Delta phase resets mediate non-rhythmic temporal prediction

Neural oscillations adjust their phase towards the predicted onset of rhythmic stimulation to optimize the processing of upcoming relevant information. Whether such phase alignments can be observed in non-rhythmic contexts, however, remains unclear. Here, we recorded the magnetoencephalogram while healthy participants were engaged in a temporal prediction task judging the visual or crossmodal (tactile) reappearance of a uniformly moving visual stimulus after it disappeared behind an occluder. The temporal prediction conditions were contrasted with a luminance matching control condition to dissociate phase adjustments of endogenous neural oscillations from stimulus-driven activity. During temporal predictions, we observed stronger delta band inter-trial phase consistency (ITPC) in a network of sensory, parietal and frontal brain areas. Delta ITPC further correlated with individual prediction performance in parts of the cerebellum and in visual cortex. Our results provide evidence that phase alignments of low-frequency neural oscillations underlie temporal predictions in non-rhythmic unimodal and crossmodal contexts.


Introduction 18
Neural oscillations reflect alternating states of higher or lower neural excitability, 19 modulating the efficiency by which coupled neurons engage in mutual interactions 1 . As a 20 result, neural communication and information processing has been shown to occur in a phase-21 dependent manner 2,3 , reflected for example by fluctuations in perception thresholds 22 correlating with the phase of ongoing oscillations 4 . Based on these assumptions, oscillations 23 were also linked to temporal predictions of upcoming relevant information 2,5,6 . Studies have 24 shown that animals can utilize predictive aspects of environmental stimuli in a way that 25 reaction times are reduced 7-10 or stimulus processing is enhanced 11,12 . By means of top-down 26 induced phase resets of neural oscillations, phases of high excitability might be adjusted 27 towards the expected onset of relevant upcoming stimulation in order to optimize behavior 13 . 28 Due to the rhythmic and therefore temporally highly predictable nature of many auditory 29 stimuli such as speech or music, particularly in the auditory domain, many studies gathered 30 evidence that oscillations reset and thereby adjust their phase towards rhythmic stimuli of 31 various frequencies 14,15 . Also in the visual domain, studies showed that neural oscillations 32 align to rhythmic visual input 8,11,16,17 . However, whether temporal predictions indeed involve 33 phase resets of endogenous neural oscillations remains a matter of debate [18][19][20] . Despite their 34 ecological relevance, using rhythms for the investigation of an involvement of oscillations in 35 temporal predictions entails methodological and conceptual challenges. Rhythmic input leads 36 to a continuous stream of regularly bottom-up evoked potentials, which are -at least -37 difficult to distinguish from top-down phase adjusted endogenous neural oscillations within 38 the same frequency 21 . Rather than phase resets of endogenous neural oscillations, temporal 39 predictions could therefore also be reflected by stimulus-induced potentials that appear to be 40 rhythmic during rhythmic stimulation 18 . Conclusive evidence that temporal predictions 41 involve phase resets of endogenous neural oscillations rather than stimulus evoked potentials 42 is still lacking. 43 Moreover, using only rhythmic stimulation excludes the opportunity to link phase 44 adjustments to a more general neural mechanism that predicts the temporal structure of any 45 external input. If phase adjustments form the basis of tracking the temporal regularities of any 46 relevant information, neural oscillations should align also to predictable temporal regularities 47 that are inferred from input that does not itself comprise rhythmic components, such as, for 48 instance, monotonic motion. Nevertheless, the vast majority of studies investigating phase 49 adjustments in the context of temporal predictions presented participants with streams of 50 (quasi-)rhythmic stimulation. Disentangling phase alignments of neural oscillations from a 51 continuous stream of event-related potentials in a non-rhythmic predictive context therefore 52 constitute important aspects for examining the involvement of endogenous neural oscillations 53 in temporal prediction processes. 54 For this reason, we set out to investigate whether phase adjustments of neural oscillations 55 can be observed for non-rhythmic, but predictable visual motion stimuli. We measured 56 magnetoencephalography (MEG) while healthy participants watched a visual stimulus 57 continuously moving across the screen until it disappeared behind an occluder. We 58 manipulated the time for the stimulus to reappear on the other side of the occluder (on average 59 1.5 s). The task was to judge whether the stimulus reappeared too early or too late based on 60 the speed of the stimulus earlier to disappearance. Hence, participants were required to 61 temporally predict the correct time point of reappearance to be able to accomplish the task. 62 Participants further performed a control task, in which the task was to judge the luminance of 63 the reappearing stimulus instead of its timing. Importantly, physical appearance of both 64 conditions was exactly the same in all aspects of the stimulation. Any purely stimulus-related, 65 bottom-up activity should therefore level out between the two conditions. 66 Moreover, since it has been shown that sensory stimulation can lead to crossmodal phase 67 adjustments also in relevant but unstimulated other modalities 22,23 , we further introduced a 68 third condition, in which a tactile instead of a visual stimulus was presented at reappearance. 69 By contrasting it to the luminance matching control condition, we sought to determine 70 whether phase adjustments can be observed in regions associated with tactile stimulus 71 processing, when sensory information was in fact only provided to the visual system. 72 In the two temporal prediction tasks, as compared to luminance matching, we observed 73 stronger delta band inter-trial phase consistency (ITPC) within time windows between 74 disappearance and expected reappearance in frontoparietal brain areas. Enhanced delta ITPC 75 specifically in these time windows reflected phase resets of ongoing oscillations at 76 disappearance of the stimulus, where temporal prediction might be initialized. By introducing 77 a novel design, in which physical stimulation was exactly the same between the visual 78 temporal prediction and the luminance matching task, we provide profound evidence that 79 purely bottom-up evoked processes could not explain observed differences in ITPC between 80 the condition. In the crossmodal setting, we show that temporal information provided to the 81 visual modality leads to phase adjustments also in the tactile modality. and fitted a linear model to reaction time data in each condition. Reaction times were 105 significantly predicted by timing difference in all, the visual prediction (first-order 106 coefficient: -7.77 x 10 -4 ± 5.27 x 10 -4 , t(22) = -7.08, p < .001; second-order coefficient: -1.42 107 x 10 -6 ± 1.20 x 10 -6 , t(22) = -5.68, p < .001), the tactile prediction (first-order coefficient: -108 2.88 x 10 -4 ± 4.43 x 10 -4 , t(22) = -3.12, p = .005; second-order coefficient: -1.26 x 10 -6 ± 1.10 109 x 10 -6 , t(22) = -5.50, p < .001) as well as in the luminance matching task (first-order 110 coefficient: -1.60 x 10 -4 ± 1.44 x 10 -4 , t(22) = -5.31, p < .001; second-order coefficient: 2.75 x 111 10 -7 ± 3.51 x 10 -7 , t(22) = 3.76, p = .001). Hence, although the timing of the stimulus was not 112 relevant in the luminance matching task, reaction times in that condition were (in part) also 113 dependent on the timing of the reappearing stimulus and faster the later the stimulus 114 reappeared. 115 until it disappeared behind an occluder. The task was to judge whether the stimulus reappeared too early or too 117 late. In the luminance matching condition, task was to judge whether the luminance became brighter or darker. 118 Importantly, physical stimulation was exactly the same as in the visual prediction task. In the tactile temporal 119 prediction task, at reappearance a tactile stimulus was presented contralateral to the disappearance of the visual

125
Temporal prediction was associated with reduced beta power in sensory regions 126 Analyzing the neural data, we were first interested in investigating which frequency 127 bands showed modulated spectral power during windows of temporal predictions, and tested 128 an average of spectral power across all sensors and conditions against a pre-stimulus baseline 129 window. As a first step, we obtained a general overview of power modulations at each event 130 in the experimental paradigm. Due to the jittered stimulation built into the design (see 131 Materials and Methods), we computed cluster-based permutations statistics in three separate 132 time windows centered on: (a) the onset of the moving stimulus ("Movement"), (b) 133 disappearance of the stimulus behind the occluder ("Disappearance"), and (c) reappearance of 134 the stimulus ("Reappearance"; Fig. 2A). 135 In time bins around movement onset as well as reappearance (but not disappearance) of 136 the stimulus, clusters of frequencies in the theta and delta range showed a statistically 137 significant increase of spectral power as compared to the baseline window. All time windows 138 further depicted a significant decrease of spectral power in frequencies within the beta and 139 gamma range (all cluster p-values < .008). Importantly, even with using a liberal cluster alpha 140 level of .05 (one-sided), we did not find a statistically significant modulation of delta power 141 during the disappearance window. This was also not the case when reducing the test to 142 sensors from occipital regions only (see Fig. S1). 143 Since we were most interested in examining power modulations associated with temporal 144 predictions, i.e., during the disappearance window, we further compared spectral power 145 estimates between the temporal prediction tasks and the luminance matching task in all 146 sensors within the disappearance window while ignoring the other windows. We restricted 147 our analysis to the classical beta band ranging from 13 to 30 Hz, showing the strongest 148 modulation as compared to baseline during the disappearance window. Cluster-based 149 permutation statistics revealed reduced beta power during visual temporal prediction in 150 occipital sensors during all time-bins of the disappearance window (cluster-p = .01). Source 151 level statistics revealed a statistically significant decrease of beta power in a cluster of 152 bilateral occipital voxels (cluster-p = .01). Beta power was further reduced during tactile 153 prediction in a cluster of occipital as well as left lateralized frontocentral sensors (cluster-p = 154 .002). At source level, a significant power reduction in the beta band was most strongly 155 apparent in parts of bilateral visual as well as left-lateralized somatosensory cortex (cluster-p 156 = .01). 157

Inter-trial phase consistency between conditions 166
For the analysis of ITPC, we followed a similar approach. First, we tested ITPC 167 differences to baseline in the three time windows for an average across all sensors and 168 conditions. ITPC was significantly increased across a range of different frequencies in time 169 bins around movement onset, disappearance and reappearance of the stimulus (all cluster-p < 170 .001; Fig. 3A). For time windows centered on movement onset as well as reappearance 171 significant ITPC increases were strongest in the delta to alpha range. At disappearance of the 172 stimulus, significant ITPC increases were observed up to the low beta range with strongest 173 increases in the delta band. 174 Hence, the delta band showed no increase in power but the strongest increase in ITPC as 175 compared to baseline during the disappearance window for an average across all conditions 176 (see Fig. 2A, 3A, and S1). For further statistical comparisons between conditions, we 177 therefore restricted our analyses to an average of frequencies between 0.5 to 3 Hz. For a better 178 estimation of when differences in ITPC between the conditions became apparent, we enlarged 179 the analysis of ITPC to time bins ranging from -1,900 ms to 1,900 ms centered on the 180 disappearance of the stimulus. Note that in this enlarged analysis window the timing of the 181 movement onset as well as the reappearance of the stimulus strongly jittered across trials. The 182 effect of these events on ITPC estimates were thus strongly reduced (see Fig. S3; for 183 condition-specific ITPC differences during disappearance to baseline, see Fig. S4). 184 We found two clusters that showed significantly stronger ITPC during visual temporal 185 predictions as compared to luminance matching (Fig. 3B). One cluster included sensors from 186 right temporal, frontal and occipital regions in time bins from -400 to 1,900 ms (cluster p < 187 .001). The second cluster included left frontotemporal sensors in time bins ranging from 0 to 188 1,900 ms (cluster p = .01) Source level analysis revealed that for an average of the time 189 window from -400 to 1,900 ms ITPC differences between the two conditions were strongest 190 in right-lateralized central and inferior frontal voxels (cluster p < .001). 191 ITPC was also significantly enhanced in bilateral temporal sensors during tactile 192 temporal predictions, evolving around -400 ms in right temporal sensors and shifting towards 193 left hemisphere with ongoing disappearance time (cluster p < .001; Fig. 3C). In this contrast, 194 however, differences in ITPC were more strongly apparent also in frontal and central sensors. 195 Besides strongest differences in ITPC again in right superior parietal and inferior frontal 196 voxels, source level analysis also revealed strong differences in bilateral somatosensory 197 voxels for the contrast of tactile prediction to luminance matching (cluster p < .001). 198 To make sure that differences in eye movements do not explain the observed differences 199 in ITPC between the conditions, we analyzed horizontal eye movements recorded by an eye 200 tracker (ET) during the MEG measurement. Eye movements as well as ITPC computed from 201 the ET data did not show any differences between the conditions (see Fig. S5A,B,C). 202 Moreover, we did not observe significant correlations between ITPC values computed from 203 the ET and the MEG signal in any of the conditions across participants (see Fig. S5D). 204 Figure 3D depicts absolute ITPC estimates for all three conditions in the enlarged 205 disappearance time window. ITPC was averaged across participants and all the sensors that 206 exhibited the top 20% of t values in the ITPC contrast between visual temporal prediction and 207 luminance matching between 0 and 1,500 ms (see Fig. 3B; similar results were obtained for 208 sensors showing the top 10% or 5% of t values, see Fig. S3D). ITPC also increased in the 209 luminance matching condition around disappearance of the stimulus, but dropped down to 210 stimulus movement level shortly afterwards. ITPC in the visual as well as tactile temporal 211 prediction tasks stayed elevated throughout the entire disappearance window. 212  ROTs, all phases extracted at ROT should be randomly distributed across the unit circle, since 250 individual ROTs strongly differed across participants as well (see Fig. 1B). 251 In order to test that, we extracted the mean phase of that delta frequency that showed the 252 strongest ITPC within each temporal prediction task as compared to the luminance matching 253 task at ROT in each participant. We again used the sensors that showed the strongest 254 statistical differences in ITPC for the contrasts of each prediction task to the luminance 255 matching (see Fig. 3B and C). Moreover, only trials in which the stimulus actually reappeared 256 later than each individuals ROT were considered, so that stimulus onset related brain activity 257 would not distort phase estimates at ROT. Mean phases extracted at ROT from each channel 258 and all participants were then combined and plotted into a histogram for each condition ( Fig.  259 5, upper row; each plot shows participants x channel data). We quantified the distance of the 260 observed distribution to a uniform distribution by means of the modulation index MI; 24 . 261 To test whether the observed MI was significantly stronger than a random distribution 262 obtained from surrogate MIs, we repeated the analysis 10,000 times using a randomly chosen 263 frequency from the same delta band for each participant in each repetition. We found that for 264 both, the visual prediction (p = .03) as well as the tactile prediction task (p = 0), the observed 265 MI was significantly stronger than the surrogate MIs. Phases at ROT from both tasks 266 clustered roughly around ±90°. In the luminance matching task, no significant clustering at a 267 specific phase was found (p = .96). 268 Our reaction time analysis revealed that also in the luminance matching task, participants 269 had a certain expectation about the temporal reappearance of the stimulus. Therefore, we 270 hypothesized that the phase of the frequency that showed the strongest ITPC during the visual 271 prediction task might also code for the timing of the reappearing stimulus in the luminance 272 matching task, since physical stimulation was identical in both tasks. We repeated the above 273 described analysis for the luminance matching condition, now using the same frequencies as 274 obtained from the visual prediction condition and again tested the observed MI against 10,000 275 repetitions with randomly chosen frequencies (Fig. 5, Panel 4: LM (VP)). With frequencies 276 obtained from the visual prediction task, the MI observed for the luminance matching task 277 was significantly stronger than MIs obtained from the random repetitions (p = .02). 278 during temporal predictions are inconsistent. On the one hand, studies found that beta power 306 was even increased shortly before the onset of the expected stimulus in auditory 25 and visual 307 rhythmic stimulation 16 . On the other hand, van Ede et al. 26 found that predicting the onset of 308 a tactile stimulus was specifically associated with a reduction of beta power in contralateral 309 tactile areas and accompanied by faster reaction times. The authors suggest that a reduction in 310 beta power might signal preparatory processes in the sensory system that expects the 311 upcoming event. 312 The observed decrease in beta power in task-relevant sensory regions in the current study 313 largely match the results reported by van Ede et al. 26 . During visual temporal predictions, 314 beta band power was reduced in visual sensory regions as compared to the visual control 315 condition during the entire disappearance time. During crossmodal predictions, in which 316 temporal information was provided to the visual system, but reappearance was expected in the 317 tactile domain, beta band power was decreased in both, visual as well as tactile regions. 318 Since also in the luminance matching condition participants expected to perceive a visual 319 stimulus, preparatory processes alone cannot explain this reduction in beta power. This is 320 especially the case in the crossmodal condition, in which no visual stimulus was expected, but 321 stronger decreases in beta were also observed in visual areas. Moreover, since we observed 322 beta decreases also in tactile regions at the time of visual stimulus disappearance, the decrease 323 could not solely be an effect of external stimulation. 324 Beta decreases observed during temporal predictions might therefore relate to more than 325 only to preparatory processes to an upcoming stimulus. Cross-modal decreases in beta band 326 activity in both the temporal information providing visual as well as the stimulation expecting 327 tactile system might reflect that both sensory modalities are continuously involved in 328 temporal prediction processes, not only in processes preparing for the upcoming stimulation. 329 We found no significant increases in beta power during temporal predictions, even if the time 330 window was centered on the time point of predicted reappearance (ROT) in each participant 331 in either of the two prediction conditions (see Fig. S2). Whether decreases in beta power are 332 associated with non-rhythmic temporal predictions while increases might reflect temporal 333 predictions during rhythmic stimulation, remains subject to future research. 334

Neural oscillations at low frequencies adapt to the temporal structure of visual moving 335
stimuli 336 Studies found that neural oscillations entrain towards rhythmic sensory input to track the 337 low-frequency temporal regularities of the stimulation, especially in the auditory domain 14 . 338 Such phase entrainment does not only occur in the delta band but can flexibly adapt to the 339 frequency of the external input also at higher frequencies such as the theta or the alpha band 340 during auditory stimulation 15 . However, in the visual system, evidence for the tracking of 341 temporally predictive input by neural oscillations is not as clear. On the one hand, studies 342 showed that the phase of neural oscillations is involved in temporal predictions of low-343 frequency visual input 11,12,16 . On the other hand, studies suggested that temporal predictions 344 in the visual system were specific to the alpha band, although sensory input was provided in 345 lower frequencies 10,27 . Rohenkohl  function of the phase of entrained delta oscillations. In their study, the strongest contrast 375 sensitivity for visual stimuli was also observed at a delta phase around 90°. This phase range 376 might therefore indicate an optimal phase for processes related to temporal prediction. 377 Importantly, our study suggests that the mechanism of phase adjustments for temporal 378 predictions can be extended to external stimulation that does not as such involve rhythms. We 379 found that low-frequency oscillations can adjust their phase also to the temporal structure of 380 external stimulation that had to be inferred from motion. Many natural stimuli comprise 381 highly predictable regularities, but not all of them are intrinsically rhythmic. Our results 382 therefore indicate that the framework of phase adjustments during temporal predictions might 383 be generalized to all forms of predictive stimulation. 384

Enhanced ITPC cannot be explained by stimulus-driven processes 385
In earlier investigations of phase adjustments to external stimulation participants were 386 mostly presented with streams of rhythmic input. However, rhythmic input also causes 387 evoked brain activity within the same frequency range, which makes it difficult to disentangle 388 streams of evoked activity from entrained endogenous neural oscillations 18,21 . 389 Our results provide evidence that phase resets of low-frequency oscillations observed 390 during temporal predictions cannot solely be explained by stimulus-evoked, bottom-up brain 391 activity see also, 21,28 . In the current study, we aimed at reducing such brain responses to a 392 minimum by presenting participants with a continuously moving stimulus instead of several 393 discrete stimuli. We were particularly interested in the time point at which the stimulus 394 transiently disappeared behind an occluder (as opposed to sharp onsets and offsets in 395 rhythms). At disappearance, we did not observe an increase in low-frequency power as 396 compared to pre-stimulus baseline in any of the conditions, which could have been associated 397 with evoked brain activity such as, for instance, the contingent negative variation CNV; 18 . 398 Moreover, by introducing a novel experimental design, in which physical stimulation was 399 exactly the same as during temporal predictions as well as a control condition, we controlled 400 for brain responses that could be driven by bottom-up stimulus processing and are not specific 401 to temporal predictions. Importantly, delta ITPC but not power was stronger during temporal 402 predictions (see also Fig. S1). This provides strong evidence that ongoing, endogenous neural 403 oscillations underwent a phase reset around the time point of disappearance, which was more 404 consistent during temporal predictions than during the luminance matching task. These phase 405 resets can therefore not be solely related to brain responses evoked by the offset of the visual 406 movement, since we did not observe power differences at low frequencies. 407 which might be an important mechanism for multisensory integration processes 22,23 . 420

Phase resets occurred in a network of frontoparietal and sensory brain areas
Moreover, strong correlations between ITPC and behavior were also observed in the 421 cerebellum, supporting earlier reports on a involvement of the cerebellum in temporal 422 prediction processes 31 . Roth and coworkers 32 , for instance, found that cerebellar patients 423 were significantly impaired in recalibrating sensory temporal predictions of a reappearing 424 visual stimulus. This finding is of particular interest as we adapted the authors' experimental 425 paradigm for the use in the current study. Theirs and our results therefore indicate that the 426 cerebellum might be crucially involved in accurate and consistent judgments of temporal 427 regularities deployed in perceiving object motion. 428

Conclusions 429
We provide strong evidence that the phase of neural oscillations can adjust to the 430 temporal regularities of external stimulation and do not arise as a byproduct of bottom-up 431 stimulus processing. Such phase alignments could provide a key mechanism that predicts the 432 onset of upcoming events in order to optimize processing of relevant information and thereby 433 adapt behavior. We show that temporal information provided to one modality leads to phase 434 adjustments in another modality when crossmodal temporal predictions are necessary, 435 providing further evidence that such crossmodal phase resets could be the neuronal basis of 436 multisensory integration processes. Importantly, we observed that these phase adjustments 437 reflected each individual's subjective temporal predictions time points. This supports the 438 notion that the phase of neural oscillation indeed codes for the subjective estimation of 439 elapsed time. Taken together, our results provide important insights into the neural 440 mechanisms that might be utilized by the brain to predict the temporal onsets of upcoming 441 events. 442

Materials and Methods 443
An exhaustive description of the methods can be found in the SI. 444

Participants and experimental procedure 445
Twenty-three healthy volunteers took part in the study. The ethics committee of the 446 Medical Association Hamburg approved the study protocol and the experiment was carried 447 out in accordance with the approved guidelines and regulations. 448 The experimental paradigm used in the current study was adopted from an earlier report 449 investigating visual temporal predictions in cerebellar patients 32 . Our experiment consisted of 450 three conditions: a visual temporal prediction task, a crossmodal (tactile) temporal prediction 451 task, and a luminance matching (control) task. The trials of all conditions started with the 452 presentation of a randomly generated, white noise occluder presented in the middle of the 453 screen. We instructed participants to fixate the central fixation dot throughout the entire trial. 454 After 1500 ms, an oval stimulus moved from the periphery towards the occluder with constant 455 speed. The luminance of the stimulus differed in all trials (6 steps). In each trial, the starting 456 point of the stimulus differed such that the stimulus took 1,000 to 1,500 ms to disappear 457 completely behind the occluder from starting point, randomly jittered with 100 ms 458 (counterbalanced). The size of the occluder and the speed of the stimulus were chosen so that 459 the stimulus would need exactly 1,500 ms to reappear on the other side of the occluder. 460 However, we manipulated the timing and the luminance of the reappearing stimulus. In each 461 trial, the reappearance of the stimulus differed between ±17 to ±467 ms from the correct 462 reappearance time of 1,500 ms. Hence, the stimulus was covered by the occluder for 1,033 to 463 1,967 ms and was reappearing at 20 different time points. In the visual prediction task as well 464 as in the luminance matching task, we also manipulated the luminance of the reappearing 465 stimulus relative the luminance the stimulus had before disappearance in each trial (also using 466 20 different values). After reappearance, the stimulus moved to the other side of the screen for 467 500 ms with the same speed until it set off the screen. The occluder was presented throughout 468 the entire trial. 469 The visual temporal prediction as well as the luminance matching task had the exact 470 equal physical appearance throughout all trials. They only differed in their cognitive set. In 471 the visual temporal prediction task, we asked participants to judge whether the stimulus was 472 reappearing too early or too late. In the luminance matching task, participants were asked to 473 judge whether the luminance of the reappearing visual stimulus became brighter or darker. 474 The tactile temporal prediction task was equal to the visual temporal prediction task, with 475 the only difference that a tactile stimulus instead of a visual was presented at the time of 476 reappearance to the right or left index finger. The tactile stimulus was presented by means of 477 a Braille piezostimulator for 200 ms. Participants did not receive trial-wise feedback about the 478 correctness of their response. After a short delay of 200 ms, the white-noise occluder was 479 randomly re-shuffled to signal the start of a new trial. We performed an independent component analysis (infomax algorithm) to remove 509 components containing eye-movements, muscle, and cardiac artefacts. As a final step, using 510 procedures described by Stolk et al. 34 we identified trials in which the head position of the 511 participant differed by 5 mm from the mean circumcenter of the head position from the whole 512 session and excluded them from further analysis. 513

Quantification and statistical analysis 514
In the current experiment, we introduced a control condition that was physically identical 515 to our temporal prediction tasks (until reappearance in the tactile condition) in order to 516 account for processes that are not directly related temporal predictions. Hence, for most of our 517 statistical analyses, we were interested in comparing the two temporal prediction tasks with 518 the luminance matching control task, respectively, and not in comparing the two temporal 519 prediction tasks with each other. Therefore, instead of computing an analysis of variance 520 across all three conditions, we directly computed two separate t-tests for the comparison of 521 the visual or the tactile temporal prediction with the luminance matching task, respectively, 522 and accounted for multiple comparisons by adjusting the alpha level. 523

Psychometric curve 524
We fitted a psychometric curve to the behavioral data of each participant from all trials in 525 each condition. First, for each timing difference or luminance difference, respectively, we 526 computed the proportion of "too late" or "brighter" answers for each participant. Then, we 527 fitted a binomial logistic regression (psychometric curve) using the glmfit.m and gmlval.m 528 functions provided in MATLAB. The fitted timing or luminance difference value at 50% 529 proportion "too late" or "brighter" answers was determined as ROT or PSE for each 530 participant, respectively. To test for a significant bias towards one of the answers, we tested 531 the ROT or PSE from all participants against zero using one-sample t-tests (α = .05 / 3 = 532 .017). The steepness of the psychometric function was computed as the reciprocal of the 533 difference between fitted timing or luminance difference values at 75% and 25% proportion 534 "too late" or "brighter" answers, respectively. 535

Linear model 536
We averaged RT across all luminance differences within each timing difference bin in 537 each condition and then utilized a second-order (quadratic) polynomial regression model with 538 timing difference as predictor for reaction times and computed the first-and second-order 539 coefficients for each participant in each condition. The coefficients from all participants were 540 then tested against zero using one-sample t-tests in all conditions (α = .05 / 3 = .017). 541

Spectral power 542
We decomposed the MEG recordings into time-frequency representations by convolving 543 the data with complex 40 Morlet's wavelets 37 , logarithmically spaced between 0.5 to 100 Hz 544 and with logarithmically increasing number of cycles from two to ten cycles. For all analyses 545 of the MEG data, we considered subjectively correct trials only, i.e., trials in which 546 participants answered correctly based on their individual ROT. To obtain an estimate of 547 spectral power modulations related to the different events in our experimental paradigm, we 548 cut each trial further into four separate, partly overlapping windows (see Fig. 2A): a 549 "Baseline" window from -550 to -50 ms earlier to movement onset; a "Movement" window 550 from -50 to 950 ms relative to the movement onset; a "Disappearance" window from -350 to 551 950 ms relative to complete disappearance of the stimulus behind the occluder; and a 552 "Reappearance" window from -350 to 450 ms relative to the (first frame) reappearance of the 553 stimulus. Spectral power estimates were then averaged across all trials belonging to the same 554 condition in each window and binned into time windows 100 ms (centered on each full deci-555 second). All power estimates were normalized using the pre-stimulus baseline window from -556 500 to -200 ms earlier to movement onset. 557 In order to obtain an overview of the spectral power modulations related to the different 558 events within the trials, we then averaged the power estimates across all channels and 559 conditions (grand average) and tested each time-frequency pair against the pre-stimulus 560 baseline using paired-sample t-tests. We controlled for multiple comparisons by employing 561 cluster-based permutation statistics as implemented in FieldTrip 38 . For each window, a 562 separate cluster-permutation test was performed (α = .05; liberally chosen to observe all 563 ongoing power modulations; see Results section). 564 We subsequently compared the spectral power estimates averaged within the beta range 565 (13-30 Hz; see Results section) at each time point within the disappearance window and all 566 channels from the visual or tactile temporal prediction task with the luminance matching task. 567 We again employed cluster-permutation statistics, this time by clustering neighboring 568 channels and time points. We used a one-sided α = .025 / 2 = .0125, since negative and 569 positive clusters were tested separately, and to adjust for the two separate comparisons 570 between the conditions (used throughout the study unless stated differently). 571 To estimate spectral power in source space, we computed separate leadfields for each 572 recording session and participant based on each participant's mean head position in each 573 session and individual magnetic resonance images. We used the single-shell volume 574 conductor model 39 with a 5,003 voxel grid that was aligned to the MNI152 template brain 575 (Montreal Neurological Institute, MNI; http://www.mni.mcgill.ca) as implemented in the 576 METH toolbox. Cross-spectral density (CSD) matrices were computed from the complex 577 wavelet convolved data in steps of 100 ms in the same time windows as outlined above. To 578 avoid biases in source projection, common adaptive linear spatial filters (DICS beamformer 579 40 ) pointing into the direction of maximal variance were computed from CSD matrices 580 averaged across all time bins and conditions for each frequency. 581 All time-frequency resolved CSD matrices were then multiplied with the spatial filters to 582 estimate spectral power in each of the 5,003 voxels and normalized with the pre-stimulus 583 baseline window. We then averaged across all time bins within the disappearance window and 584 utilized cluster-based permutation statistics to identify clusters of voxels that show statistical 585 difference in beta power between each of the temporal prediction tasks and the luminance 586 matching task. 587 Inter-trial phase consistency 588 We computed ITPC estimates from the complex time-frequency representations obtained 589 from the wavelet convolution as described in the Spectral power section above. where n is the number of trials and k the phase angle in trial r at time-frequency point tf 595 37 . Similar to spectral power, we averaged ITPC estimates again in bins of 100 ms and plotted 596 all time windows averaged across all channels and conditions to obtain a general overview of 597 ITPC estimates at all events during the trial. 598 Since we were most interested in ITPC related to stimulus disappearance behind the 599 occluder, we subsequently computed ITPC in a longer time window from -1,900 ms to 1,900 600 ms centered around time of complete stimulus disappearance behind the occluder. For 601 statistical analysis, we first averaged ITPC estimates within a frequency band of 0.5 to 3 Hz 602 (see Results) and then computed cluster-based permutation statistics across all 100 ms time 603 bins and all sensors between each of the temporal prediction tasks and the luminance 604 matching task. ITPC on source level was computed using the same leadfields and common 605 beamformer filters as for spectral power (see above). 606 Correlations between condition-wise source level ITPC estimates and the steepness of 607 each individual's psychometric function were computed using Pearson correlations in each of 608 the 5,003 voxels within the grid. For this analysis, we averaged ITPC estimates from time 609 bins of 0 to 1,500 ms with respect to the disappearance of the stimulus within the pre-defined 610 delta band of 0.5 to 3 Hz. Multiple comparisons were accounted for by using cluster-based 611 permutation statistics as implemented in FieldTrip (α = .025 / 3 = .008) 612 Delta phase clustering at ROT 613 To determine whether each participant's subjective ROT was associated with a specific 614 phase in the delta band, we extracted the phase at each individual's ROT from sensors 615 showing the strongest ITPC effect and computed the distance from this distribution to a 616 uniform distribution over all possible phases. 617 For this analysis, we only considered trials in which the stimulus reappeared later than 618 each individual's ROT and the participant answered subjectively correct. By this, we 619 prevented possible phase distortions by the external stimulation earlier to or at ROT. 620 Moreover, to make sure that we reduced also activity that was related to external stimulations 621 after each individual's ROT, we first aligned all trials from the same condition to the time 622 point of stimulus reappearance, computed the average across trials (event-related field, ERF) 623 and subtracted the ERF caused by the reappearance from all trials in that condition. 624 Subsequently, in each trial we centered a 2,500 ms long window on each participant's ROT, 625 computed a complex wavelet convolution for all frequencies between 0.5 and 3 Hz (14 626 frequencies; same procedure and frequencies as above) in all channels, and computed the 627 mean phase angle at ROT, i.e., the center time bin, across all considered trials in each 628 condition. This procedure is similar to computing ITPC as described above, except for 629 extracting the angle of the mean phase vector instead of the length. Since for the luminance 630 matching task we did not have an estimate of each individual's ROT, we applied the estimate 631 of ROT from the visual prediction task also to the luminance matching trials, since based on 632 their equal physical appearance temporal predictions should also be equal. 633 As a next step, from the result of the cluster-based permutation statistics on ITPC 634 estimates described above, we determined the sensors that showed the strongest ITPC effect 635 for the two contrasts between the temporal prediction tasks and the luminance matching task 636 for a time window between 0 and 1,500 ms after disappearance behind the occluder. For the 637 contrast between the visual prediction and the luminance matching task, we considered the 638 sensors showing the top 20% of t-values (37 channels). To keep the number of sensors 639 comparable, we also considered the top 37 sensors from the contrast of the tactile prediction 640 task against luminance matching. 641 Within these channels, for each individual participant we determined the frequency 642 within the 0.5 to 3 Hz delta band, which showed the strongest ITPC for the visual or the 643 tactile prediction as compared to the luminance matching task, respectively, in the same time 644 window of 0 to 1.500 ms. For the luminance matching condition, we extracted the frequencies 645 showing the strongest estimates of ITPC in the luminance matching as compared to the visual 646 temporal prediction task and used individual ROTs from the visual prediction task. For these 647 individual frequencies, we plotted the phase angle at ROT (as described above) from all the 648 considered channels and all participants in a histogram (in bins of 10°; see Fig. 5). We 649 computed the distance from the observed phase distribution to a uniform distribution using a 650 discrete and normalized version of the Kullback-Leibler distance, i.e., the modulation index 651 (MI) 24 . 652 For statistical analysis, we repeated the same procedure as described above for 10,000 653 times and randomly picked any frequency from the 14 frequencies within the 0.5 to 3 Hz band 654 in each repetition. By that we obtained a distribution of surrogate MI estimates (but still based 655 on real data from all individual participants), from which we computed the percentile 656 determined by the MI that was observed using the individually strongest ITPC frequency. MI 657 estimates above the 95 th percentile were considered significantly stronger as compared to the 658 randomly obtained surrogate MIs (p-value = 1 -percentile). 659