Covert Waking Brain Activity Reveals Instantaneous Sleep Depth
Citation: McKinney SM, Dang-Vu TT, Buxton OM, Solet JM, Ellenbogen JM (
Covert Waking Brain Activity Reveals Instantaneous Sleep Depth
Scott M. McKinney 0
Thien Thanh Dang-Vu 0
Orfeu M. Buxton 0
Jo M. Solet 0
Jeffrey M. 0
Naomi Rogers, Central Queensland University, Australia
0 1 Department of Neurology, Massachusetts General Hospital , Boston , Massachusetts, United States of America, 2 Division of Sleep Medicine, Harvard Medical School , Boston , Massachusetts, United States of America, 3 Cyclotron Research Centre, University of Liege, Liege, Belgium, 4 Department of Medicine, Brigham and Women's Hospital , Boston , Massachusetts, United States of America, 5 Department of Medicine, Cambridge Health Alliance , Cambridge, Massachusetts , United States of America
The neural correlates of the wake-sleep continuum remain incompletely understood, limiting the development of adaptive drug delivery systems for promoting sleep maintenance. The most useful measure for resolving early positions along this continuum is the alpha oscillation, an 8-13 Hz electroencephalographic rhythm prominent over posterior scalp locations. The brain activation signature of wakefulness, alpha expression discloses immediate levels of alertness and dissipates in concert with fading awareness as sleep begins. This brain activity pattern, however, is largely ignored once sleep begins. Here we show that the intensity of spectral power in the alpha band actually continues to disclose instantaneous responsiveness to noise-a measure of sleep depth-throughout a night of sleep. By systematically challenging sleep with realistic and varied acoustic disruption, we found that sleepers exhibited markedly greater sensitivity to sounds during moments of elevated alpha expression. This result demonstrates that alpha power is not a binary marker of the transition between sleep and wakefulness, but carries rich information about immediate sleep stability. Further, it shows that an empirical and ecologically relevant form of sleep depth is revealed in real-time by EEG spectral content in the alpha band, a measure that affords prediction on the order of minutes. This signal, which transcends the boundaries of classical sleep stages, could potentially be used for real-time feedback to novel, adaptive drug delivery systems for inducing sleep.
Funding: This study was funded by the Academy of Architecture for Health, the Facilities Guidelines Institute, the Center for Health Design, and the
Massachusetts General Hospital. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
Sleep is not uniform, and certain moments are sounder than
others. Indeed, resistance to acoustic disturbancea measure of
sleep depthdisplays considerable variability throughout a night
of sleep, even within sleep stage . The factors that influence
sleeps vulnerability to sensory insult have not been fully
The very transition from wake to sleep involves a dissociation
from the external world and a crescendo of internal brain rhythms.
Heralding this transition is attenuation of the alpha rhythm, an
813 Hz electroencephalographic (EEG) oscillation prominent
over posterior brain regions, and the signature of relaxed
wakefulness . Diminishing during the descent into sleep, alpha
amplitude shadows the decline in external awareness that
accompanies sleep onset [3,4]. And while it appears to vanish as sleep
begins, quantitative analysis reveals that power in the alpha band
actually fluctuates dynamically throughout the night (Fig. 1A) .
Given alpha activitys association with wakefulness and sensory
intake, we hypothesized that covert levels of alpha activity would
reveal a sleepers instantaneous sensitivity to the environment.
That is, inconspicuous fluctuations in wake-like background brain
activity might correspond to changes in sleep depth, even beyond
sleep stage designation.
To study this question in a realistic setting, we used ecological
noises to probe environmental sensitivity throughout sleep,
simultaneously monitoring subjects brain activity with EEG. The sound
intensity required to disturb subjects provided an empirical
measure of their instantaneous sleep depth. In this paradigm, sleep
stability denotes resistance to disruption, while sleep fragility denotes
vulnerability to disruption. We sought to evaluate whether these
qualities could be predicted using the covert level of waking brain
activity just before each stimulus.
We systematically challenged sleep with auditory stimulation in
thirteen healthy subjects throughout two nights of sleep. Brain
activity was monitored on each night using EEG. Ten-second,
ecological noises (e.g., road and air traffic, a telephone ringing)
were presented during bouts of stable sleep (Fig. 2). Each sound
was initiated at 40 decibels (dB) and replayed every thirty seconds
in 5 dB increments until the EEG signal was perturbed according
to standard guidelines (i.e., an arousal was observed ).
We interrogated the relationship between alpha activity and
sleep fragility using Cox regression, a tool from survival analysis
(see Materials and Methods). The output of Cox regression is the
hazard ratio (HR): this number represents the relative hazard of
Figure 1. Alpha power fluctuates dynamically throughout the night. A. The trajectory of relative alpha power throughout a quiet night of
sleep is shown from one representative subject. Simultaneous sleep stage designations run beneath the time course of alpha power. Diminishing as
sleep begins, alpha power fluctuates throughout the night, in tandem with sleep depth. For display, the alpha power time-series was approximated
using local linear regression in 4 minute windows, corresponding to the approximate length of each stimulation series (see Materials and Methods).
This procedure removes noise and emphasizes slower fluctuations with fewer distortions than those imposed by simple low-pass filtering .
B. These histograms show the distribution of alpha power during NREM sleep, revealing that a range of values can be observed within each of stages
N2 and N3. Power was computed in non-overlapping 10-second bins; epochs containing arousals, which may represent transient departures from
stable sleep, were discarded.
disruption in one condition compared to another. For continuous
covariates, the HR represents the relative hazard of disruption
incurred by a one-unit increase of the covariate. Hazard ratios
greater than 1 imply that the covariate is associated with sleep
fragility (vulnerability to disruption), while those less than 1 denote
covariates accompanying sleep stability (resistance to disruption).
We focused our analysis on factors contributing to sleep fragility
during non-rapid-eye-movement (NREM) sleep (stages N2 and
N3, accounting for the majority of sleep ), as several difficulties
arise when considering alpha activity during rapid-eye-movement
(REM) sleep (see Discussion). The regression model contained two
covariates, one indicating the visually scored sleep stage
designation , the other indicating the spectral content preceding each
stimulus (see Materials and Methods).
When comparing noise sensitivity across sleep stage, Cox
regression yielded a HR of 0.54 (P,0.0001) associated with stage
N3, so-called slow-wave sleep, relative to N2. In line with previous
reports [1,8], this value indicates a suppressed hazard of disruption
in N3 compared with N2 (the probability of tolerating noise at any
loudness in N3 being roughly the square root of that in N2).
We next addressed the influence of occipital alpha activity on
sleep fragility. Figure 1A shows that, on an undisturbed night of
sleep, relative alpha power shadows the trajectory of qualitatively
assessed sleep depth. Like the probability of disruption, alpha
power is generally suppressed in N3 relative to N2 (Fig. 1B).
Although relative alpha power correlates well with sleep stage, a
wide spectrum of variation still exists within each category. We
therefore sought to determine whether fluctuations in this quantity
even within sleep stagecorrespond to concurrent variations in sleep
To address this question, we included in the statistical model a
measure of the alpha content during the ten seconds immediately
preceding each sound (Fig. 2, light gray windows). Even
controlling for stage, we observed a highly significant relationship
between alpha power and sleep fragility (HR = 5.74, P,0.001).
This suggests that, well beyond sleep stage designation, latent
alpha content betrays heightened sensitivity to impending sounds.
To investigate the timescale over which alpha power predicts
sleep fragility, we further characterized each sound series by a
single spectral measure derived from a reference window of stable
sleep preceding the sound series (Fig. 2, dark gray windows). This
interval anticipated the eventual disruption by a variable latency of
up to four minutes, as arousal may have occurred as late as 70 dB.
Still, alpha power during this ninety-second baseline period
predicted the probability of disruption in the moments that
followed (HR = 7.33, P,0.001), suggesting that the brain state
disclosed by alpha activity persists for several minutes (see also
Results S1 and Figure S1).
Figure 3 illustrates a summary of our results, rendering the
probability of sleep disruption in the face of noise as a function of
Figure 2. Sleep depth was probed with auditory stimulation. We systematically probed sleep depth with auditory stimulation during bouts of
N2, N3 and REM sleep. Ten-second noises were initiated at 40 decibels (dB) and presented every thirty seconds in 5 dB increments until the EEG signal
was perturbed (arousal, vertical bars on the bottom line). Each color represents a different sound type; a sample of four is shown here. The sound
intensity required to disturb subjects provided an experimental measure of their immediate sleep depth. The gray windows beneath the sound level
delineate periods during which alpha power was measured to predict sleep fragility.
Figure 3. Alpha content reveals immediate sleep fragility. Using Cox regression, we found that alpha activity disclosed noise sensitivity during
NREM sleep, even when controlling for stage. Here we reconstruct probability surfaces for sleep stages N2 and N3, rendering sleep fragility as a
function of both stimulus intensity and EEG alpha content.
both stimulus intensity and EEG alpha content. Here we depict a
distinct surface for each NREM sleep stage, in which separate
mechanisms may also regulate sensory perception [9,10]. Just as
the probability of disruption increases monotonically with
loudness, so too is sleeps vulnerability modulated by coincident
We next explored the relationship between immediate sleep
fragility and the broader EEG power spectrum. Toward this end,
we estimated the power at frequencies between 0.5 and 25 Hz (in
0.5 Hz intervals) expressed over occipital electrodes during the ten
seconds immediately preceding each stimulus (Fig. 2, light gray
windows). To facilitate a meaningful comparison across
frequencies, power values were standardized based on their waking levels
and their dynamic ranges observed during NREM sleep (see
Materials and Methods). The power at each frequency was then
analyzed independently using Cox regression.
The resulting spectral portrait shows how power at each
frequency, beyond stage designation, covaries with sleep fragility
(Fig. 4). (For comparison across the entire EEG spectrum,
estimates of the Cox regression coefficients reflect a change of
one standard deviation in the log-power at each frequency.) The
large, sustained contribution throughout the alpha band suggests
that this region of the spectrum indeed contains a meaningful
signal. We moreover observed strong tendencies toward sleep
stability in conjunction with low-frequency power (including
slowwave, delta, and theta activity) and toward fragility in conjunction
with high-frequency power (beta activity). Nonetheless, the only
power value that achieved significance after a liberal correction for
multiple comparisons (Holm-Bonferroni method) was that at
10.5 Hz (P = 0.025), centrally located within the alpha band.
As the approach just described manages to isolate the power at
different frequencies, we took the opportunity to once more study
the relationship between alpha activity and sleep fragility, this time
including in our statistical model, in place of sleep stage
designation, a measure of low-frequency oscillatory EEG activity
(0.54 Hz), which may more faithfully track changes in sleep
depth at the neuronal level . This moreover teases apart the
effects of alpha and delta activity, which may interact in the
relative measure of alpha content employed earlier. In this context,
slow-wave activity was associated with sleep stability (HR = 0.73;
P,10211), and alpha activity again demonstrated a significant
relationship with sleep fragility (HR = 1.13; P = 0.002).
The present results show that the soundness of sleep, defined
empirically and with ecological relevance, is revealed in real-time
by EEG spectral content: greater vulnerability to noise-induced
sleep disruption accompanies elevated alpha activity. Such spectral
interrogation of sleep fragility has predictive power on the order of
minutes. Furthermore, this effect transcended traditional sleep
staging, imparting a greater sense of fluidity to what is typically
seen as a rigid process.
From a behavioral perspective, alpha activity has been shown to
resolve fine gradations in the sleep-wake continuum. On visual
and auditory vigilance tasks, reduced alpha activity is associated
with sluggish reaction times and an elevated probability of lapse
[12,13,14,15,16]. Even during wakefulness, immediate levels of
alertness are revealed by ongoing alpha activity: moments of
higher parietal alpha amplitude have been associated with
receptiveness to tactile stimuli and heightened attention .
These observations concerning alphas relationship to sensory
intake, in conjunction with several others, have emboldened some
investigators to include the alpha oscillation among the neural
correlates of consciousness . Here we extend alpha activitys
association with environmental awareness beyond wakefulness and
drowsiness, and into NREM sleep.
Though the alpha oscillation was one of the first brain rhythms
to be described in the human EEG , little is currently
understood about its underlying generators or functional
significance. The thalamus, which has been found to influence cortical
alpha synchronization , might be the critical link between
alpha activity and the brains vulnerability to acoustic disruption.
As the thalamus is involved in relaying sensory information to the
cortex, alpha activity could be a reflection of this regions
propensity for conveying external stimuli to cortical processing
centers where it is capable of interrupting sleep. Intriguingly, it was
recently shown that global expression of alpha power (and, to a
weaker extent, beta power) is positively correlated with activity in a
tonic-alertness network, comprised of the dorsal anterior
cingulate cortex, anterior insula, and thalamus . The
constituents of this network, with access to sensory information
and broad projections throughout the cortex , are well
positioned to support alerting functions and a general readiness
for perception and action [21,23]. At least during wakefulness,
then, elevated alpha activity seems to reflect the engagement of
regions supporting sensory intake and alertness. Future studies
should address the existence of a similar intrinsic connectivity
network during sleep, and its connection with EEG alpha content.
The specificity of alpha power as a maker of NREM sleep
When we broadened the scope of our analysis to include the rest
of the EEG power spectrum during NREM sleep, only an alpha
frequency (10.5 Hz) remained significant after correction for
multiple comparisons. Rather than suggesting that this lone
frequency contains information regarding sleep fragility, we
suspect that inter-individual variability in peak alpha rhythm
frequency  undermined the effect when small slivers of the
band were considered alone.
Although large scale associations between EEG power and sleep
depth might be expected based on inherent correlations across
frequencies in the power spectrum of the sleeping brain , we
nonetheless observed several trends outside the alpha band that
warrant attention. In particular, we noted a tendency toward sleep
stability in conjunction with increased power in the frequencies
below 8 Hz. This accords well with the view that low-frequency
oscillatory activity (including slow-wave and delta activity)
intensifies with increasing depth of NREM sleep . It should
be noted, however, that our analysis controlled for NREM sleep
stage, so the overall relationship between sleep stability and
lowfrequency power, which is enhanced in stage N3 relative to N2,
was necessarily blunted in this context. The association between
reduced sound sensitivity and EEG spectral power in the low
frequencies appeared to extend even to the theta band (47 Hz).
In light of this observation, it is interesting to note that during
vigilance tasks, theta-rich EEG has been found to be associated
with reduced arousal  and deteriorated stimulus detection
We further observed a tendency for increased vulnerability to
disruption in conjunction with greater EEG power in higher
frequencies, including the beta band (1525 Hz). As with alpha
activity, previous work has also shown a connection between
variation in beta activity and fluctuations in cortical arousal and
vigilance behavior [27,28]. A similar observation was made in
sleep, with enhanced beta activity now thought to signify
heightened arousal in patients with insomnia .
As might be expected, the association between alpha power and
sleep fragility did not yield significance when REM sleep was
considered alone (P = 0.45). During REM, the relative alpha
power is more erratic and this activity may stem from
heterogeneous brain sources. Alpha activity during REM occurs
in at least two forms, conspicuous alpha bursts and background
alpha activity, which are thought to be electrophysiologically
distinct from one another and from that evident during
wakefulness. Further, alpha amplitude may be modulated by
visual imagery in the context of dreaming . While the function
of alpha activity during REM remains hypothetical, the present
results suggest that it does not accompany heightened sensitivity to
Future directions and applications
Previous electrophysiological studies have demonstrated that
ongoing network activity profoundly influences evoked cortical
responses and explains their dramatic variability . Here we
further emphasize the role of the immediate brain state in
modulating perception by showing that beyond sleep stage  and the
overt rhythms of sleep , inconspicuous background activity
also varies with the soundness of sleep. In this light, alpha activity
provides a potent window onto the instantaneous responsiveness of
the sleeping brain. Future research should investigate the extent to
which other features of EEG dynamics, such as spectral coherence
[32,33], cross-frequency phase synchrony [34,35], or nested
oscillations [36,37] offer useful information about empirical
measures of sleep depth.
Given that real-time fluctuations in EEG parameters provide
immediate information about sleeps depth and its vulnerability to
disruption, it is enticing to speculate that this kind of information
could be employed by adaptive hypnotic agents guided by direct
feedback from neural activity. Such technology might be capable
of combating the disruptive effects of environmental noise on sleep
and next-day cognitive performance [38,39], while optimally
preserving natural sleep physiology. At present, sleep medications
are a blunt instrument. Administered before bed, conventional
hypnotics last for a rigid duration fixed by their pharmacokinetic
properties. These drugs dominate consciousness, inducing
sleeplike sedation of unclear authenticity [40,41]. A system that allows
for dynamic drug delivery based on instantaneous feedback (using
a metric derived from alpha activity or the broader EEG power
spectrum) could momentarily protect or facilitate sleep when
vulnerable, otherwise letting natural brain rhythms run their
course. Further, such an arrangement might allow for emergency
interruptions or scheduled wake-times; such specificity is
prohibited by the crude sleep medications used today. Besides using
smaller doses, then, this system would afford enhanced precision
and flexibility. The present study establishes a conceptual
framework for such research, showing that sleep can be monitored
in real-time and characterized along a rich continuum of depth.
Materials and Methods
The findings described here stem from an experiment
conducted to study the disruptive salience of different sounds in
sleep. Biomarkers for individual noise tolerance (i.e., traits) were
presented in , whereas the current analysis seeks to elucidate
moment-to-moment variations in sleeps vulnerability to
disruption (i.e., states).
Study procedures were approved by the Human Research
Committees of the Brigham and Womens Hospital, the
Massachusetts General Hospital (MGH), and the Cambridge
Health Alliance. Written informed consent was obtained for all
Thirteen healthy volunteers (9 females and 4 males, age
24.967.3; mean 6 SD) were determined to be free from medical
or psychiatric conditions on the basis of clinical history and a
physical examination. Participants were also screened for drug,
alcohol, or caffeine dependency. Subjects reported taking no
medications that affect sleep or circadian rhythms. All participants
demonstrated normal hearing on the basis of audiometric
screening of each ear (minimum hearing level of 25 decibels
[dB] at 500, 1000, 2000 and 4000 Hz).
Participants slept on a consistent schedule for at least 4 days
prior to the study, as confirmed by wrist actigraphy (AW-64,
Minimitter, Bend, OR). During the study, subjects stayed at the
MGH Sleep Laboratory for 3 consecutive nights. Each night,
subjects were given the opportunity to sleep for 8.5 hours at their
normal bedtime. Research staff monitored the subjects 24 hours a
day to ensure that they did not nap. Light levels were maintained
at approximately 90 lux during waking periods, and ,1 lux
during sleep periods. The first night was used for adaptation;
subjects adjusted to the laboratory environment and were screened
for any sleep disorders visible on the polysomnogram. Acoustic
stimulation was applied only on the second and third nights.
Polysomnographic recordings were collected using a Comet XL
system (Grass-Telefactor, West Warwick, RI, USA). Skin surface
electrodes (Beckman Instrument Company, Schiller Park, IL)
captured EEG from frontal (F3 and F4), central (C3 and C4) and
occipital (O1 and O2) positions; electrooculogram (EOG);
submental electromyogram (EMG); and electrocardiogram (ECG). Data
were conditioned by analogue filters (high-pass: 0.3 Hz; low-pass:
70 Hz), and digitally sampled at 200 Hz.
On the second and third nights of the experiment, acoustic
stimulation was applied systematically throughout stages N2, N3
and REM sleep. Once stable sleep was achieved (at least 90
consecutive seconds of the same stage scored in real time), sounds
were initiated at 40 dB and replayed every thirty seconds in 5 dB
increments until an arousal was observed or 70 dB was reached
(Fig. 2). A 70 dB limit was imposed to minimize full awakenings
from sleep and prevent significant disruption of sleep architecture.
Each time an arousal was elicited, sound was withheld until stable
sleep resumed, at which time a new sound was chosen.
Acoustic stimuli were each ten seconds in duration, and drawn
from diverse sources. Noises included a telephone ringing, a toilet
flushing, an IV alarm, a hospital intercom, a door creaking and
slamming, a laundry machine, an ice machine, a towel dispenser,
road traffic, snoring, a jet engine, a helicopter, and two
conversations of positive and negative emotional valence. All
sounds except the jet and helicopter were recorded on site in a
medical unit of Somerville Hospital, Somerville, MA. Stimuli,
which were repeated through each graduated sound series, were
selected at random for each participant on each night.
Sound levels were measured using dBA-Leq-10 s, consistent with
standard methods used to evaluate the clinical effects of noise. A
refers to the weighting of sounds in ranges audible to humans,
while Leq-10 s denotes an average intensity derived from the
10 seconds of the sounds duration. The sound level in the patient
room was logged with an environmental sound monitor (Rion
Type NL-31, with Type 1 microphone) located 10 inches above
the subjects head. Stimuli were presented on a measured average
background of 3435 dB due to continuous ventilation in the
Stimuli were delivered in surround sound using an array of four
studio-monitor loudspeakers (Event, model PS6) placed at the
circumference of a circle centered around the subjects head. This
arrangement enabled sounds with moving sources (e.g., the
airplane) to be reproduced with apparent motion through space.
Sleep stages (in 30-second epochs) and arousals were identified
in adherence with the recommendations of the American
Academy of Sleep Medicine . According to these criteria, an
arousal consists of an abrupt increase in EEG frequency lasting at
least 3 seconds, excluding that caused by a spindle, and preceded
by at least 10 seconds of stable sleep. Sleep scoring was conducted
by a registered polysomnographic technician under the
supervision of the medical director of the MGH Sleep Laboratory.
The period preceding sound presentation was used to assay the
electroencephalographic sleep depth associated with each sound.
Power spectra were estimated using the multitaper method .
Spectra were derived from occipital electrodes (average of O1 and
O2), as waking alpha tends to predominate over these posterior
For each segment of analysis, alpha activity was computed as
the integral of the power spectrum in the alpha band (813 Hz)
divided by the total power generated in that interval. As utilized
elsewhere [4,44,45,46], this metric seeks to eliminate variance
resulting from non-brain-based factors (e.g., degradation of
electrode contact) that occur during all-night EEG recordings.
Moreover, this process facilitates an aggregate analysis across two
experimental nights in each of thirteen subjects. To control for the
degree to which alpha power signifies wakefulness in each
individual (i.e., the subjects native alpha generation ), this
measure was normalized to the corresponding value derived from
a baseline period of eyes-closed wakefulness on the same night.
When a broader range of EEG oscillatory activity was considered
(Fig. 4), the power at frequencies of 0.5 Hz to 25 Hz (in steps of
0.5 Hz) was estimated using Bartletts method (2-second segments)
and the Goertzel algorithm . The quantities derived from
occipital electrodes O1 and O2 were averaged for subsequent
analysis. As before, the power spectral density was normalized to a
baseline waking spectrum. To facilitate meaningful comparison
across frequencies, which have different dynamic ranges, power
values were log-transformed  and divided by the standard
deviation of the log-spectrum observed during quiet NREM sleep
(absent sound presentation) on the same night. When the power in
the slow/delta band (0.54 Hz) and alpha band (813 Hz) were
considered as absolute, as opposed to relative, measures, the Bartlett
spectra were integrated in the corresponding ranges and the resulting
power values were standardized in the manner just described.
The influence of EEG spectral content on sleep fragility was
interrogated using survival analysis . Each sound series defined
a distinct risk period (a lifetime) during which sleep could be
disruptedmaintenance of sleep constitutes survival, disruption of
sleep, a failure.
Only sound series that were preceded by three contiguous
30second epochs of the same sleep stage and terminated in a
soundinduced arousal were used for analysis. (An arousal was judged to
be evoked from stimulation if the arousal occurred during the
sound or within 5 seconds from its conclusion.) Among these
sound series, 109 out of 724 in NREM and 45 out of 267 in REM
were right-censored, meaning that sound presentation ended
before arousal occurred.
In this paradigm, sleep stability, a function of loudness, describes
the probability of tolerating sounds of any given intensity. Sleep
fragility, the stability curves complement, describes the probability
of disruption due to sounds of any given intensity.
The effect of EEG spectral features on sleep fragility was evaluated
with a Cox proportional hazards regression model. The model was
stratified across subjects in order to account for individual differences
in noise tolerance. Since our loudness scale grew in discrete, 5 dB
increments, we employ the exact-partial likelihood method to handle
multiple arousals at each sound intensity . A categorical stage
covariate was also included to control for the conventional measures
available to characterize sleep depth.
When the power at distinct frequencies through 25 Hz were
tested independently, p-values for each frequency were adjusted
using the Holm-Bonferroni method for multiple comparisons .
Figure S1 Alpha power is stable for minutes. This plot
shows an unbiased estimate of the autocorrelation function of relative
spectral content in the alpha band (813 Hz) measured in 10-second
intervals (depicted smoothed in Figure 1A). The autocorrelogram
portrays the correlation of alpha content with its subsequent values
for a range of lags. The trajectory used for this figure transcended
multiple sleep stages, thus portraying the global stability of alpha
content that might be observed at an arbitrary time of night.
We thank B. Healy, M. Bianchi, and S. Cash for advice; A. Carballeira, M.
Merlino, K. Gannon, D. Cooper, S. OConnor, V. Castro, and C. Smales
Conceived and designed the experiments: JME OMB JMS. Performed the
experiments: JME OMB. Analyzed the data: SMM TTD-V JME. Wrote
the paper: SMM TTD-V JME.
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