Single-trial characterization of neural rhythms: Potential and challenges

The average power of rhythmic neural responses as captured by MEG/EEG/LFP recordings is a prevalent index of human brain function. Increasing evidence questions the utility of trial-/group averaged power estimates however, as seemingly sustained activity patterns may be brought about by time-varying transient signals in each single trial. Hence, it is crucial to accurately describe the duration and power of rhythmic and arrhythmic neural responses on the single trial-level. However, it is less clear how well this can be achieved in empirical MEG/EEG/LFP recordings. Here, we extend an existing rhythm detection algorithm (extended Better OSCillation detection: "eBOSC"; cf. Whitten et al., 2011) to systematically investigate boundary conditions for estimating neural rhythms at the single-trial level. Using simulations as well as resting and task-based EEG recordings from a micro-longitudinal assessment, we show that alpha rhythms can be successfully captured in single trials with high specificity, but that the quality of single-trial estimates varies greatly between subjects. Despite those signal-to-noise-based limitations, we highlight the utility and potential of rhythm detection with multiple proof-of-concept examples, and discuss implications for single-trial analyses of neural rhythms in electrophysiological recordings. Using an applied example of working memory retention, rhythm detection indicated load-related increases in the duration of frontal theta and posterior alpha rhythms, in addition to a frequency decrease of frontal theta rhythms that was observed exclusively through amplification of rhythmic amplitudes.


Towards a single-trial characterization of neural rhythms 46 47
Episodes of rhythmic neural activity in electrophysiological recordings are of prime 48 interest for research on neural representations and computations across multiple scales of 49 measurement (e.g. Buzsáki, 2006;Wang, 2010). At the macroscopic level, the study of 50 rhythmic neural signals has a long heritage, dating back to Hans Berger's classic investigations 51 into the Alpha rhythm (Berger, 1938). Since then, advances in recording and processing 52 techniques have facilitated large-scale spectral analysis schemes (e.g. Gross, 2014) that were 53 not available to the pioneers of electrophysiological research, who often depended on the 54 manual analysis of single time series to indicate the presence and magnitude of rhythmic events. 55 Interestingly, improvements in analytic methods still do not capture all of the information that 56 can be extracted by manual inspection. For example, current analysis techniques are largely 57 naïve to the specific temporal presence of rhythms in the continuous recordings, as they often 58 employ windowing of condition-or group-based averages to extract putative rhythm-related 59 characteristics (Cohen, 2014). However, the underlying assumption of stationary, sustained 60 rhythms within the temporal window of interest might not consistently be met (Jones, 2016;61 Stokes & Spaak, 2016), thus challenging the appropriateness of the averaging model (i.e., the 62 ergodicity assumption (Molenaar & Campbell, 2009)). Furthermore, in certain situations, 63 single-trial characterizations become necessary to derive unbiased individual estimates of 64 neural rhythms (Cohen, 2017 Muthukumaraswamy & Singh, 2011). This is exemplified by the bias that arrhythmic periods 73 exert on rhythmic power estimates. Most current time-frequency decomposition methods of 74 neurophysiological signals (such as the electroencephalogram (EEG)) are based on the Fourier 75 transform (Gross, 2014). Following Parceval's theorem (e.g. Hansen, 2014), the Fast Fourier 76 Transform (FFT) decomposes an arbitrary time series into a sum of sinusoids at different 77 frequencies. Importantly, FFT-derived power estimates do not differentiate between high-78 amplitude transients and low-amplitude sustained signals. In the case of FFT power, this is a 79 direct result of the violated assumption of stationarity in the presence of a transient signal. 80 Short-time FFT and wavelet techniques alleviate (but do not eliminate) this problem by 81 analyzing shorter epochs, during which stationarity is more likely to be obtained. However, 82 whenever spectral power is averaged across these episodes, both high-amplitude rhythmic and 83 low-amplitude arrhythmic signal components may once again become intermixed. In the 84 presence of arrhythmic content (often referred to as the "signal background," or "noise"), this 85 results in a reduced amplitude estimate of the underlying rhythm, the extent of which relates to 86 the duration of the rhythmic episode relative to the length of the analyzed segment (which we 87 will refer to as 'abundance') (see Figure 1A). Therefore, integration across epochs that contain 88 a mixture of rhythmic and arrhythmic signals results in an inherent ambiguity between the 89 strength of the rhythmic activity (as indexed by power/amplitude) and its duration (as indexed 90 by the abundance of the rhythmic episode within the segment) (see Figure 2B). 91 Crucially, the strength and duration of rhythmic activity theoretically differ in their 92 neurophysiological interpretation. Rhythmic power most readily indexes the magnitude of 93 synchronized changes in membrane potentials within a network (Buzsáki,Anastassiou,& 94 Koch, 2012), and is thus related to the size of the participating neural population. The duration 95 of a rhythmic episode, by contrast, tracks how long population synchrony is upheld. Notably, 96 measures of rhythm duration have recently gained interest as they may provide additional 97 information regarding the biophysical mechanisms that give rise to the recorded signals 98 ( In general, the accurate estimation of process parameters depends on a sufficiently strong 104 signal in the neurophysiological recordings under investigation. Especially for scalp-level 105 M/EEG recordings it remains elusive whether neural rhythms are sufficiently strong to be 106 clearly detected in single trials. Here, a large neural population has to be synchronously active 107 to give rise to potentials that are visible at the scalp surface. This problem intensifies further by 108 signal attenuation through the skull (in the case of EEG) and the superposition of signals from 109 diverse sources of no interest both in-and outside the brain (Schomer & Lopes da Silva, 2017). 110 In sum, these considerations lead to the proposal that the signal-to-noise ratio (SNR), here 111 operationally defined as the ratio of rhythmic to arrhythmic variance, may fundamentally 112 constrain the accurate characterization of single-trial rhythms. 113 Following those considerations, we set out to answer the following hypotheses and 114 questions: (1) A precise differentiation between rhythmic and arrhythmic timepoints can 115 disambiguate the strength and the duration of rhythmicity.
(2) To what extent does the single-116 trial rhythm representation in empirical data allow for an accurate estimation of rhythmic 117 strength and duration in the face of variations in the signal-to-noise ratio of rhythmicity? (3) 118 What are the empirical benefits of separating rhythmic (and arrhythmic) duration and power? 119 Recently, the Better OSCillation Detection (BOSC; Caplan, Madsen, Raghavachari,& 120 Kahana, 2001; Whitten, Hughes, Dickson, & Caplan, 2011) method has been proposed to 121 identify rhythmicity at the single-trial level. BOSC defines rhythmicity based on the presence 122 of a spectral peak that is superimposed on an arrhythmic 1/f background and that remains 123 present for a minimum number of cycles. Here, we extend the BOSC method (i.e., extended 124 BOSC; eBOSC) to derive rhythmic temporal episodes that can be used to further characterize 125 rhythmicity. Using simulations, we derive rhythm detection benchmarks and probe the 126 boundary conditions for unbiased rhythm indices. Furthermore, we apply the eBOSC algorithm 127 to resting-and task-state data from a micro-longitudinal dataset to systematically investigate 128 the feasibility to derive reliable and valid indices of neural rhythmicity from single-trial scalp 129 EEG data and to probe their modulation by working memory load. 130 We focus on alpha rhythms (~8-15 Hz; defined here based on individual FFT-peaks) due to 131 (a) their high amplitude in human EEG recordings, (b) the previous focus on the alpha band in 132 the rhythm detection literature ( Resting state and task data were collected in the context of a larger assessment, 143 consisting of eight sessions in which an adapted Sternberg short-term memory task (Sternberg,144 1966) and three additional cognitive tasks were repeatedly administered. Resting state data are 145 from the first session, task data are from sessions one, seven and eight, during which EEG data 146 were acquired. Sessions one through seven were completed on consecutive days (excluding 147 Sundays) with session seven completed seven days after session one by all but one participant 148 (eight days due to a two-day break  (Oldfield, 1971), and had normal or corrected-to-normal vision, as assessed with the Freiburg 162 Visual Acuity test (Bach, 1996;2007 report (Sternberg, 1966). Participants started each trial by pressing the left and right response 183 key with their respective index fingers to ensure correct finger placement and to enable fast 184 responding. An instruction to blink was given, followed by the sequential presentation of 2, 4 185 or 6 digits from zero to nine. On each trial, the memory set size (i.e., load) varied randomly 186 between trials, and participants were not informed about the upcoming condition. Also, the 187 single digits constituting a given memory set were randomly selected in each trial. Each 188 stimulus was presented for 200 ms, followed by a fixed 1000 ms blank inter-stimulus interval 189 (ISI). The offset of the last stimulus coincided with the onset of a 3000 ms blank retention 190 interval, which concluded with the presentation of a probe item that was either contained in the 191 presented stimulus set (positive probe) or not (negative probe  Figure 1 & Figure S1): (1) 266 we remove the spectral alpha peak and use robust regression to establish power thresholds; (2) 267 we combine detected time points into continuous rhythmic episodes and (3) we reduce the 268 impact of wavelet convolution on abundance estimates. We benchmarked the algorithm and 269 compared it to standard BOSC using simulations (see section 2.8).  Rhythmic events were detected within subjects for each channel and condition. Time-295 frequency transformation of single trials was performed using 6-cycle Morlet wavelets 296 (Grossmann & Morlet, 1985) with 49 logarithmically-spaced center frequencies ranging from 297 to improve the linear fit of the background spectrum (cf. Haller et al., 2018), which was 308 characterized by frequency peaks in the alpha range for almost all subjects ( Figure S4). In 309 contrast to ordinary least squares regression, robust regression iteratively down-weights outliers 310 (in this case spectral peaks) from the linear background fit. To improve the definition of 311 rhythmic power estimates as outliers during the robust regression, power estimates within the 312 wavelet pass-band around the individual alpha peak frequency were removed prior to fitting 1 . 313 The in which IAF denotes the individual alpha peak frequency and WL refers to wavelet length 317 (here, six cycles in the main analysis). IAF was determined based on the peak magnitude within 318 the 8-15 Hz average spectrum for each channel and condition (Grandy, Werkle-Bergner, 319 Chicherio, Schmiedek, et al., 2013b). This ensures that the maximum spectral deflection is 320 removed across subjects, even in cases where no or multiple peaks are present 2 . This procedure 321 1 This procedure is similar to calculating the background spectrum from conditions with attenuated alpha power (e.g., the eyes open resting state; Caplan, Bottomley, Kang & Dixon (2015)). However, here we ensure that alpha power is sufficiently removed, whereas if conditions with reduced alpha peak magnitudes are selected, alpha power may still remain sufficiently elevated to influence slope or intercept estimates. Furthermore, the reliance on conditions with decreased rhythmicity appears less suitable given inter-individual differences in alpha engagement in e.g., the eyes open condition. This may induce an implicit contrast to eyes open rhythmicity. Note that when the frequency range is chosen so that the alpha peak represents the middle of the chosen interval, the alpha-induced bias would be captured by a linear increment in the intercept of the background fit, which may also be alleviated by choosing a higher percentile for the power threshold. Notably, removing the alpha peak as done here attenuates such bias, even in cases where the alpha peak biases the slope of the background fit, as would happen if the alpha peak is not centered within the range of sampled frequencies. 2 When multiple alpha-band peaks are present or the peak has a broader appearance, the spectral peak may not be removed entirely, which could result in misfits of the background spectrum. For this purpose, we employed robust regression to down-weight potential residuals around the alpha peak. Our current implementation only accounts for a peak in the alpha range, but could effectively removes a bias of the prevalent alpha peak on the arrhythmic background estimate 322 (see Figure 1B and C & Figure 3C). The power threshold for rhythmicity at each frequency was 323 set at the 95 th percentile of a χ 2 (2)-distribution of power values, centered on the linearly fitted 324 estimate of background power at the respective frequency (for details see Whitten et al., 2011). 325 This essentially implements a significance test of single-trial power against arrhythmic 326 background power. A three-cycle threshold was used as the duration threshold to exclude 327 transients, unless indicated otherwise (see section 2.12). The conjunctive power and duration 328 criteria produce a binary matrix of 'detected' rhythmicity for each time-frequency point (see 329 Figure S1C). To account for the duration criterion, 1000 ms were discarded from each edge of 330 this 'detected' matrix. 331 The original BOSC algorithm was further extended to define rhythmic events as 332 continuous temporal episodes that allow for an event-wise assessment of rhythm characteristics 333 (e.g. duration). The following steps were applied to the binary matrix of 'detected' single-trial 334 rhythmicity to derive such sparse and continuous episodes. First, to account for the spectral 335 extension of the wavelet, we selected time-frequency points with maximal power within the 336 wavelet's spectral smoothing range (i.e. the pass-band of the wavelet; 5 67 *frequency; see 337 Formula 1). That is, at each time point, we selected the frequency with the highest indicated 338 rhythmicity within each frequency's pass-band. This served to exclude super-threshold 339 timepoints that may be accounted for by spectral smoothing of a rhythm at an adjacent 340 frequency. Note that this effectively creates a new frequency resolution for the resulting 341 rhythmic episodes, thus requiring sufficient spectral resolution (defined by the wavelet's pass-342 band) to differentiate simultaneous rhythms occurring at close frequencies. Finally, continuous 343 rhythmic episodes were formed by temporally connecting extracted time points, while allowing 344 for moment-to-moment frequency transitions (i.e. within-episode frequency non-stationarities; 345 Atallah & Scanziani, 2009) (for a single-trial illustration see Figures 1D and Figure S1D). 346 In addition to the spectral extension of the wavelet, the choice of wavelet parameter also 347 affects the extent of temporal smoothing, which may bias rhythmic duration estimates. To 348 decrease such temporal bias, we compared observed rhythmic amplitudes at each time point 349 within each rhythmic episode with those expected by smoothing adjacent amplitudes using the 350 wavelet ( Figure S1E). By retaining only those time points where amplitudes exceeded the 351 smoothing-based expectations, we removed supra-threshold time points that can be explained 352 by temporal smoothing of nearby rhythms (e.g., 'ramping' up and down signals). In more detail, 353 we simulated the positive cycle of a sine wave at each frequency, zero-shouldered each edge 354 and performed (6-cycle) wavelet convolution. The resulting amplitude estimates at the zero-355 padded time points reflect the temporal smoothing bias of the wavelet on adjacent arrhythmic 356 time points. This bias is maximal (BiasMax) at the time point immediately adjacent to the 357 rhythmic on-/offset and decreases with temporal distance to the rhythm. Within each rhythmic 358 episode, the 'convolution bias' of a time-frequency (TF) point's amplitude on surrounding 359 points was estimated by scaling the points' amplitude by the modelled temporal smoothing bias. 360 be extended to other frequency ranges using the same logic (see discussion on limitations in section 4.6). Subscripts F and T denote frequency and time within each episode, respectively. 363 BiasVector is a vector with the length of the current episode (L) that is centered around the 364 current TF-point. It contains the wavelet's symmetric convolution bias around BiasMax. Note 365 that both BiasVector and BiasMax respect the possible frequency variations within an episode 366 (i.e., they reflect the differences in convolution bias between frequencies). The estimated 367 wavelet bias was then scaled to the amplitude of the rhythmic signal at the current TF-point. 368 PT refers to the condition-and frequency-specific power threshold applied during rhythm 369 detection. We subtracted the power threshold to remove arrhythmic contributions. This 370 effectively sensitizes the algorithm to near-threshold values, rendering them more likely to be 371 excluded. Finally, time points with lower amplitudes than expected by the convolution model 372 were removed and new rhythmic episodes were created ( Figure S1F). The resulting episodes 373 were again checked for adhering to the duration threshold. 374 As an alternative to the temporal wavelet correction based on the wavelet's simulated 375 maximum bias ('MaxBias'; as described above), we investigated the feasibility of using the 376 wavelet's full-width half maximum ('FWHM') as a criterion. Within each continuous episode 377 and for each "rhythmic" sample point, 6-cycle wavelets at the frequency of the neighbouring 378 points were created and scaled to the point's amplitude. We then used the amplitude of these 379 wavelets at the FWHM as a threshold for rhythmic amplitudes. That is, points within a rhythmic 380 episodes that had amplitudes below those of the scaled wavelets were defined as arrhythmic. 381 The resulting continuous episodes were again required to pass the duration threshold. As the 382 FWHM approach indicated decreased specificity of rhythm detection in the simulations ( Figure  383 S2) we used the 'MaxBias' method for our analyses. 384 Furthermore, we considered a variant where total amplitude values were used (vs. 385 supra-threshold amplitudes) as the basis for the temporal wavelet correction. Our results 386 suggest that using supra-threshold power values leads to a more specific detection at the cost 387 of sensitivity ( Figure S2). Crucially, this eliminated false alarms and abundance 388 overestimation, thus rendering the method highly specific to the occurrence of rhythmicity. As 389 we regard this as a beneficial feature, we used supra-threshold amplitudes as the basis for the 390 temporal wavelet correction throughout the manuscript.

Schematic of rhythmic amplitude estimates
A central goal of rhythm detection is to disambiguate rhythmic power and duration 403 ( Figure 2). For this purpose, eBOSC provides multiple indices. We describe the different 404 indices for the example case of alpha rhythms. Please note that eBOSC can be applied in a 405 similar fashion to any other frequency range. The abundance of alpha rhythms denotes the 406 duration of rhythmic episodes with a mean frequency in the alpha range (8 to 15 Hz), relative 407 to the duration of the analyzed segment. This frequency range was motivated by clear peaks 408 within this range in individual resting state spectra ( Figure S4). Note that abundance is closely 409 related to standard BOSC's Pepisode metric (Whitten et al., 2011), with the difference that 410 abundance refers to the duration of the continuous rhythmic episodes and not the 'raw' detected 411 rhythmicity of BOSC (cf. Figure S1C and D). We further define rhythmic probability as the 412 across trials probability to observe a detected rhythmic episode within the alpha frequency 413 range at a given point in time. It is therefore the within-time, across-trial equivalent of 414 abundance. 415 As a result of rhythm detection, the magnitude of spectral events can be described using 416 multiple metrics (see Figure 2A for a schematic). Amplitudes were calculated as the square-417 root of wavelet-derived power estimates and are used interchangeably throughout the 418 manuscript. The standard measure of window-averaged amplitudes, overall amplitudes were 419 computed by averaging across the entire segment at its alpha peak frequency. In contrast, 420 rhythmic amplitudes correspond to the amplitude estimates during detected rhythmic episodes. 421 If no alpha episode was indicated, abundance was set to zero, and amplitude was set to missing.  background fit incorporating the entire frequency range with no post-editing of the detected 448 matrix); the eBOSC method using wavelet correction by simulating the maximum bias 449 introduced by the wavelet ("MaxBias); and the eBOSC method using the full-width-at-half-450 maximum amplitude for convolution correction ("FWHM"). The background was estimated 451 separately for each amplitude-duration combination. 500 edge points were removed bilaterally 452 following wavelet estimation, 250 additional samples were removed bilaterally following 453 BOSC detection to account for the duration threshold, effectively retaining 14 s of simulated 454 signal. 455 Detection efficacy was indexed by signal detection criteria regarding the identification 456 of rhythmic time points between 8 and 12 Hz (i.e., hits = simulated and detected points; false 457 alarms = detected, but not simulated points). These measures are presented as ratios to the full 458 amount of possible points within each category (e.g., hit rate = hits/all simulated time points). 459 For the eBOSC pipelines, abundance was calculated identically to the analyses of empirical 460 data. As no consecutive episodes (cf. Pepisode and abundance) are available in standard BOSC, 461 abundance was defined as the relative amount of time points with detected rhythmicity between 462 8 to 12 Hz. 463 A separate simulation aimed at establishing the ability to accurately recover amplitudes. 464 For this purpose, we simulated a whole-trial alpha signal (i.e., duration = 1) and a quarter-trial 465 alpha signal (duration = .25) with a larger range of amplitudes (1:16 [a.u.]) and performed 466 otherwise identical procedures as described above. To assess eBOSC's ability to disambiguate 467 power and duration ( Figure 2B), we additionally performed simulations in the absence of noise 468 across a larger range of simulated amplitudes and durations. 469 A major change in eBOSC compared to standard BOSC is the exclusion of the rhythmic 470 peak prior to estimating the background. To investigate to what extent the two methods induce 471 a bias between rhythmicity and the estimated background magnitude (for a schematic see Figure  472 1C and D), we calculated Pearson correlations between the overall amplitude and the estimated 473 background amplitude across all levels of simulated amplitudes and durations ( Figure 3C). 474 As the empirical data suggested a trial-wise association between amplitude and 475 abundance estimates also at high levels of signal-to-noise ratios (Figure 7), we investigated 476 whether such associations were also present in the simulations. removal of signal shoulders as described above). In reference to the duration threshold for 493 power-based rhythmicity, we calculated the averaged lagged coherence using two adjacent 494 epochs à three cycles. We computed an index of alpha rhythmicity by averaging values across 495 epochs and posterior-occipital channels, finally extracting the value at the maximum lagged 496 coherence peak in the 8 to 15 Hz range. 497 498 2.10 Dynamics of rhythmic probability and rhythmic power during task performance 499 500 To investigate the detection properties in the task data, we analysed the temporal 501 dynamics of rhythmic probability and power in the alpha band. We created time-frequency 502 representations as described in section 2.6 and extracted the alpha peak power time series, 503 separately for each person, condition, channel and trial. At the single-trial level, values were 504 allocated to rhythmic vs. arrhythmic time points according to whether a rhythmic episode with 505 mean frequency in the respective range was indicated by eBOSC. These time series were 506 averaged within subject to create individual averages of rhythm dynamics. Subsequently, we z-507 scored the power time series to accentuate signal dynamics and attenuate between-subject 508 power differences. To highlight global dynamics, these time series were further averaged 509 within-and between-subjects. Figure captions indicate which average was used. 510 511 2.11 Rhythm-conditional spectra and abundance for multiple canonical frequencies 512 513 To assess the general feasibility of rhythm detection outside the alpha range, we 514 analysed the retention interval of the adapted Sternberg task, where the occurrence of theta, 515 alpha and beta rhythms has been reported in previous studies (Brookes et  cover the final 2 s of the retention interval +-3 s of edge signal that was removed during the 519 eBOSC procedure. We performed eBOSC rhythm detection with otherwise identical 520 parameters to those described in section 2.6. We then calculated spectra across those time points 521 where rhythmic episodes with a mean frequency in the range of interest were indicated, 522 separately for four frequency ranges: 3-8 Hz (theta), 8-15 Hz (alpha), 15-25 Hz (beta) and 25-523 64 Hz (gamma). We subtracted spectra across the remaining arrhythmic time-points for each 524 range from these 'rhythm-conditional' spectra to derive the spectra that are unique to those time 525 points with rhythmic occurrence in the band of interest. For the corresponding topographic 526 representations, we calculated the abundance metric as described in section 2.7 for the apparent 527 peak frequency ranges. 528 529 2.12 Post-hoc characterization of sustained rhythms vs. transients 530 531 Instead of exclusively relying on a fixed a priori duration threshold as done in previous 532 applications, eBOSC's continuous 'rhythmic episodes' also allow for a post-hoc separation of 533 rhythms and transients based on the duration of identified rhythmic episodes. This is afforded 534 by our extended post-processing that results in a more specific identification of rhythmic 535 episodes (see Figure 3) and an estimated length for each episode. For this analysis (Figure 10), 536 we set the a priori duration threshold to zero and separated the resulting episodes post-hoc 537 based on their duration (shorter vs. longer than 3 cycles) at their mean frequency. That is, any 538 episode crossing the amplitude threshold was retained and episodes were sorted by their 539 'transient' or sustained appearance afterwards. We conducted this analysis in the extended task 540 data to illustrate the temporal dynamics of rhythmic and transient events. To investigate the 541 modulation of rhythm-and transient-specific metrics between the retention phase and the probe 542 phase, we averaged metrics within these two intervals and performed a paired t-test between 543 the two respective intervals for four indices: episode number, duration, frequency and power. 544 Cluster at the edges of episodes, we included additional data padding around the trough prior to 561 averaging. The trough was chosen to be the local minimum during the spectral episode that was 562 closest to the maximum power of the wavelet-transformed signal. To better estimate the local 563 minimum, the time domain signal was low-pass filtered at 25 Hz for alpha and beta, 10 Hz for 564 theta and high-pass-filtered at 20 Hz for gamma using a 6 th order Butterworth filter. Filters only 565 served the identification of local minima, whereas unfiltered data were used for plotting. 566 Averaged event dynamics during the first session were visualized for theta at Fz, alpha at O2, 567 beta at FCz and gamma at Fz. To visualize single-trial time-domain signals, we computed 568 moving averages of 150 trials across rhythmic episodes concatenated across all subjects. 569 We further assessed a potential load-modulation of the rate of rhythmic events during 570 working memory retention by counting the number of individual rhythmic episodes with a 571 mean frequency that fell in a moving window of 3 adjacent center frequencies. This produced 572 a channel-by-frequency representation of spectral event rates, which were the basis for 573 subsequent significance testing using dependent sample regression t-tests and implemented in 574 permutation tests as described in section 2.12. 575 576 577 2.14 Modulation of rhythm estimates by working memory load and eye closure 578 579 To assess the sensitivity of rhythm-derived indices to experimental manipulations, we 580 compared (1) the effect of eye closure ("Berger effect") and (2) the effect of working memory 581 load between select rhythm indices. To compare rhythm-specific results with traditional 582 approaches, traditional wavelet estimates were derived using identical parameters as used for 583 eBOSC. We performed confirmatory tests of a parametric increase in posterior alpha power 584 and frontal theta power with memory load based on previous reports in the literature ( Beyond probing effects on each estimate individually, we probed whether rhythm-595 specific estimates of duration and magnitude uniquely captured task effects over and above 596 traditional indices. For this purpose, we performed post-hoc linear mixed effects analyses, 597 averaging within the abundance effects clusters. Prior to modelling, values were z-scored across 598 subjects and conditions. In each model, a rhythm-specific index (e.g. abundance) served as the 599 dependent variable, while traditional amplitudes served as a fixed dependent variable. Load or 600 eye closure were modelled as fixed effects with random subject intercepts, assuming compound spectrum. This resulted in rhythm-specific amplitude values with an identical frequency 613 resolution across episodes. In contrast, to derive rhythm-unspecific FFT amplitude estimates, 614 we included the entire two-second retention period in the estimation and used the respective 615 length for normalization, thus resulting in traditional 'overall' FFT amplitude estimates that 616 were unspecific to rhythmic occurrence. To assess, whether a theta frequency modulation 617 would be observed with traditional FFT spectra, we detected condition-dependent theta 618 frequency peaks. Peaks were defined as frequencies at which the first derivative of the spectrum 619 changed from positive to negative (Grandy et al., 2013b). In case no peak was identified, the 620 frequency with peak amplitude was selected. Finally, we performed paired-t-tests to estimate 621 potential load effects. 622 In figures, we display within-subject standard errors (Cousineau, 2005)

646
We extended the BOSC rhythm detection method to characterize rhythmicity at the 647 single-trial level by creating continuous 'rhythmic episodes' (see Figure 1 & Figure S1). A 648 central goal of this approach is the disambiguation of rhythmic power and duration, which can 649 be achieved perfectly in data without background noise (upper row in Figure 2B). However, 650 the addition of 1/f noise reintroduces a partial coupling of the two parameters (lower row in 651 Figure 2B). To better understand the boundary conditions to derive specific amplitude and 652 duration estimates, we compared the detection properties of the standard and the extended 653 (eBOSC) pipeline by simulating varying levels of rhythm magnitude and duration. Considering 654 the sensitivity and specificity of detection, both pipelines performed adequately at high levels 655 of SNR with high hit and low false alarm rates ( Figure 3A). However, whereas standard BOSC 656 showed perfect sensitivity above SNRs of ~4, specificity was lower than for eBOSC as 657 indicated by higher false alarm rates (grand averages: .160 for standard BOSC; .015 for 658 eBOSC). This specificity increase was observed across simulation parameters, suggesting a 659 general abundance overestimation by standard BOSC (see also Figure 3D). In addition, 660 standard BOSC did not show a reduced detection of transient rhythms below the duration 661 threshold of three cycles, whereas hit rates for those transients were clearly reduced with 662 eBOSC ( Figure 3A2). This suggests that wavelet convolution extended the effective duration 663 of transient rhythmic episodes, resulting in an exceedance of the temporal threshold. In contrast, 664 by creating explicit rhythmic episodes and reducing convolution effects, eBOSC more strictly 665 adhered to the specified target duration. However, there was also a notable reduction in 666 sensitivity for rhythms just above the duration threshold, suggesting a sensitivity-specificity 667 trade-off ( Figure 3A2). In addition to decreasing false alarms, eBOSC also more accurately 668 estimated the duration of rhythmicity ( Figure 3A1), although an underestimation of abundance 669 persisted (and was increased) at low SNRs. In sum, while eBOSC improved the specificity of 670 identifying rhythmic content, there were also noticeable decrements in sensitivity (grand 671 averages: .909 for standard BOSC; .614 for eBOSC), especially at low SNRs. Comparable 672 results were obtained with a 3-cycle wavelet ( Figure S3). Notably, while sensitivity remains an 673 issue, the high specificity of detection suggests that the estimated rhythmic abundance serves 674 as a lower bound on the actual duration of rhythmicity. 675 In a second set of simulations, we considered eBOSC's potential to accurately estimate 676 rhythmic amplitudes. As expected, in signals with stationary rhythms (duration = 1), the time-677 invariant 'overall' amplitude estimate most accurately represented simulated amplitudes 678 ( Figure 3B left), as any methods-induced underestimation biased rhythm-specific amplitudes. 679 Specifically, at low SNRs, underestimation of rhythmic content resulted in an overestimation 680 of rhythmic amplitudes, as some low-amplitude time points were incorrectly excluded prior to 681 averaging. At those low SNRs, subtraction of the background estimate (cf. baseline 682 normalization) alleviated this overestimation. The general impairment at low SNRs was 683 however outweighed by the advantage of rhythm-specific amplitude estimates in time series 684 where rhythmic duration was low and thus arrhythmicity was prevalent ( Figure 3B right). Here, 685 rhythm-specific estimates accurately tracked simulated amplitudes, whereas a strong 686 underestimation was observed for unspecific power indices. In both scenarios, we observed an 687 underestimation of rhythmic abundance with decreasing amplitudes (cf. Figure 3A1). 688 An adaptation of the eBOSC method is the exclusion of the rhythmic alpha peak prior 689 to fitting the arrhythmic background. This serves to reduce a potential bias of rhythmic content 690 on the estimation of the arrhythmic content (see Figure 1C for a schematic). Our simulations 691 indeed indicated a bias of the spectral peak amplitude on the background estimate in the 692 standard BOSC algorithm, which was substantially reduced in eBOSC's estimates ( Figure 3C). 693 To gain a visual representation of duration estimation performance, we plotted 694 abundance against amplitude estimates across all simulated trials, regardless of simulation 695 parameters ( Figure 3D). This revealed multiple modes of abundance at high amplitude levels, 696 which in the eBOSC case more closely tracked the simulated duration. This further visualizes 697 the decreased error in abundance estimates, especially at high SNRs (e.g., Figure 3A), while an 698 observed rightward shift towards higher amplitudes indicated the more pronounced 699 underestimation of rhythmicity at low SNRs. 700 Finally, we investigated the trial-wise association between amplitude and duration 701 estimate based on the observed coupling in empirical data (see Figure 7). Our simulations 702 suggest that both standard BOSC and eBOSC can induce spurious positive correlations between 703 amplitude and abundance estimates, which are most pronounced at low levels of SNR ( Figure  704 3E). Notably, these associations are strongly reduced in eBOSC, especially when rhythmic 705 power is high. This indicates that eBOSC provides a better separation between the two (here 706 independent) parameters, although a spurious association remains. 707 In sum, our simulations suggest that eBOSC specifically separates rhythmic and 708 arrhythmic time points in simulated data at the expense of decreased sensitivity, especially 709 when SNR is low. However, the increase in specificity is accompanied by an increased accuracy 710 of duration estimates at high SNR, theoretically allowing a more precise investigation of 711 rhythmic duration.

722
Estimates were extracted from posterior-occipital channels.

724
While the simulations provide a gold standard to assess detection performance, we 725 further probed eBOSC's detection performance in empirical data from resting and task states 726 to investigate the practical feasibility and utility of rhythm detection. As the ground truth in real 727 data is unknown, we evaluated detection performance by contrasting metrics from detected and 728 undetected timepoints regarding their topography and time course. 729 Individual power spectra showed clear rhythmic alpha peaks for every participant 730 during eyes closed rest and for most subjects during eyes open rest and the task retention period, 731 indicating the general presence of alpha rhythms during the analysed states ( Figure S4). In line 732 with a putative source in visual cortex, alpha abundance was highest over parieto-occipital 733 channels during the resting state ( Figure 4A) and during the WM retention period (Figure 8), 734 with high collinearity between abundance and rhythmic amplitudes within resting conditions 735 ( Figure 4B). As expected, rhythmic time-points exhibited increased alpha power compared with 736 arrhythmic time points ( Figure 4A; white cluster). As one of the earliest findings in cognitive 737 electrophysiology (Berger, 1938), alpha amplitudes increase in magnitude upon eye closure. 738 Here, eye closure was reflected by a joint shift towards higher amplitudes and durations for 739 almost all participants ( Figure 4C). To assess unique contributions of the Berger effect on 740 rhythm indices while controlling for the high collinearity between indicators, we performed 741 linear mixed modelling within the common effects cluster (see Supplementary Table 1). We 742 focussed on the continuous condition here, due to the similarity of the effects in the interleaved 743 case. Notably, rhythmic abundance was modulated by eye closure while statistically controlling 744 for either rhythmic or arrhythmic amplitudes. In contrast, rhythmic alpha amplitudes were not 745 indicate successful rhythm detection. While such an investigation is difficult for induced 772 rhythmicity during rest, evoked rhythmicity offers an optimal test case due to its systematic 773 temporal deployment. For this reason, we analysed task recordings with stereotypic design-774 locked alpha power dynamics at encoding, retention and probe presentation ( Figure 5AB). 775 Rhythmic probability closely tracked power dynamics ( Figure 5A) and time points designated 776 as rhythmic exhibited pronounced alpha power compared with those labelled arrhythmic 777 ( Figure 5A left vs. Figure 5A right). While rhythm-specific dynamics closely captured standard 778 power trajectories, we observed a dissociation concerning arrhythmic power. Here, we 779 observed transient increases during stimulus onsets that were absent from either abundance or 780 rhythmic power (Figure 5A right). This suggests an increase in high-power transients that were 781 excluded due to the 3 cycle duration threshold. Indeed, a significant increase in transient events 782 was observed without an a priori duration threshold (see Figure 10). 783 At the single-trial level, rhythmicity was indicated for periods with visibly elevated 784 alpha power with strong task-locking ( Figure 5B left). Conversely, arrhythmicity was indicated 785 for time points with low alpha power and little structured dynamics ( Figure 5B right). However, 786 strong inter-individual differences were apparent, with little detected rhythmicity when global 787 alpha power was low ( Figure 5B bottom; plots are sorted by descending power as indicated by 788 the frame colour of the depicted subjects and scaled using z-scores to account for global power 789 differences). Crucially, those subjects' single-trial power dynamics did not present a clear 790 temporal structure, suggesting a prevalence of noise and therefore a correct rejection of 791 rhythmicity. Notably, those individual rhythmicity estimates were stable across multiple 792 sessions ( Figure 5C), suggesting that they are indicative of trait-like characteristics rather than 793 idiosyncratic measurement noise (Grandy et al., 2013). 794 In sum, these results suggest that eBOSC successfully separates rhythmic and 795 arrhythmic episodes in empirical data, both at the group and individual level. However, they 796 also indicate prevalent and stable differences in single-trial rhythmicity in the alpha band that 797 may impair an accurate detection of rhythmic episodes. rhythmicity. This indicates that the BOSC-detected rhythmic spectral peak above the 1/f spectrum contains the 816 rhythmic information that is captured by phase-based duration estimates. All data are from the resting state.

818
While the empirical results suggest a successful separation of rhythmic and arrhythmic 819 content at the single-trial level, we also observed strong (and stable) inter-individual differences 820 in alpha-abundance. This may imply actual differences in the duration of rhythmic engagement 821 (as indicated in Figure 5B). However, we also observed a severe underestimation of abundance 822 as a function of the overall signal-to-noise ratio (SNR) in simulations (Figure 3), thus leading 823 to the question whether empirical data fell into similar ranges where an underestimation was 824 likely. During the resting state, we indeed observed that many overall SNRs were in the range, 825 where simulations with a stationary alpha rhythm suggested an underestimation of abundance 826 (cf. black and blue lines in Figure 6A. The black line indicates simulation-based estimates for 827 A B

Abundance underestimation
stationary alpha rhythms at different overall SNR levels; see section 2.8). Moreover, the 828 coupling of individual SNR and abundance values took on a deterministic shape in this range, 829 whereas the association was reduced in ranges where simulations suggest sufficient SNR for 830 unbiased abundance estimates (orange line in Figure 6A). As overall SNR is influenced by the 831 duration of arrhythmic signal, rhythmic SNR may serve as an even better predictor of 832 abundance due to its specific relation to rhythmic episodes (Figure 2). In line with this 833 consideration, rhythmic SNR exhibited a strong linear relationship to abundance ( Figure 6B). 834 Importantly, the background estimate was not consistently related to abundance ( Figure 6C), 835 emphasizing that it is the 'signal' and not the 'noise' component of SNR that determines 836 detection. Similar observations were made in the task data during the retention phase ( Figure  837 S5), suggesting that this association reflects a general link between the magnitude of the spectral 838 peak and duration estimates. The joint analysis of simulated and empirical data thus questions 839 the accuracy of individual duration estimates, especially at low SNRs, due to the dependence 840 of unbiased estimates on sufficient rhythmic power. 841 As eBOSC defines single-trial power deviations from a stationary power threshold as a 842 criterion for rhythmicity, it remains unclear whether this association is exclusive to such a 843 'power thresholding'-approach or whether it constitutes a more general feature of single-trial 844 rhythmicity. To probe this question, we calculated a phase-based measure of rhythmicity, 845 termed 'lagged coherence' (Fransen et al., 2015), which assesses the stability of phase 846 clustering at a single sensor for a chosen cycle lag. Here, 3 cycles were chosen for comparability 847 with eBOSC's duration threshold. Crucially, this definition of rhythmicity led to highly 848 concordant estimates with eBOSC's abundance measure 3 ( Figure 6D), suggesting that power-849 based rhythm detection above the scale-free background overlaps to a large extent with the 850 rhythmic information captured in the phase-based lagged-coherence measure. Moreover, it 851 suggests that duration estimates are more generally coupled to rhythmic amplitudes, especially 852 when overall SNR is low. investigated whether such coupling also persists between trials in the absence of between-867 person differences. In the present data, we indeed observed a positive coupling of trial-wise 868 fluctuations of rhythmic SNR and abundance (mean Fisher's z: .60; p < 6.5e-19) ( Figure 7A), 869 whereas the estimate of the scale-free background was less consistently, though significantly 870 (mean Fisher's z: .20; p = 2.6e-6), related to the estimated duration of rhythmicity ( Figure 7B). 871 This suggests that the level of estimated abundance primarily relates to the magnitude of 872 ongoing power fluctuations around the stationary power threshold. Figure 7C schematically 873 shows how such an amplitude-abundance coupling may be reflected in single trials as a function 874 of rhythmic SNR. These relationships were also observed in our simulations and in other 875 frequency bands, although they were reduced in magnitude at higher levels of simulated 876 empirical SNR ( Figure 3E) and for other frequencies ( Figure S6), suggesting that partial 877 dissociations of the two parameters are feasible. 878 In sum, these results strongly caution against the interpretation of duration measures as 879 a 'pure' duration metric that is independent from rhythmic power, especially at low levels of 880 SNR. The strong within-subject coupling may however also indicate an intrinsic coupling 881 between the strength and duration of neural synchrony as joint representations of a rhythmic 882 mode. Notably, covariations were not constrained to amplitude and abundance, but were 883 widespread, including covariations between 'SNR' and the instability (or variability) of the 884 individual alpha peak frequency (see Supplementary Materials; Figure S7). Combined, these 885 results suggest that the efficacy of an accurate single-trial characterization of neural rhythms 886 relies on sufficient individual rhythmicity and can not only constrain the validity of duration 887 estimates, but broadly affect a range of rhythm characteristics that can be inferred from single 888 trials. 889 890 3.4 Rhythm detection improves amplitude estimates by removing arrhythmic episodes 891 892 From the joint assessment of detection performance in simulated and empirical data, it 893 follows that low SNR constitutes a severe challenge for single-trial rhythm characterization. 894 However, while the magnitude of rhythmicity at the single trial level constrains the detectability 895 of rhythms, abundance represents a lower bound on rhythmic duration due to eBOSC's high 896 specificity. This allows the interpretation of rhythm-related metrics for those time points where 897 rhythmicity is indicated, leading to tangible benefits over standard analyses. In this section, we 898 highlight multiple proof-of-concept cases of such benefits. Furthermore, the presence of a rhythm is a fundamental assumption for the 942 interpretation of rhythm-related metrics, e.g., phase (Aru et al., 2015). This is often verified by 943 observing a spectral peak at the frequency of interest. However, sparse single-trial rhythmicity 944 may not produce an overt peak in the average spectrum due to the high prevalence of low-power 945 arrhythmic content. Crucially, knowledge about the temporal occurrence of rhythms in the 946 ongoing signal can be used to investigate the spectral content that is specific to those time 947 points, thereby creating 'rhythm-conditional spectra'. Figure 9A highlights that such rhythm-948 conditional spectra can recover spectral peaks for multiple canonical frequency bands, even 949 when no clear peak is observed in the grand average spectrum. This showcases that a focus on 950 detected rhythmic time points allows the interpretation of rhythm-related parameters. 951 Abundance topographies for the different peaks observed in the rhythm-conditional spectra, 952 were in line with the canonical separation of these frequencies in the literature ( Figure 9B). 953 Notably, while some rhythmicity was identified in higher frequency ranges, the associated 954 abundance topographies suggests a muscular generator rather than a neural origin for these 955 events. 956 Related to the recovery of spectral amplitudes from 'overall amplitudes', a central 957 prediction of the present work was that the change from overall to rhythmic amplitudes (i.e., 958 rhythm-specific gain; see Figure 2 for a schematic) scales with the presence of arrhythmic 959 signal. Stated differently, if most of the overall signal is rhythmic, the difference between 960 overall and rhythm-specific amplitude estimates should be minimal. Conversely, if the overall 961 signal consists largely of arrhythmic periods, rhythm-specific amplitude estimates should 962 strongly increase from their unspecific counterparts. In line with these expectations, we 963 observed a positive, highly linear, relationship between a subject's estimated duration of 964 arrhythmicity and the rhythm-specific amplitude gain ( Figure 9C). Thus, for subjects with 965 sparse rhythmicity, rhythm-specific amplitudes were strongly increased from overall 966 amplitudes, whereas differences were minute for subjects with prolonged rhythmicity. Note 967 however that in the case of inter-individual collinearity of amplitude and abundance (as 968 observed in the present data) the rhythm-specific gains are unlikely to change the rank-order of 969 subjects as the relative gain will not only be proportional to the abundance, but due to the 970 collinearity also to the original amplitude. While such collinearity was high in the alpha band, 971 decreased amplitude-abundance relationships were observed for other canonical frequency 972 bands ( Figure S6), where such 'amplitude recovery' may have the most immediate benefits. 973 To assess whether these single-trial amplitude estimates validly reflected fluctuations 974 in time series magnitude, we performed a triadic split based on single-trial amplitude estimates 975 across all detected episodes (across channels and sessions) in the alpha band. We aligned time-976 series representations of rhythmicity to the maximal negative peak and compared power in a 977 window of 200 ms around this peak. Notably, rhythm-specific amplitude estimates reflected 978 time series amplitudes during rhythmic periods ( Figure 9D)  In sum, eBOSC provides sensible single-trial amplitude estimates of narrow-band 988 rhythmicity that are boosted in magnitude due to the removal of arrhythmic episodes.  In turn, focusing on these sparse rhythmic events can drastically increase their amplitude 1102 estimates and may thus improve dependent metrics (e.g., see Figure 9C). During our exploration 1103 of rhythmic parameters, we observed a parametric load-related decrease of frontal theta 1104 frequency ( Figure 12C) that spatially aligned with the frontal topography of theta rate and cannot be resolved at the level of data averages (Jones, 2016;van Ede et al., 2018). In short, 1146 due to the non-negative nature of power estimates, time-varying transient power increases may 1147 be represented as sustained power upon averaging, indicating an ambiguity between the 1148 duration and power of rhythmic events (cf., Figure 2B). Importantly, sustained and transient 1149 events may differ in their neurobiological origin (Sherman et al., 2016), indicating high 1150 theoretical relevance for their differentiation. Moreover, many analysis procedures, such as 1151 phase-based functional connectivity, assume that estimates are directly linked to the presence 1152 of rhythmicity, therefore leading to interpretational difficulties when it is unclear whether this 1153 condition is met (Aru et al., 2015;Muthukumaraswamy & Singh, 2011). Clear identification of 1154 rhythmic time periods in single trials is necessary to resolve these issues. In the current study, 1155 we extended a state-of-the-art rhythm detection algorithm, and systematically investigated its 1156 ability to characterize the power and duration of neural alpha rhythms at the single-trial level 1157 in scalp EEG recordings. 1158 While the standard BOSC method provides a sensible detection of rhythmic activity in 1159 empirical data (Caplan et al., 2015;Whitten et al., 2011), its' ability to detect rhythmicity and 1160 disambiguate rhythmic power and duration has not yet been investigated systematically. 1161 Furthermore, we introduced multiple changes that aimed to create rhythmic episodes with a 1162 time-point-wise indication of rhythmicity. For these reasons, we assessed the performance of 1163 both algorithms in simulations. We observed that both algorithms were able to approximate the 1164 duration of rhythmicity across a large range of simulated amplitudes and durations. However, 1165 standard BOSC systematically overestimated rhythmic duration ( Figure 3A). Furthermore, we 1166 observed a bias of rhythmicity on the estimated background ( Figure 3C) as also noted by Haller 1167Haller et al. (2018. In contrast, eBOSC accounts for these problems by introducing multiple changes: 1168 First, by excluding the rhythmic peak prior to fitting the arrhythmic background, eBOSC 1169 decreased the bias of narrow-band rhythmicity on the background fit ( Figure 3C), thereby 1170 effectively uncoupling the estimated background amplitude from the indicated rhythmicity. 1171 Second, the post-processing of detected segments provided a more specific characterization of 1172 neural rhythms compared to standard BOSC. In particular, accounting for the temporal 1173 extension of the wavelet increased the temporal specificity of rhythm detection as indicated by 1174 a better adherence to the a priori duration threshold along with more precise duration estimates 1175 (Figures 3). In contrast to the high specificity, the algorithm did trade off sensitivity, leading to 1176 sensitivity losses that were most pronounced at low signal-to-noise ratios (SNR). In sum, the 1177 simulations highlight that eBOSC provides a sensible differentiation of rhythmic and 1178 arrhythmic time points as well as accurate duration estimates, but also highlight challenges for 1179 empirically disentangling rhythmic power and duration that arise from sensitivity problems 1180 when the magnitude of rhythms is low. We discuss this further in section 4.2. In empirical data, 1181 eBOSC likewise led to a sensible separation of rhythmic from arrhythmic topographies ( Figure  1182 4A, Figure 8, Figure S8) and time courses, both at the average ( Figure 5A) and the single-trial 1183 level ( Figure 5B). This suggests a sensible separation of rhythmic and arrhythmic time points 1184 also in empirical scenarios. 1185 The specific separation of rhythmic and arrhythmic time points has multiple immediate 1186 benefits that we validated using empirical data from resting and task states. First, eBOSC 1187 separates the scale-free background from superimposed rhythmicity in a principled manner. 1188 The theoretical importance of such separation has previously been highlighted (Haller et al., 1189 increases from the background), and highlights the temporal specificity of eBOSC's rhythmic 1233 episodes. 1234 In total, eBOSC's single-trial characterization of neural rhythms provides multiple 1235 immediate benefits over traditional average-based analyses temporally precise indication of 1236 rhythmic and arrhythmic periods. It thus appears promising for improving a mechanistic 1237 understanding of rhythmic processing modes during rest and task. 1238 1239 4.2 Single-trial detection of rhythms: rhythmic SNR as a central challenge 1240 1241 The aforementioned examples highlight the utility of differentiating rhythmic and 1242 arrhythmic periods in the ongoing signal. However, the simulations also indicated problems to 1243 accurately do so when rhythmic power is low. That is, the recognition of rhythms was more 1244 difficult at low levels of SNR, leading to problems with their further characterization. In 1245 particular, our simulations suggest that estimates of the duration ( Figure 6A) and frequency 1246 stationarity ( Figure S7)  power differences between conditions and individuals. Our empirical analyses suggest an 1252 increased trial-by-trial variability of individual alpha frequency estimates as SNR decreases 1253 ( Figure S7). Meanwhile, simulations suggest that such increased variance -both estimated 1254 within indicated rhythmic periods and across whole trials -may result from lower SNR. While 1255 our results do not negate the possibility of real frequency variations of the alpha rhythm with 1256 changes in task load, they emphasize the importance of controlling for the presence of rhythms, 1257 mirroring considerations for the interpretation of phase estimates (Muthukumaraswamy & 1258 Singh, 2011) and amplitudes. This exemplifies how stable inter-individual differences in 1259 rhythmicity (whether due to a real absence of rhythms or prevalent measurement noise; e.g., 1260 distance between source and sensor; head shape; skull thickness) can affect a variety of 'meta'-1261 indices (like phase, frequency, duration) whose estimation accuracy relies on apparent 1262 rhythmicity. 1263 The challenges for characterizing rhythms with low rhythmic power also apply to the 1264 estimated rhythmic duration, where the issue is particularly challenging in the face of legitimate 1265 interest regarding the relationship between the power and duration of rhythmic events. In 1266 particular, sensitivity problems at low rhythmic magnitudes challenge the ability to empirically 1267 disambiguate rhythmic duration and power, as it makes the former dependent on the latter in 1268 the presence of noise (e.g., Figure 2B). Crucially, a tight link between these parameters was 1269 also observed in the empirical data. During both rest and task states, we observed gradual and 1270 stable inter-individual differences in the estimated extent of rhythmicity that were most strongly 1271 related to the overall SNR in ranges with a pronounced sensitivity loss in simulations (see 1272 Figure 4A black line). Given the observed detection problems in our simulations, this 1273 ambiguates whether low empirical duration estimates indicate temporally constrained rhythms 1274 or estimation problems. Conceptually, this relates to the difference between lower SNR subjects 1275 having (A) low power, transient alpha engagement or (B) low power, sustained alpha 1276 engagement that was too faint to be detected (i.e., sensitivity problems). While the second was