhaus, I., Busse, L., Carandini, M., & Ringach, D. L. (2009). Stimulus contrast modulates functional connectivity in visual cortex. Nature neuroscience, 12(1), 70-76. https://doi.org/10.1038/nn.2232, PubMed: 19029885 Norcia, A. M., Appelbaum, L. G., Ales, J. M., Cottereau, B. R., & Rossion, B. (2015). The steady-state visual evoked potential in vision research: A review. Journal of vision, 15(6), 4-4. https://doi.org/10.1167/15.6.4, PubMed: 26024451 Nowak, L. G., & Bullier, J. (1996). Spread of stimulating current in the cortical grey matter of rat visual cortex studied on a new in vitro slice preparation. Journal of neuroscience methods, 67(2), 237-248. https://doi.org/10.1016/0165-0270(96)00065-9, PubMed: 8872891 Prechtl, J. C., Bullock, T. H., & Kleinfeld, D. (2000). Direct evidence for local oscillatory current sources and intracortical phase gradients in turtle visual cortex. Proceedings of the National Academy of Sciences, 97(2), 877-882. https://doi.org/10.1073/pnas.97.2.877, PubMed: 10639173 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994

Prechtl, J. C., Cohen, L. B., Pesaran, B., Mitra, P. P., & Kleinfeld, D. (1997). Visual stimuli induce waves of electrical activity in turtle cortex. Proceedings of the National Academy of Sciences, 94(14), 7621-7626. https://doi.org/10.1073/pnas.94.14.7621, PubMed: 9207142 Rubino, D., Robbins, K. A., & Hatsopoulos, N. G. (2006). Propagating waves mediate information transfer in the motor cortex. Nature neuroscience, 9(12), 1549-1557. https://doi.org/10.1038/nn1802, PubMed: 17115042 Samaha, J., Gosseries, O., & Postle, B. R. (2017). Distinct oscillatory frequencies underlie excitability of human occipital and parietal cortex. Journal of Neuroscience, 37(11), 28242833. https://doi.org/10.1523/JNEUROSCI.3413-16.2017, PubMed: 28179556 Sanchez-Vives, M. V., & McCormick, D. A. (2000). Cellular and network mechanisms of rhythmic recurrent activity in neocortex. Nature neuroscience, 3(10), 1027-1034. https://doi.org/10.1038/79848, PubMed: 11017176 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040

Sato, T. K., Nauhaus, I., & Carandini, M. (2012). Traveling waves in visual cortex. Neuron, 75(2), 218-229. https://doi.org/10.1016/j.neuron.2012.06.029, PubMed: 22841308 Senoussi, M., Moreland, J. C., Busch, N. A., & Dugué, L. (2019). Attention explores space periodically at the theta frequency. Journal of Vision, 19(5), 22-22. https://doi.org/10.1167/19.5.22, PubMed: 31121012 Shao, Z., & Burkhalter, A. (1996). Different balance of excitation and inhibition in forward and feedback circuits of rat visual cortex. Journal of Neuroscience, 16(22), 7353-7365. https://doi.org/10.1523/JNEUROSCI.16-22-07353.1996, PubMed: 8929442 Sharon, D., Jancke, D., Chavane, F., Na'aman, S., & Grinvald, A. (2007). Cortical response field dynamics in cat visual cortex. Cerebral Cortex, 17(12), 2866-2877. https://doi.org/10.1093/cercor/bhm019, PubMed: 17395608 Sit, Y. F., Chen, Y., Geisler, W. S., Miikkulainen, R., & Seidemann, E. (2009). Complex dynamics of V1 population responses explained by a simple gain-control model. Neuron, 64(6), 943-956. https://doi.org/10.1016/j.neuron.2009.08.041, PubMed: 20064399 Slovin, H., Arieli, A., Hildesheim, R., & Grinvald, A. (2002). Long-term voltage-sensitive dye imaging reveals cortical dynamics in behaving monkeys. Journal of neurophysiology, 88(6), 3421-3438. https://doi.org/10.1152/jn.00194.2002, PubMed: 12466458 Sokoliuk, R., & VanRullen, R. (2016). Global and local oscillatory entrainment of visual behavior across retinotopic space. Scientific Reports, 6(1), 25132. https://doi.org/10.1038/srep25132, PubMed: 27126642 Song, K., Meng, M., Chen, L., Zhou, K., & Luo, H. (2014). Behavioral oscillations in attention: rhythmic α pulses mediated through θ band. Journal of Neuroscience, 34(14), 4837-4844. https://doi.org/10.1523/JNEUROSCI.4856-13.2014, PubMed: 24695703 Spaak, E., de Lange, F. P., & Jensen, O. (2014). Local entrainment of alpha oscillations by visual stimuli causes cyclic modulation of perception. Journal of Neuroscience, 34(10), 35363544. https://doi.org/10.1523/JNEUROSCI.4385-13.2014, PubMed: 24599454 Stefanics, G., Hangya, B., Hernádi, I., Winkler, I., Lakatos, P., & Ulbert, I. (2010). Phase entrainment of human delta oscillations can mediate the effects of expectation on reaction speed. Journal of Neuroscience, 30(41), 13578-13585. https://doi.org/10.1523/JNEUROSCI.0703-10.2010, PubMed: 20943899 Sreekumar, V., Wittig Jr, J. H., Chapeton, J., Inati, S. K., & Zaghloul, K. A. (2020). Low frequency traveling waves in the human cortex coordinate neural activity across spatial scales. BioRxiv, 2020-03. https://doi.org/10.1101/2020.03.04.977173 Takahashi, K., Kim, S., Coleman, T. P., Brown, K. A., Suminski, A. J., Best, M. D., & Hatsopoulos, N. G. (2015). Large-scale spatiotemporal spike patterning consistent with wave propagation in motor cortex. Nature communications, 6(1), 7169. https://doi.org/10.1038/ncomms8169, PubMed: 25994554 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 VanRullen, R. (2007). The continuous Wagon Wheel Illusion depends on, but is not identical to neuronal adaptation. Vision Research, 47(16), 2143-2149. https://doi.org/10.1016/j.visres.2007.03.019, PubMed: 17559904 VanRullen, R., Reddy, L., & Koch, C. (2006). The continuous wagon wheel illusion is associated with changes in electroencephalogram power at∼ 13 Hz. Journal of Neuroscience, 26(2), 502-507. https://doi.org/10.1523/JNEUROSCI.4654-05.2006, PubMed: 16407547 VanRullen, R., Reddy, L., & Koch, C. (2005). Attention-driven discrete sampling of motion perception. Proceedings of the National Academy of Sciences, 102(14), 5291-5296. https://doi.org/10.1073/pnas.0409172102, PubMed: 15793010 VanRullen, R., & Koch, C. (2003). Is perception discrete or continuous?. Trends in cognitive sciences, 7(5), 207-213. https://doi.org/10.1016/s1364-6613(03)00095-0, PubMed: 12757822 Watt, J., Borhani, R., & Katsaggelos, A. K. (2020). Machine learning refined: Foundations, algorithms, and applications. Cambridge University Press.

Wickelgren, W. A. (1977). Speed-accuracy tradeoff and information processing dynamics. Acta psychologica, 41(1), 67-85. https://doi.org/10.1016/0001-6918(77)90012-9 Yang, Z., Heeger, D. J., Blake, R., & Seidemann, E. (2015). Long-range traveling waves of activity triggered by local dichoptic stimulation in V1 of behaving monkeys. Journal of neurophysiology, 113(1), 277-294. https://doi.org/10.1152/jn.00610.2013, PubMed: 25343785 1085 1086 1087 Zhang, Q. F., Wen, Y., Zhang, D., She, L., Wu, J. Y., Dan, Y., & Poo, M. M. (2012). Priming with real motion biases visual cortical response to bistable apparent motion. Proceedings of the National Academy of Sciences, 109(50), 20691-20696. https://doi.org/10.1073/pnas.1218654109, PubMed: 23188797