PRESENTING

FOR YOUR READING PLEASURE

AN ANNOTATED VERSION OF

Synchronization of Neural Activity across Cortical Areas Correlates with Conscious Perception.

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Table of Contents

Introduction 3

Synchronization of Neural Activity across Cortical Areas Correlates with Conscious Perception 4

FIGURES 25Figure 1 26Figure 2 27Figure 3 28Figure 4 29

APPENDICES 30Zeroth Appendix – Oscillations 31First Appendix – A description of the two experiments 45Second Appendix – Variables 50Third Appendix – EEG signals 51Fourth Appendix – Digital signal processing 56Fifth Appendix – Fourier analysis 62 Sixth Appendix – Fast Fourier transformSeventh Appendix – EEG frequencies 76Eighth Appendix – Complex number representation

of Fourier series and Fourier coefficients 84

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Ninth Appendix - Getting the info from the complex number representations 110

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Introduction

Drs. Baars, McGovern and Montandon have worked mighty hard to bring you an

annotated version of Synchronization of Neural Activity across Cortical Areas Correlates with Conscious Perception.

If, like us, you have studied a fair share of literature, philosophy, etc., you have read annotated papers in those areas. But so far as we know, this is

By reading this paper, you are helping to make history! Thank you.

Another annotated paper is from the Exploratorium. It is the paper that Watson and Crick wrote to announce that they had figured out the structure of the DNA molecule! Here’s the link:

http://www.exploratorium.edu/origins/coldspring/ideas/printit.html

Everyone is always surprised to find that this paper, one of the most famous and important in the entire history of science, is one page long!

We hope that someday soon, someone will publish a paper announcing the solution to consciousness. It probably won’t be one page long.

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Behavioral/Systems/Cognitive

Synchronization of Neural Activity across Cortical Areas Correlates with Conscious Perception

Lucia Melloni,1* Carlos Molina,1,2 Marcela Pena,1,3 David Torres,1 Wolf Singer,4,5 and Eugenio Rodriguez1,4,5*1Laboratorio de Neurociencias, Escuela de Psicologı´a, Pontificia Universidad Cato´lica de Chile, Vicun˜a Mackenna 4860, San Joaquin, 8940000 Santiago,Chile, 2Radboud University Nijmegen, 6525 EK Nijmegen, The Netherlands, 3International School for Advanced Studies, Cognitive Neuroscience Sector,34014 Trieste, Italy, 4Department of Neurophysiology, Max Planck Institute for Brain Research, 60528 Frankfurt am Main, Germany, and 5FrankfurtInstitute for Advanced Studies, Johann Wolfgang Goethe University, 60438 Frankfurt am Main, Germany

Received Oct. 25, 2006; revised Jan. 16, 2007; accepted Feb. 5, 2007.L.M. was supported by the Comisio´n Nacional de Investigacio´n Cientı´fica y Tecnolo´gica (Chile) and DeutscherAkademischer Austausch Dienst (Germany). E.R. was supported by Max Planck Gesellchaft, Volkswagen Stiftung,and the Frankfurt Institute for Advanced Studies.*L.M. and E.R. contributed equally to this work.Correspondence should be addressed to Dr. Lucia Melloni, Brain Imaging Center and Cognitive Neurology Unit,Johann Wolfgang-Goethe Universita¨t, Schleusenweg 2-16, 60528 Frankfurt am Main, Germany. E-mail:melloni@mpih-frankfurt.mpg.de.DOI:10.1523/JNEUROSCI.4623-06.2007Copyright©2007 Society for Neuroscience 0270-6474/07/272858-08$15.00/0

Subliminal stimuli can be deeply processed and activate similar brain areas as consciously perceived stimuli. This raises the questionwhich signatures of neural activity critically differentiate conscious from unconscious processing. Transient synchronization of neuralactivity has been proposed as a neural correlate of conscious perception. Here we test this proposal by comparing the electrophysiological responses related to the processing of visible and invisible words in a delayed matching to sample task. Both perceived and nonperceived words caused a similar increase of local (gamma) oscillations in the EEG, but only perceived words induced a transient long-distance synchronization of gamma oscillations across widely separated regions of the brain. After this transient period of temporal coordination, the electrographic signatures of conscious and unconscious processes continue to diverge. Only words reported as perceived induced (1)enhanced theta oscillations over frontal regions during the maintenance interval, (2) an increase of the P300 component of the event related potential, and (3) an increase in power and phase synchrony of gamma oscillations before the anticipated presentation of the test

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word. We propose that the critical process mediating the access to conscious perception is the early transient global increase of phasesynchrony of oscillatory activity in the gamma frequency range.

Key words: visual awareness; electroencephalography; event-related potentials; gamma-band oscillations; long-range coordination; oscillatoryneural synchrony

Introduction

Stimuli that are masked and presented so briefly that they cannotbe reported can still be highly processed and even activate motorresponses (Marcel, 1983; Dehaene et al., 1998, 2001, 2004; Naccacheet al., 2005). Evidence from patients suffering from blindsight (Goebel et al., 2001), hemineglect (Vuilleumier et al., 2002;Cappelletti and Cipolotti, 2006), or prosopagnosia (Renault etal., 1989) supports the notion that unconsciously processed stimuliactivate high-level cortical areas. This implies that complexcognition can proceed in the absence of consciousness, raisingthe question how the neuronal substrates of conscious and nonconsciousprocesses differ. Several studies have suggested thatconscious perception associates with enhanced sensory responses(Grill-Spector et al., 2000; Bar et al., 2001) and with activation ofareas higher in the processing hierarchy (Beck et al., 2001; Dehaeneet al., 2001; Kleinschmidt et al., 2002; Marois et al., 2004;Carmel et al., 2005). However, other studies suggest that this maynot be a sufficient condition, because invisible stimuli activatesimilar structures as visible stimuli (Moutoussis and Zeki, 2002,2006).

Alternatively, it has been proposed that conscious perceptiondepends on the transient synchronization of widely distributedneural assemblies (Engel et al., 1999; Engel and Singer, 2001;Thompson and Varela, 2001; Singer, 2002). The neural signatureof unconscious perception would be local coordination of neuralactivity and propagation along sensory processing pathways,whereas conscious perception would require global coordinationof widely distributed neural activity by long-distance synchronization(Dehaene et al., 2006). Indeed, _ and gamma frequency

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band phase synchrony is enhanced for consciously perceivedstimuli (Meador et al., 2002; Gross et al., 2004; Nakatani et al.,2005; Palva et al., 2005) and correlates with conscious perceptionin binocular rivalry (Fries et al., 1997, 2002; Srinivasan et al.,1999; Doesburg et al., 2005). However, these studies have investigatedsynchronization in spatially restricted neural assemblies,or without distinguishing between local and global coordination.The purpose of this study was to disentangle the role of localprocessing and global coordination in conscious and unconsciousperception and to determine the nature and the timecourse of electrophysiological events that discriminate betweenthem.

We recorded electroencephalographic (EEG) signals in subjectsengaged in a delayed matching to sample task. The visibilityof the target stimulus was manipulated such that the word waseither consciously perceived or remained invisible but was stillprocessed. As indicators of local and global processing (Varela etal., 2001), we measured over a wide frequency range (1) time resolvedpower changes of local signals and (2) phase synchronizationacross recording sites. We found that visible and invisibleconditions differed with respect to large-scale synchronizationbut not local neural processing. In addition, only consciouslyperceived stimuli gave rise to a cascade of electrographic eventsthat have been proposed to be associated with perception stabilization,maintenance in working memory, and generation of expectancies.

We propose that the transient large-scale synchronizationis the critical event that triggers these subsequent processesby enhancing the saliency of the activation patterns sufficiently topermit access to consciousness.

Materials and Methods

Experiment 1

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Note to readers: I found the descriptions of the two experiments difficult to follow. There were also discrepancies between the verbal descriptions and Figure 1a. I have clarified (I hope) the presentation in the First Appendix.

Subjects. Fifteen normal healthy subjects gave written informed consentto participate in the study (seven males; mean age, 20.6 years). All werenative Spanish speakers, right handed, had normal or corrected-to normalvision, and were naive to the purpose of the experiment.

Stimuli and task. Participants were engaged in a two-alternative,forced-choice-delayed matching to sample task (320 trials), in which thesample stimuli could be either visible or invisible. The subjects’ task wasto determine as accurately as possible whether a first briefly presented 33ms “sample word” was the same or different from a second “test word”presented 533 ms later (see Fig. 1a). In each trial, participants respondedby pressing one of two different buttons mounted on a response pad,with their right or left index fingers. In seven participants, the sameresponse was at the right button, whereas in eight participants, it was atthe left button. The first word was preceded and followed by maskingstimuli (67 ms each), which changed in luminance between trials renderingthe sample word visible or invisible (experimental conditions). Toassess the responses to the masking stream itself, sample words werereplaced by a blank screen, while the masking stream was kept constant(control conditions). To render control trials perceptually similar to experimental trials, another word, the “control word,” was presented after the mask stream and before test word presentation (see Fig. 1a). Thisdesign enabled us to isolate the response to the sample word by subtractingthe response elicited by the masking stimuli.The stimulus set consisted of 40 disyllabic Spanish words. Syllableswere consonant–vowel. All words were nouns matched in frequency ofusage (S. Sadowsky and R. Martı´nez, unpublished observation) and presented in Howard light font. The geometric masks were presented inwhite or gray color (luminance change) on a black background, renderingthe sample word visible or invisible. The luminance values used inthis experiment were set in a previous control experiment and were keptconstant throughout the subjects. Masks were constructed by mixing anumber of squares and diamonds drawn with identical line thickness asthe font used for the sample words. All stimuli were presented on acomputer screen in enhanced graphic adapter mode (150 Hz refreshrate), located in the central area of the screen, and subtended 2.5 _ 1° of

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visual angle. Each participant ran a training block of 20 trials. Experimentaland control trials were pseudo-randomized within four blocks of 80trials each, interrupted with a variable rest pause. All conditions wereequally presented within a block. The intertrial interval had a randomlength between 1000 and 1500 ms. The experiment was performed in asilent, dimly lit, and electrically shielded room. Special consideration wasgiven to the potential contamination of the EEG signal by the 50 Hz ACcomponent, because the gamma band response includes this frequency.This nonbiological artifact was reduced by recording inside a completelyhermetic Faraday cage. All of the electrical equipment was outside of therecording room with the only exception of the monitor, which was electrically shielded.

Experiment 2

Twenty subjects took part in an unconscious semantic priming experiment(11 males; mean age, 23.8 years), with the same word set and masksas used in the previous experiment. All subjects gave written informedconsent, were native Spanish speakers, right handed, had normal orcorrected-to normal vision, and were naive of the purpose of the experiment.Participants performed a simple semantic classification task byclicking with the left or right index finger (response pattern was reversedfor half of the subjects) to indicate whether the target word was natural ormanmade, respectively. Unknown to them, another word, which couldbe either semantically congruent (e.g., pair key– house) or incongruent(e.g., pair key– dog) with the target word was presented for 33 ms beforethe target and surrounded by forward and backward masks that renderedit invisible. The duration of the prime and mask were the same as in theprevious experiment (mask _ prime _ mask _ 67 _ 33 _ 67 ms,respectively). The target word was presented for 300 ms, and the thirdmask remained on the screen until subjects responded. The prime-targetstimulus onset asynchrony was 100 ms (33 ms prime _ 67 ms forwardmask).

Electrophysiological recording and analysisEEG activity was recorded from a 64-electrode geodesic sensor net referencedto the vertex. The electroencephalogram was digitized at 1000 Hz,and the initial bandpass recording filter was set at 0.01–100 Hz.For the event-related potential (ERP) analysis, the continuous EEGsignal was bandpass filtered (0.5–20 Hz) with a finite impulse response

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(FIR) filter (Kaiser type), which has a linear phase response [passbandgain, 99% (50 –99.9%; _0.1 dB); stopband gain, 1% (1– 49.9%; _40.0dB); Rollof, 2Hz (0.3–10 Hz)]. Then, the filtered signal was segmented ina series of 1100-ms-long epochs. Each epoch started 100 ms before theonset of the first mask. Trials that contained voltage fluctuations exceeding_200 _V, transients exceeding _100 _V, or electro-oculogram activityexceeding _70 _V were rejected. Artifact free trials were averagedin synchrony with first mask presentation, digitally transformed to anaverage reference, and baseline corrected over a 100 ms window. TheEEGLAB Matlab toolbox was used for visualization and topographicplots (Delorme and Makeig, 2004).

For the analysis of time-frequency distributions and phase synchrony,a filter was designed that eliminated only the continuous 50 Hz (AC)component but kept the biological 50 Hz signal. The amplitude andphase of the AC signal was estimated and subtracted from the originalsignal. This eliminated selectively the periodic part of the 50 Hz component(line frequency). Then, a FIR (350 order Hanning window) bandpassfilter (10–100 Hz) was applied, and the filtered signal was analyzedwith a sliding-window fast Fourier transform (window length, 128 ms;step, 10 ms; window overlap, 90%). For every time window and frequencybin, amplitude and phase were computed as follows: signal windows(128 points) were zero-padded to complete 1024 points and fastFourier transformed to get an interpolated frequency resolution of _1Hz per frequency bin. Instantaneous amplitude was then computed bytaking the real and imaginary Fourier coefficients (C( f, t)r and C( f, t)i),squaring and adding them, and taking the square root (sqrt) (i.e., for agiven time window t and frequency bin f ), as follows:

Amp( f, t) _ sqrt(C( f, t)r 2 _ C( f, t)I 2).

This amplitude corresponds to the length of the vector specified by thereal and imaginary Fourier coefficient computed by Pythagora’s law andis equivalent to the magnitude of the observed oscillation at a given timeand frequency point.

During the same time window and frequency bin, phase was computedas the arc tangent (arctg) of the imaginary Fourier coefficientdivided by the real one, as follows:

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Phi( f, t) _ arctg(C( f, t)i/C( f, t)r).

Phi is thus the angle of the vector specified by the real and imaginaryFourier coefficient. For a given time and frequency point, it corresponds to aposition inside the oscillation cycle (peak, valley, rising, or falling slope).These amplitude and phase values are evaluated in the 10–100 Hzfrequency range and in the _500 to _1000 ms period relative to firstmask presentation. Phase information was then used to compute a timevarying phase-locking value (PLV), an index of neural synchrony(Lachaux et al., 1999; Rodriguez et al., 1999). In brief, the method involvescomputing the phase difference in a time window for an electrodepair and assessing the stability of such phase difference through all trials.If _i and _j are unitary vectors representing the phase of signals in electrodesi and j, then the phase difference between such electrodes is aunitary vector obtained by multiplying the first vector by the complexconjugate (conj) of the second:

_ij __i conj(_j).

The PLV is thus the length of the vector resulting from the vector sumof difference vectors through the trials:

PLVij _ abs(1/N___ij),

with the sum operating throughout all of the trials and where N is thenumber of trials. The PLV index ranges from 0 to 1, with value 1 indicatingperfect synchronization (phase difference is perfectly constantthroughout the trials) and value 0 representing total absence of synchrony(phase differences are random). Time-frequency charts of bothphase synchrony and spectral power were normalized to a baseline of 500ms preceding the first mask onset. The normalization involves subtractingthe baseline average and dividing by the baseline SD on a frequency by-frequency basis in the following manner: S is a signal,_ is the averageof the signal during the baseline period, and _ is the SD of the samebaseline period. Then, the normalized signal is given by the following:

SN _ (S __)/_.

In another analysis aiming to analyze the theta activity associated withthe retention interval (from sample-word offset to test-word onset), a

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fast Fourier transform was computed over a 467 ms window, on the rawunfiltered EEG signal. Afterward, the Fourier coefficients correspondingto the theta frequency that showed significantly ( p _ 0.05) higher amplitude(5– 6 Hz) were added over trials and subjects to generate a topographicalmap of theta activity.

Statistical analysisBecause we were interested in long-range coordination of neural activity,we included all electrodes in the calculation to produce a global index ofsynchronization across a large frequency range. Behavioral and EEG datawere analyzed with two-tailed, within-subject ANOVA. The _ level wasset at 0.05 for all tests.

The statistical analyses of the time-frequency distributions and phasesynchrony were all performed on time-frequency charts resulting fromaveraging the electrophysiological responses of all sensors during theentire segment (_500 to 1000 ms after sample-word onset). This resultedin a grand average time-frequency and phase-synchrony chart per experimental condition per subject. Then, those charts were grouped by condition and analyzed by means of a permutation test in search of time frequency windows showing significant effects (Burgess and Gruzelier,1999). Subsequently, those significant time-frequency windows were analyzed with a two-tailed, within-subject ANOVA. The _ level was set at0.05 for all tests.

In the permutation test, the time-frequency charts belonging to differentconditions are mixed to compute a random distribution. This is thenused to evaluate the statistical significance of the results. The permutationtest assumes that the “real” differences between conditions shouldexceed the random differences. The permutation test has advantages overthe Bonferroni correction for multiple comparisons, because the Bonferronicorrection assumes that all measures are independent, an assumptionthat is too strong and weakens the power of the statistical test. Incontrast, the permutation test considers the true dependency among allof the measures.

For the topographical analysis of phase synchrony, we controlled forthe statistical effects of multiple comparisons by choosing a very conservative significance threshold ( p _ 0.00005). This threshold was set as a function of the distribution of synchrony values during the baseline. The

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threshold was chosen to give a probability smaller than 0.00005. Thisthreshold was computed by counting the number of cases larger than thethreshold divided by the total number of cases. This fraction should givea value smaller than 0.00005. By choosing this significance level, one lineper analysis window could be explained, by chance, given the fact thatthere were 64 electrodes with 2016 possible combinations (64 _ 63/2 _2016).

Results

Behavioral measures of visibilityBehavioral results showed that, in the experimental condition inwhich sample words could be perceived, 94.5% of the words wereclassified correctly (F(1,14)_904.5; p_0.001), the mean d being3.85, which implies a highly significant difference from chance(F(1,14) _ 192.2; p _ 0.001). Conversely, in the experimentalcondition that rendered sample words invisible, performancedropped to chance level (52.2%; F(1,14) _ 2.097; p _ 0.170), andthe mean d value did not differ from zero (d _ 0.16; F(1,14) _2.598; p _ 0.129) (Fig. 1b). In control conditions, the success pared with the invisible condition (923 and 1418 ms, respectively;F(1,14) _ 76.139; p _ 0.000018), despite the fact that speed ofresponse was not stressed in the task. Reaction times between thetwo control conditions did not differ (1269 and 1296 ms; F(1,14)_0.361; p _ 0.557).

To determine to which extent the invisible words in the experimentalcondition were still processed, we assessed the depth ofprocessing of the invisible words in an unconscious priming task(Marcel, 1983), using the same stream of stimuli (mask-sampleword_mask-target word), and determined priming effects with areaction time task. This control experiment revealed strongpriming effects of the invisible word. That is, subjects respondedsignificantly faster in the congruent condition (prime and targetword belong to the same semantic category) compared with theincongruent condition (prime and target word belong to differentsemantic categories) (effect size was 15 ms difference between

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congruent and incongruent trials; n_20 subjects; F(1,19)_8.981;p _ 0.007). Therefore, masked words, although invisible, werestill processed.

Activity patterns related to perceptual awarenessThe analyses described below have all been performed after eliminatingeffects caused by differences in mask luminance. The EEGtraces obtained after presentation of the high and low luminancemask alone (control condition) were subtracted from the tracesof the corresponding experimental condition for an analysis windowextending from 500 ms before to 1000 ms after presentationof the first mask. The subtracted conditions are referred here as“visible” and “invisible,” respectively.

The first significant difference between visible and invisiblewords was observed from 80 to 130 ms after sample-word presentation.During this period, the mean phase synchrony at50–57 Hz over all electrode pairs was significantly higher for thevisible than the invisible condition (F(1,14) _ 5.041; p _ 0.044)(Fig. 2b). During the same interval, neither the mean amplitudeof the gamma oscillations (50–57 Hz; F(1,14) _ 0.616; p _ 0.448)nor the mean ERPs calculated over all as well as over occipitalelectrodes differed between conditions (ERP effect over all electrodes:F(1,14) _ 0.005, p _ 0.774, 0.0245 _V difference; ERPeffect over occipital electrodes: F(1,14) _ 1.036, p _ 0.329, 0.3350_V difference) (Figs. 2a, 3).

To obtain more detailed information about activation patterns related to thevisible and invisible conditions, regional distributions of gamma spectral power and phase synchrony were computed for the interval from 260 ms before to 330 ms after onset of the sample word (frequency,50–57 Hz; 150 ms sliding window). Although the patterns of gamma activity

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were spatially homogeneous and similar for the two conditions, the patterns of phase synchrony were markedly different(Fig. 4). In the invisible condition, only few electrode pairs exhibited significant phase synchronization. In the visible condition,in contrast, numerous electrode pairs, both within and across hemispheres,showed significant phase-locking between occipital, parietal, and frontalsites in the time window 40–180 ms after sample-word presentation. In the window between 180 and 330 ms, the pattern of phase synchrony became lateralized over the left hemisphere and restricted to occipito-parietal electrodes, which agrees with the fact that the task involves language processing.

The finding that phase-locking in the visible condition increaseswithout a concomitant increase of gamma power, evenwhen the comparison was restricted to individual electrodes, suggeststhat the main difference between visible and invisible conditions,in this early period, is the coherence of activity among cortical regions rather than the amount of local neural synchronization.

Electrophysiological signatures of further processing ofvisible stimuliA second significant difference between perceptual conditionswas apparent in the ERP from 130 to 430 ms after sample-wordpresentation. In this interval, the mean amplitude of a frontocentralpositivity, peaking at 240 ms after sample-word presentationand resembling P3a, was higher in the visible than in theinvisible condition (F(1,14)_37.766; p_0.00002; 2.3394_V difference).Interestingly, the amplitude of the P3-like componentstarts to diverge at a point in time when the differences in phasesynchrony have vanished. The P3-like component has been relatedto the updating of contents kept in working memory(Donchin, 1981). In addition, the mean amplitude of theta activity

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(5–6 Hz) increased significantly over frontal electrodes in thevisible condition during the interval in which the sample wordhad to be kept in memory (time interval, 67–520 ms) (see supplementalFig. 1, available at www.jneurosci.org as supplementalmaterial). Frontal theta oscillations have been assigned a role inthe maintenance of short-term memories (Jensen and Tesche,2002; Schack et al., 2005). Although it would have been interestingto see whether the theta enhancement started only after theepisode of gamma phase-locking, the necessity to use long windowsfor the assessment of the low-frequency oscillations precludeddetermination of the precise onset of enhanced theta.

A third and more delayed difference between the visible andinvisible conditions was observed immediately after test-wordpresentation. Here, both phase synchrony and gamma powerwere significantly higher during the visible than the invisible conditions.The increase in synchrony, averaged over all electrodes,occurred in the high gamma range (67–80 Hz) and during theinterval 10–40 ms after test-word presentation (visible vs invisible: F(1,14)_11.803; p _ 0.005). Interestingly, in this case thepower of oscillations was also enhanced and in exactly the same frequency range (visible vs invisible: F(1,14) _ 8.006; p _0.015). Because of their short latency, these effects might reflect anticipatoryprocesses that occur only when the subjects have seen the sample word (Courtemanche and Lamarre, 2005). This anticipationwas possible because the interval between sample- and test-word presentation was fixed. The significantly shorter reaction times observed in the visible condition support this interpretation.Finally, there were two significant effects related to test-word presentation that did not differentiate between visible and invisible conditions. First, there was a significant increase in phase synchrony in the

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frequency band from 63 to 83 Hz in the interval 185–240 ms after test-word presentation (visible vs baseline: F(1,14) _22.869, p _ 0.001; invisible vs baseline: F(1,14)_18.720, p_0.001; visible vs invisible conditions: F(1,14)_0.199, p_0.663)Second, there was a significant increase in power of gammaoscillations in a broad frequency range (36–85 Hz) during theinterval of 155–230 ms after test-word presentation (visible vsbaseline: F(1,14) _ 63.524, p _ 0.001; invisible vs baseline:F(1,14)_52.626, p_0.001; visible vs invisible condition: F(1,14)_2.030, p _ 0.180).

In the ERP, test-word presentation evoked P1–N1 components,the latency, amplitude, and spatial distribution of whichwere similar in the visible and invisible conditions (F(1,14) _2.896; p _ 0.115; 1.205 _V difference).Because word visibility was manipulated by changing maskluminance, it could be argued that the differences between visibleand invisible conditions are attributable to luminance variations.To control for this possibility, we performed an additional analysisin which visible trials were subtracted from invisible trials(visible plus light effect) and contrasted with the difference betweencontrol visible and control invisible trials (referred to aslight effect). This contrast should remove any remaining luminanceeffects, and persisting effects should only reflect processesrelated to conscious perception of the sample word. This analysisconfirmed the results described above. There were two episodesof enhanced phase synchrony. One was associated with sample wordpresentation (starting 80 ms after sample-word presentation;frequency range, 50–57 Hz; F(1,14) _ 5.806; p _ 0.033) andthe other with test-word presentation (starting10 ms after test wordpresentation, frequency range 75–80 Hz (F(1,14) _ 8.811,p _ 0.012). In addition, the power of gamma oscillations wasenhanced in association with the presentation of the test word(starting 20 ms after test-word presentation; frequency range,60–75 Hz; F(1,14) _ 6.875; p _ 0.022) (see supplemental Fig. 2,

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available at www.jneurosci.org as supplemental material).Enhanced synchronization can be mimicked by volume conductionif it occurs with zero phase lag. In this case, the possibilityneeds to be considered that a single generator oscillating in therespective frequency increases its power leading to stronger synchronizationof the signals measured on the scalp. Conversely,reduction in the activity of other oscillators can unmask the contributionof a single source, producing again stronger synchronizationon the scalp.We consider it unlikely that this had occurredin the present experiment for the following reasons. First, if theobserved synchronization were attributable to activation or inactivationof one or several generators, it should show up as a differencein the induced gamma activity or in the ERPs betweenexperimental conditions. This was not the case in our experiment.During the interval of enhanced phase-locking, neither theERPs nor the induced gamma oscillations differed between conditions,suggesting that the activity of the contributing generatorswas unchanged.

Second, synchronization caused by volume conduction mustoccur with zero phase difference between electrodes. In our experiment,the phase angles at which synchronization occurredwere not centered on zero and exhibited considerable scatter(__rads) (see supplemental Fig. 3, available at www.jneurosci.org as supplemental material). This means that the most prominentsynchronization did not occur with zero phase lag, as expectedfrom volume conduction. Furthermore, the scatter inphase lag implies that the observed synchronization occurs withvarying time delays from trial to trial, which is incompatible withinstantaneous volume conduction. Third, phase synchronizationcaused by volume conduction should exhibit a distancedependentgradient on the scalp (i.e., phase synchrony should

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decay with interelectrode distance). In our experiment there, wasno evidence for a distance-dependent gradient in PLVs. In fact,the scalp topography shows that synchronization occurred morefrequently between distant electrodes.

Discussion

The first electrographic difference between conscious and nonconsciousstimulus processing was increased phase-locking ofinduced gamma oscillations across widely distributed cortical regions.This suggests that early large-scale synchronization couldbe the event that triggers ignition of the global workspace ofconsciousness, as postulated by Dehaene and Naccache (2001)and Dehaene et al. (2006).

Local and long-range neural synchrony and their putativerole in conscious and unconscious perceptionOur results show similar activation patterns at individual electrodesin the visible and invisible conditions, suggesting that thesame neural generators are activated in both cases. In contrast,phase synchronization across electrodes clearly differentiated betweenconditions, suggesting enhanced long-range coordinationof oscillatory activity only in the visible condition. Several authorshave proposed that conscious perception should be relatedto coordinated dynamical states of the cortical network, ratherthan to the activation of specific brain regions (Fries et al., 1997,2002; Engel et al., 1999; Engel and Singer, 2001; Thompson andVarela, 2001; Singer, 2002; Lamme, 2006). Our results offer directsupport for this notion. In addition, our results and the resultsfrom a previous study investigating the neural dynamics of perceivedand unperceived somatosensory stimuli (Palva et al.,2005) are in line with a recent proposal (Dehaene et al., 2006)relating unconscious processing of information with local coordination

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of neural activity in resonant loops of medium rangeand relating conscious perception with global coordination ofdistant neural activity by long-range synchronization. Interestingly,the global long-distance synchronization found in the visiblecondition was very transient and the earliest event differentiatingconscious from nonconscious processing. After this, otherelectrophysiological measures, such as P3a and theta oscillations,continue to differentiate between consciously and nonconsciouslyperceived words. This suggests that long-distance synchronizationplays a role in triggering the cognitive processesassociated with conscious awareness (Dehaene et al., 2006).However, it remains to be clarified through which mechanismlong-distance synchronization exerts an impact on subsequentcognitive processes.The transient character of the long-distance synchronizationis not entirely compatible with models such as global workspace(Dehaene and Changeux, 2005; Dehaene et al., 2006) and reentrantactivity (Lamme, 2006) because these predict a more sustainedresponse for consciously perceived stimuli. Our resultsshow increased neural synchrony for the visible condition, whichlasts _100 ms but reaches significance only during a short timewindow (_50 ms), suggesting that neural synchronization couldlast longer but is nonetheless transient.The discrepancy between sustained and transient activityfound in different studies could also be attributable to the differentexperimental paradigms. Most of the experiments that havereported sustained activity used either the attentional blink paradigm(Gross et al., 2004; Sergent et al., 2005) or inattentionalblindness (Dehaene and Changeux, 2005). It is still controversialwhether the attentional blink paradigm assesses conscious perceptionor memory processes. It has been argued that subjectscould have conscious access to the stimulus at the moment of itspresentation, yet simply forget it when they are asked to report it(Wolfe, 1999). In fact, experiments on the related phenomenon

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of change blindness show that unattended objects could be fleetinglyrepresented and reported but that their representations disappearas soon as a new object is presented or if the eyes move toa new location (Landmann et al., 2003). Thus, the sustained activityoften reported using such experimental paradigms couldreflect the transfer or maintenance of a stable representation inworking memory and are not necessarily a correlate of consciousperception itself.Early wave of activation that distinguishes conscious fromunconscious processingIn contrast to previous experiments, the results of which suggesta late wave of activation as correlate of sensory awareness (Grosset al., 2004; Sergent et al., 2005), our results indicate that access toconsciousness is triggered by an early coordination (synchronization)of widely distributed neuronal assemblies starting as earlyas 80 ms after stimulus presentation [see also Palva et al. (2005)and Fries et al. (2001) for a similar finding]. This difference mightbe explained by two factors. First, the fast stream of stimuli usedin our experiment might have imposed pressure on the perceptualprocesses, leading to a shortening of the processing timedevoted to each stimulus. Second, in contrast to previous experiments,in our study the neural processes related to perceptionwere segregated in time from those related to decision makingand execution of motor responses. The late correlates of consciousperception described previously might thus reflect a mixtureof cognitive processes (e.g., perception and decision making)that may have masked the brief and early episode of phaselocking.The responses observed after test-word presentationsupport this latter interpretation. The presentation of the testword also triggered a sequence of cognitive processes, but these

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could be executed without imposed delays (e.g., perception, decisionmaking, and acting). In this case, the induced synchronizationoccurred with much longer latency (_200 ms) and was inthe range described in previous experiments. The present findingthat the first electrographic signature of conscious processing hasa short latency is in agreement with the evidence that areas at thehighest level of the processing hierarchy (frontal areas) becomeactive as early as 100 ms after stimulation (Nowak and Bullier,1997) and that high cognitive processes, such as stimulus categorization,can be accomplished within 120 ms (Thorpe et al., 1996;Kirchner and Thorpe, 2006). In addition, our results agree with aseries of studies showing that conscious and unconscious perceptioncan be rapidly distinguished after stimulus presentation (Dehaeneet al., 2001; Pins and Ffytche, 2003; Palva et al. 2005).Additionally, in the same time window, where we found a synchronizationepisode (80–120 ms), Walsh and Cowey (1998)found that applying a TMS magnetic pulse over V1 and/or circumstriateareas can impair visual perception of a briefly presentedstimulus, suggesting that this time window is relevant forconscious perception. In accordance with the present data, theseresults suggest that the brain can process information remarkablyfast and that the divergence of conscious and unconscious processingoccurs within 100 ms after stimulus presentation, implyingthat this early wave of activation might be an essential correlateof conscious perception (Pins and Ffytche, 2003).

Late correlates of conscious processingPrevious studies investigating electrographic correlates of consciousand unconscious processing have evaluated eitherstimulus-locked ERPs (Sergent et al., 2005) or dynamic measuressuch as spectral power or phase synchrony (Srinivasan et al.,

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1999; Gross et al., 2004; Doesburg et al., 2005; Palva et al., 2005).The combination of the different methods applied here allows fora more detailed temporal characterization of the putative EEGevents differentiating between conscious and unconscious processing.Together, the data suggest that only consciously perceivedstimuli give rise to a cascade of processes that have distinctelectrophysiological signatures. In summary, these consisted of(1) an early and global phase-locking of gamma oscillations, (2)an enhancement of a P3a-like component of the ERP and ofsustained theta oscillations over frontal areas that are likely toreflect transfer and maintenance of the perceived stimuli in workingmemory, and (3) an enhancement of power and phaselockingof gamma oscillations before test stimulus presentationthat may be a correlate of the anticipation of the matching betweenshort-term memory contents and sensory input. Our resultson ERPs agree with the data of Sergent et al. (2005), whichsuggests that ERPs evoked by perceived and unperceived stimulistart to diverge around 270 ms. Interestingly, these ERP differencesoccur only after the end of the transient increase in phasesynchrony. Thus, it seems as if the fast and transient large-scalesynchronization enhances the saliency of the activation patternssufficiently to permit access to consciousness and thereby triggersa sequence of processes such as perception stabilization, maintenancein working memory, and generation of expectancies thatare associated with conscious awareness. It remains to be clarifiedwhether the early large-scale synchronization is already the neuronalcorrelate of phenomenal awareness or whether awarenessemerges only from the entirety of the processes following thiscoordinated state.

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Long-range synchronization, conscious perception, and thedepth of processingIt can be argued that the electrophysiological signatures associatedwith conscious perception are simply a reflection of moreextensive processing rather than reflecting mechanisms specificallyassociated with awareness. We consider this as unlikely forseveral reasons. The finding that visible and invisible words inducedgamma oscillations of similar power and distribution suggeststhat invisible words were thoroughly processed. In addition,in the control experiment with the subliminal priming task, weevaluated the depth of processing of the unperceived word usingthe same protocol as in the main experiment. Prime words, althoughnot perceived, had a clear behavioral effect indicating thatthe unconsciously perceived words are processed. Therefore, weconsider it likely that the key event mediating access to consciousnessis the early long-distance synchronization of neural assemblies,rather than the mere depth of processing in the variouscortical areas involved in written word processing.

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cortical activation without visual awareness revealed by fMRI studiesof hemianopic patients. Vision Res 41:1459 –1474.Grill-Spector K, Kushnir T, Hendler T, Malach R (2000) The dynamics ofobject-selective activation correlate with recognition performance in humans.Nat Neurosci 1:91–100.Gross J, Schmitz I, Schnitzler K, Kessler K, Shapiro B, Hommel A, SchnitzlerA (2004) Modulation of long-range neural synchrony reflects temporallimitations of visual attention in humans. Proc Natl Acad Sci USA101:13050 –13055.Jensen O, Tesche C (2002) Frontal theta activity in humans increases withmemory load in a working memory task. Eur J Neurosci 15:1395–1399.Kirchner H, Thorpe S (2006) Ultra-rapid object detection with saccadic eyemovements: visual processing speed revisited. Vision Res 46:1762–1776.Kleinschmidt A, Buchel C, Hutton C, Friston C, Frackowiak R (2002) Theneural structure expressing perceptual hysteresis in visual letter recognition.Neuron 34:659–666.Lachaux J, Rodriguez E, Martinerie J, Varela F (1999) Measuring phasesynchronyin brain signals. Hum Brain Mapp 8:194 –208.Lamme V (2006) Towards a true neural stance on consciousness. TrendsCogn Sci 10:494 –501.Landmann R, Spekreijse H, Lamme V (2003) Large capacity storage of integratedobjects before change blindness. Vision Res 43:149 –164.Marcel A (1983) Conscious and unconscious perception: experiments onvisual masking and word recognition. Cogn Psychol 15:197–237.

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reveal covert facial recognition in prosopagnosia. Neuropsychologia27:905–912.Rodriguez E, Lachaux JP, Martinerie J, Renault B, Varela FJ (1999) Perception’sshadow: long-distance synchronization of human brain activity.Nature 397:430–433.Schack B, Klimesch W, Sauseng P (2005) Phase synchronization betweentheta and upper alpha oscillations in a working memory task. Int J Psychophysiol57:105–114.Sergent C, Baillet S, Dehaene S (2005) Timing of the brain events underlyingaccess to consciousness during the attentional blink. Nat Neurosci8:1391–1400.SingerW (2002) Consciousness from neurobiological perspective. In: Neuralcorrelates of consciousness (Metzinger T, ed), pp 121–137. Cambridge,MA: MIT.Srinivasan R, Russell D, Edelman G, Tononi G (1999) Increased synchronizationof neuromagnetic responses during conscious perception. J Neurosci19:5435–5448.Thompson E, Varela F (2001) Radical embodiment: neural dynamics andconsciousness. Trends Cogn Sci 10:418–425.Thorpe S, Fize D, Marlot C (1996) Speed of processing in the human visualsystem. Nature 381:520 –522.Varela F, Lachaux J, Rodriguez E, Martinerie J (2001) The brain web: phasesynchronization and large-scale integration. Nat Rev Neurosci2:229 –239.Vuilleumier P, Armony J, Clarke K, Husain M, Driver J, Dolan R (2002)

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Neural response to emotional faces with and without awareness: eventrelatedfMRI in a parietal patient with visual extinction and spatial neglect.Neuropsychologia 40:2156 –2166.Walsh V, Cowey A (1998) Magnetic stimulation studies of visual cognition.Trends Cogn Sci 2:103–110.Wolfe JM (1999) Inattentional amnesia. In: Fleeting memories: cognition ofbrief visual stimuli (Coltheart V, ed), pp 71–91. Cambridge, MA: MIT

FIGURES

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.

Figure 1. Design and behavioral results of experiment. a, Stimulus sequence. The task was to compare a briefly presented word (sample word) with a subsequent word (test word). The sample word visibility was controlled by changing the luminance of the masks. Control conditions were created to assess the brain response to the mask stream. The left timeline shows the duration of eachstimulus. The right timeline shows the cumulative time. b, Behavioral performance. The left plot shows stimulus detectability for all conditions, expressed as detectability index (d ), and the middle plot is the success rate. The right plot shows the reaction time for all conditions. Plots indicate mean performance_1 SD

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Figure 2. Spectral power and phase synchrony to visible and invisible words. The visible condition (visiblecontrol_visible)and invisible condition (invisiblecontrol_invisible) are shown. The time-frequency plot shows the grand average of all electrodes.The phase-synchrony plot shows the grand average for all of the electrode pairs. The color scale indicates amplitude in SD,calculated over a 500msbaseline. Zero corresponds to first mask onset. Vertical lines indicate sample- and test-word presentation.

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a, Timefrequency plot. Two increments of gamma-power emission are visible. The first is only present in the visible condition,and the second is present in both conditions. b, Phase synchrony. There are three statistically significant bursts of synchronousactivity. The first and second peaks occur only in the visible condition. No significant differences were found for the last peak.

Figure 3. ERPs elicited by visible and invisible words. a, Time course of responses to visible and invisible words at different electrodes. The x-axis shows time, and the y-axis shows electrodes; thecolor scale is expressed in microvolts. Zero represents the first mask onset. Vertical lines indicate sample-word and test-word presentation. Small lines at the top of the graph code for the two timewindows corresponding to the voltage scalp maps in b. b, Voltage scalp map for two windows indicated for visible and invisible conditions. The first difference started at 130 ms after sample-wordpresentation, as a P300a-like component. Then, a P1-like component was observed200 ms after test-word presentation, for both conditions. c, Time course of the signal recorded from left frontal electrode F3.

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Figure 4. Scalp topography of induced gamma power and phase synchrony for the visible and invisible condition. Top row,Visible condition. Bottom row, Invisible condition. The background color indicates induced gamma power averaged in a 50 –57 Hzfrequency range. Each head represents the average of a 150 ms time window. Time 0 indicates the onset of the sample word. Linesconnect pairs of electrodes displaying significant synchronization ( p0.000001). Gamma activity does not statistically differbetween visible and invisible conditions. In contrast, phase synchrony is stronger in the visible condition during the 40 –180 mstime window involving occipito, parieto, and frontal electrodes, with intrahemispheric and interhemispheric connections. In thewindow between 180 and 330 ms, the pattern of phase synchrony lateralizes over the left hemisphere and restricts to occipitoparietalelectrodes.

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APPENDICES

35

Zeroth Appendix

C

S L A

IONS

O L I T

Everything that changes is in reality an oscillation. We deny, or ignore this knowledge through the use of idealizations (e.g. classical physics). Sometimes this is helpful.

Oscillation is the variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with "oscillation". Oscillations occur not only in physical systems but also in biological systems and in human society.

The following is a list of synonyms for “oscillation”.

OSCILLATIONActActionAmbulationBeatCadenceCadencyChangeChangeabilityChangingConvulsionDensityDisequilibriumDriftDynamicsFaltering

FlashFlightinessFlowFluctuationFluctuationFluidityFlutterFluxFrequencyGesticulationGestureGlimmerGlitterIrregularityJitterJudder

LocomotionMeterMotilityMoveMutabilityPalpitationPassagePassingPliancyPoundPressureProgressPulsationPulseQuakeQuiver

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QuiveringRepetitionRepetitionsResonanceRestlessnessReverberationRhymeRhythmRippleShakeShakeShakinessShimmerShudderSignalSparkleStammeringStirStreamStumblingStutteringSurgeSwaySwayingSweepSwellSwingTempoThrobThumbTicTickTransienceTrembleTwinkleUncertaintyUndulationUnfixednessUnpredictabilityUnsteadinessVacillationVariabilityVibrationVibrationVolatility

WaveWaveringWavering

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Below is a brief discussion of oscillations and their role in science, including neuroscience.

Simple systems

The simplest mechanical oscillating system is a mass attached to a linear spring, subject to no other forces; except for the point of equilibrium, this system is equivalent to the same one subject to a constant force such as gravity. Such a system may be approximated on an air table or ice surface. The system is in an equilibrium state when the spring is unstretched. If the system is displaced from the equilibrium, there is a net restoring force on the mass, tending to bring it back to equilibrium. However, in moving the mass back to the equilibrium position, it has acquired momentum which keeps it moving beyond that position, establishing a new restoring force in the opposite sense. The time taken for an oscillation to occur is often referred to as the oscillatory period.

The specific dynamics of this spring-mass system are described mathematically by the simple harmonic oscillator and the regular periodic motion is known as simple harmonic motion. In the spring-mass system, oscillations occur because, at the static equilibrium displacement, the mass has kinetic energy which is converted into potential energy stored in the spring at the extremes of its path. The spring-mass system illustrates some common features of oscillation, namely the existence of an equilibrium and the presence of a restoring force which grows stronger the further the system deviates from equilibrium.

The harmonic oscillator offers a model of many more complicated types of oscillation and can be extended by the use of Fourier analysis.

Damped, driven and self-induced oscillations

In real-world systems, the second law of thermodynamics dictates that there is some continual and inevitable conversion of energy into the thermal energy of the environment. Thus, damped oscillations tend to decay with time unless there is some net source of energy in the system. The simplest description of this decay process can be illustrated by the harmonic oscillator. In addition, an oscillating system may be subject to some external force (often sinusoidal), as when an AC circuit is connected to an outside power source. In this case the oscillation is said to be driven.

Some systems can be excited by energy transfer from the environment. This transfer typically occurs where systems are embedded in some fluid flow. For example, the phenomenon of flutter in aerodynamics occurs when an arbitrarily small displacement of an aircraft wing (from its equilibrium) results in an increase in the angle of attack of the wing on the air flow and a consequential increase in lift coefficient, leading to a still greater displacement. At sufficiently large displacements, the stiffness of the wing dominates to provide the restoring force that enables an oscillation.

Coupled oscillations

The harmonic oscillator and the systems it models have a single degree of freedom. More complicated systems have more degrees of freedom, for example two masses and three springs (each mass being attached to fixed points and to each other). In such cases, the behavior of each variable influences that of the others. This leads to a coupling of the oscillations of the individual degrees of freedom. For example, two pendulum clocks mounted on a common wall will tend to synchronise. The apparent motions of the individual oscillations typically appears very complicated but a more economic, computationally simpler and conceptually deeper description is given by resolving the motion into normal modes.

Continuous systems - waves

As the number of degrees of freedom becomes arbitrarily large, a system approaches continuity; examples include a string or the surface of a body of water. Such systems have (in the classical limit) an infinite number of normal modes and their oscillations occur in the form of waves that can characteristically propagate.

Neural Oscillations.

The concept of neural oscillations is close to the concept of brain waves. However, the latter usually refers to EEG recordings obtained from the skull, and the former refers to more invasive recording techniques such as single-unit recordings with extracellular electrodes, intracellular recordings of neuronal potentials and recordings of local field potentials (LFPs) using electrodes directly contacting the brain. They occur at different frequency ranges, in different brain areas, and some type of oscillations have been related to particular behaviors. It is important to note that non-action potential oscillations, such as those in LFPs and EEGs, need not be based in neuronal activity or in action potential activity, but in extracellular currents in the neuropil.

Visual system

Neuronal oscillations became a hot topic in Neuroscience in the 1990s when the studies of the visual system of the brain by Gray, Singer and others appeared to support the neural binding hypothesis. According to this idea, synchronous oscillations in neuronal ensembles bind neurons representing different features of an object. For example, when a person looks at a tree, visual cortex neurons representing the tree trunk and those representing the branches of the same tree would oscillate in synchrony to form a single representation of the tree. Some scientists have questioned whether these oscillations are prominent, or relevant, in ensembles that consider only action potential activity [1]. These oscillations are, however, prominent in differential LFP recordings taken between upper and lower cortical layers, which suggests a local current, but not action potential, basis for their origin[2].

Olfactory System

In a series of elegant papers beginning in 1994, Gilles Laurent and his colleagues at the California Institute of Technology showed that oscillations exist in the brain of the locust, that different odors lead to different subsets of neurons firing on different sets of oscillatory cycles (Wehr and Laurent, 1996), that the oscillations can be disrupted by GABA blocker picrotoxin (MacLeod and Laurent, 1996), that disruption of the oscillatory synchronization leads to impairment of behavioral discrimination of chemically similar odorants in bees (Stopfer et al., 1997) and to more similar responses across odors in downstream β-lobe neurons (MacLeod et al., 1998).

Motor system

Oscillations have been also reported in the motor system. Murthy and Fetz (1992) described motor cortical oscillations in monkey cortex when the monkeys performed motor acts that required significant attention (retrieval of raisins from unseen locations). Similar oscillations were observed in motor cortex during periods of immobility by the groups of John Donoghue and Roger Lemon.

Oscillating neurons have been also reported in somatosensory cortex (Mikhail Lebedev and Randall Nelson) and in premotor cortex (Mikhail Lebedev and Steven Wise). In these cortical areas, 20-40 Hz oscillations are often observed during periods of attentive immobility, and they typically disappear during movements. These oscillations may well be driven by the highly regular pattern of input activity from muscle spindles to somatosensory proprioceptive areas [3].

Large-scale oscillations

Oscillations recorded from multiple cortical areas can become synchronized and form a large-scale network, whose dynamics and functional connectivity can be studied by means of spectral analyses and Granger causality (Andrea Brovelli, Steven L. Bressler and their colleagues, 2004) measures.

Brain-computer interface

Pesaran, Andersen and their colleagues suggested that neural oscillations can be used as a control signal for brain-computer interfaces because oscillatory pattern depends on the direction of movement that the monkey prepares to execute. Recent study of Rickert and colleagues (2005) supports this suggestion.

Oscillations and perception

Neural oscillations may have different functional roles in different brain areas, and their functional role continues to be a matter of debate. Neural oscillations have been hypothesized to be involved in the sense of time (Buhusi and Meck, 2005) and in somatosensory perception (Ahissar and Zacksenhouse, 2001) among other functions.

Neuronal mechanisms of oscillations

Neuronal mechanisms of oscillations are complex. Scientists suggest that both intrinsic neuronal properties (Rodolfo Llinas and colleagues, 1991) and neural network properties are involved.

Let’s look at some simple oscillations and familiarize ourselves with how to describe them in detail.

Fred

Barbara

Look at the two oscillations, named Fred and Barbara. Try describing them.

Mathematics gives us a way of writing explicit and detailed instructions for how to draw lines like Fred and Barbara.

These sorts of mathematical instructions are called

FUNCTIONS

Remember, for our purposes, a function is an instruction for drawing a line in a coordinate system.

Fred and Barbara are from a family of functions called trigonometric functions.

Fred and Barbara are lines drawn by the sine function, which looks like this:

f(t) = sin Read the phrase this way: The value of

the function at time ‘t’ is equal to the sine of the angle ‘’.

f stands for “function”

t stands for “time” and is written in seconds

sin is the abbreviation for “sine”

stands for an angle between 0 and 360 degrees and is written in degrees

For a nice review of trigonometric functions, check here:

http://www.univie.ac.at/future.media/moe/galerie/wfun/wfun.html#winkelf

Go to the site below and click on the red button for Graphs of sin, cosine an tangent to see how these functions are related to the circle.

http://www.univie.ac.at/future.media/moe/galerie/fun2/fun2.html#sincostan

The sine and cosine functions give us three kinds of information:

How tall the wave is, in other words, the values of the y axis that it travels between. How many times the wave repeats itself in one second. How many degrees on the circle correspond to the wave at any time.

Look at Fred again.

Fred is 1 unit tall. This value is called Fred’s AMPLITUDE

Fred moves one cycle in 6 seconds, or 1/16 of a wave in a second. This value is Fred’s frequency. Frequency is written as cycles per second and is usually represented by the Greek letter . To convert from degrees per second to cycles per second, divide degrees per second by 360

The red dot on Fred is not a zit. It marks a spot corresponding to a place on the unit circle at a given time. This is called

Fred’s phase

These three kinds of information

AMPLITUDE

Frequency Phase

are the only kinds of information a simple sinusoidal oscillation can carry.

Here’s how to rewrite the sine function to change AMPLITUDE

Frequency Phase

Multiply the sine function itself by the amplitude you want to get the amplitude you want:

f(t) = AMPLITUDE sin

Multiply the cycles per second by the frequency you want to get the frequency you want:

f(t) = AMPLITUDE sin Frequency

To change the phase, add the phase you want to the frequency:

f(t) = AMPLITUDE sin (Frequency + Phase)With you at the controls of the sine function, you can change its amplitude, frequency and phase to be whatever you want. Well done!!!!

Now for some hands on twiddling the knobs of the sin function.

Go to: http://www.univie.ac.at/future.media/moe/galerie/fun2/fun2.html#sincostan

Click on the red button Function Plotter.

Go to the box at the bottom of the window.

Type in: sin(x)Click: DRAW

You should see a red curvy line that resembles Fred and Barbara. Indeed, this is a family resemblance, because like Fred and Barbara, this is a sine wave.

Go to the top of the pageClick: CLEAR

In the bottom box, type in: 5*sin(x)Click: DRAW

What did you think would happen?

The sine wave got bigger, because you increased the AMPLITUDE.

Click: CLEAR.

Go to the box and type: sin(4*x).

More of the up and down waves appear. You have increased the Frequency.

Click: CLEAR

Go to the box and type: sin(x+25)Go to the box again and type: sin(x)

You should see a red wave and a green wave. They are not superimposed on one another. The red wave seems to be a

little bit ahead of the green wave. You have changed the Phase of the green wave with respect to the red wave.

THE COMPLETE SINE WAVE GENERATOR

You have got a very fine new tool for your maths tool box. Before long, you will have many others. O frabjous day, Kalooh, kalay!!!

First Appendix

A description of the two experiments discussed in this paper.

Experiment 1 requires people to match words. This is assumed to be a “low order” cognitive task, like pattern matching. Can you tell if two patterns which you had never seen before were the same or different?

Experiment 2 s a study designed to explore the effects of unconscious priming on a semantic matching task. It is assumed to be a “high level” cognitive task. What effect do you think the priming will have on the semantic classification of the Target word?

Experiment 1 has four conditions:

Experimental Condition 1: Sample word visible Test word visibleExperimental Condition 2: Sample word invisible Test word visibleControl Condition 1: Blank screen Test word visibleControl Condition 2 Blank screen Control word visible Test word visible

A diagram of Experiment 1 is shown below.

Diagram of Experiment 1, Experimental Condition 1.

Sample word visible Test word visible

This is a straightforward delayed matching to sample task. See the Sample word for a split second. Wait half a secondSee the Test word. Same? Or different?

Mask Sample Mask Blank screen Mask Test 67 ms 33 ms 67 ms 153 ms 200 ms 33 ms| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |0 100 ms 200 ms 300 ms 400 ms 500 ms 600 ms

The mask is presented for 67 ms. The Sample word is presented for 33 ms. The mask is presented for 67 ms.

(NOTE: The luminance of the masks is low, so the Sample word is visible.) A blank screen is presented for 153 ms. The mask is presented for 200 ms. The test word is presented for 33 ms. After viewing the Test word, the subject must signal whether the Test word was the same or different than the

Sample word.

Diagram of Experiment 1, Experimental Condition 2.

Sample word invisible, Test word visible

Watch the screen. Do you see the Sample word? Now look at the Test word. Same? Or different?

Mask Sample Mask Blank screen Mask Test 67 ms 33 ms 67 ms 153 ms 200 ms 33 ms| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |0 100 ms 200 ms 300 ms 400 ms 500 ms 600 ms

The mask is presented for 67 ms. The sample word is presented for 33 ms. The mask is presented for 67 ms.

(NOTE: The luminance of the masks is high, so the Sample word is invisible.) A blank screen is presented for 153 ms. The mask is presented for 200 ms. The test word is presented for 33 ms. After viewing the Test word, the subject must signal whether the Test word was the same or different than the

Sample word.

Experiment 1, Control Condition 1 puts a blank screen where the Sample word was. The luminance of the masks is kept constant. We assume the masking produces its own brain signal. By having the masking without either a visible or an invisible Sample word, we can subtract the part of the signal due to the masking from the Experimental conditions.

Experiment 1, Control Condition 2 puts a blank screen where the Sample word was. It adds a Sample word somewhere during the 153 ms blank screen interval.

Experiment 2 requires people to observe a word and then indicate whether the word is “natural” or “man made”. However, there is a sneaky part. Unbeknownst to the subjects, in the place of the Sample word in the previous experiment, a Prime word was given which was either congruent with the Test word (e.g. Prime word “key”, Sample word “house”) or incongruent (e.g. Prime word “dog”, Sample word “key”). The Prime word was made invisible by the high luminance masks.

A diagram of Experiment 2 is shown below:

Diagram of Experiment 2,Prime word invisible Target word visible

Mask Prime Mask Blank screen Mask Target 67 ms 33 ms 67 ms 153 ms 200 ms 33 ms| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |0 100 ms 200 ms 300 ms 400 ms 500 ms 600 ms

The mask is presented for 67 ms. The Prime word is presented for 33 ms. The mask is presented for 67 ms.

(NOTE: The luminance of the masks is high, so the Prime word is invisible.) A blank screen is presented for 153 ms. The mask is presented for 200 ms. The Target word is presented for 33 ms. After viewing the Target word, the subject must indicate whether it is man made or natural.

Second Appendix

This is about variables.

In experimental psychology, a variable is a measurable factor, characteristic, or attribute of an individual or a system—in other words, something that might be expected to vary over time or between individuals.

There are a whole lot of variables in the experiments we are reading.

Experiment 1.

The signals from 64 electrodes.

15 different people.

40 conscious delayed-matching tasks.

40 unconscious delayed-matching tasks.

Third Appendix

EEG recording

In the old days, EEG signals were recorded by pen writers. If you scribble on a piece of paper, something like

you get a rough idea of what an EEG signal recorded by a pen writer looks like.

Here’s some real EEG signals

Don’t forget that these pen-written signals are depictions of electrical activity from the brain. There’s lots and lots of electrical activity around, so to make the signals as valid as possible (to be really careful to record the brain signals, and not the signals from somebody’s hair dryer) the raw record is filtered in various ways.

The filters remove signals that are bigger then the brain is likely to produce.

They remove frequencies that are lower or higher than the brain is likely to produce.

This is why there is all the stuff about filters in the paper.

Fourth Appendix

Digital signal processing and the discrete Fourier transform

There are two kinds of signals: 1. analog, which are continuous , like an EEG record; 2. discrete, which are a series of separate tones or flashes or voltages or what have you, like Morse code. Discrete signals can be translated into digital information.

If you recall that computers are also commonly called digital computers, you will probably surmise that digital signals are the most familiar. That’s basically right. Given an analog signal, any experimental psychologist will just itch to change it into a digital signal so that it can be analyzed by her computer.

It’s hard to characterize a continuous signal.

It’s like trying to tell somebody the shape of a big ball of tangled up string.

Where do you start? Or stop?

Luckily for us, a specialized group of human being called signal processing engineers

Ah, no. Wrong kind of engineer.

More like

have given us a bag of tricks for how to SAMPLE continuous signals. Once they are sampled, continuous signals turn into discrete signals.

What is even better, we can use discrete signals in the Fourier transform, in which case it is called

?

The DFT is our Friend.

The

discrete Fourier transform

Remember, it’s not called the discrete Fourier transform because it’s good at keeping secrets. It’s called that because it works with digital information.

“The discrete Fourier transform is a mathematical procedure used to determine the harmonic, or frequency, content of a discrete signal sequence. Although, for our purposes, a discrete signal sequence is a set of values obtained by periodic sampling of a continuous signal in the time domain, we’ll find that the DFT is useful in analyzing any discrete sequence regardless of what that sequence actually represents. The DFT’s origin, of course, is the continuous Fourier transform….”

Richard G. Lyons, UNDERSTANDING DIGITAL SIGNAL PROCESSING

Fifth Appendix

Fourier analysis

Fourier analysis is a method of mathematical analysis invented by Jean Baptiste Joseph, Baron de Fourier in the eighteenth century.

You do not have to master Fourier analysis to understand the main points of this paper, but this section tries to give you a sense of what it is.

The best beginning book on the subject is:

Transnational College of Lex 1998 Who is fourier? A mathematical adventureBoston Language Research Foundation

A good intermediate discussion is at: http://www.complextoreal.com/tutorial.htm

The gold standard is:

Fourier’s Big Discovery was

No matter how complicated it is, a wave that is periodic – with a pattern that repeats itself –consists of the sum of many simple waves.

A complicated wave is the sum of simple waves!

An EEG signal is nothing but a complicated, periodic wave. Brilliant! So we can analyze it by finding out what simple waves have to be added together to produce it.

Just for fun, let’s pretend that we are trying to discover a way to do that ourselves.

We have been looking at a whole bunch of EEG records:

Yikes, they don’t make any sense at all!

About all that we can say for sure is

They oscillate They start at a particular place

They go up and down certain distances, but no further

Put on the old thinking cap.

(Instructions for making your own thinking cap here: http://www.professorsolomon.com/thinkingcap.html)

If we want to draw something that oscillates, starts at a certain place, and goes up and down a certain distance but no further, why, that’s a job for the sine and cosine functions.

Remember, for our purposes, a function is an instruction for drawing a line in a coordinate system.

f (t) = sin

f (t) = cos

The two trigonometric functions tell us to draw lines that looks like these:

By looking at these lines, we can see the following:

The sine function starts at y = 0, x = 0 in the coordinate system. The cosine function starts at y = 1, x = 0 in the coordinate system.

If we want to make the lines start at different values than 0 or 1, or if we want the waves to be bigger or smaller, we can multiply them like this:

f (t) = a*sin

f (t) = b*cos

So if we wanted to make the sine wave twice as tall, then we would let a = 2. If we wanted to start the cosine line at 1.34789, we would make b = 1.34789.

If we wanted to have the lines start at some value other than x = 0, we just have to add the value where we want them to start, like this:

f (t) = a0 + a*sin f (t) = a0 + b*cos

Now recall the trick that Fourier used. He discovered that you can add two of these lines together to make a third line which is the sum of the others. Our mantra:

A complicated wave is the sum of simple waves!

HANDY SINE AND COSINE ADDER

We can start by adding one sine or cosine and another sine or cosine:

http://mathinsite.bmth.ac.uk/html/applets.html#sineadditionAnchor

Using the Java Applet at the web site above, can you draw a straight line using nonzero amplitudes of the waves?

What happens if you keep the amplitudes constant and vary the periods?

FOURIER SERIES GENERATOR

The site listed below allows you to create complicated waves by varying 11 cosine waves and 10 sine waves. Using this great little device, you can “reverse engineer” complicated waves.

http://www.univie.ac.at/future.media/moe/galerie.html

Can you make a square wave?

Can you make a wave that looks like an EEG?

The multiple simple waves that are added together are called the Fourier series. The mathematical formula for the Fourier series looks like this

f(t) = a0 + a1cos t + b1sin t + a2cos 2t + b2sin 2t

+ ………………………

+ ancos nt + bnsin nt

This formula can draw any periodic wave, no matter how complicated!!!!!!!

This complicated looking thing is also called a function. “A function is a set of instructions for drawing a line in a coordinate system.”

Consider each term to be a separate instruction. What do they mean?

a0 - Call this the “envelope adjuster”. Without this gizmo, all our waves could only oscillate with zero at their center.

That is, they could only oscillate very symmetrically between 1 and -1, or 5 and -5, or the like. a0 lets us draw waves that oscillate between any values that we want.

Go back to the applet for drawing complicated waves and fiddle with the a0 and you will see what this does.

a1cos t - This one draws the fundamental wave with the origin at 1. It can also be used to shift a sine wave fundamental to the right or left.

b1sin t – This one draws the fundamental wave with the origin at 0. It can also be used to shift a cosine wave fundamental to the right or left.

ancos nt These terms, where ‘n’ can be any integer from 1 to , provide increasing degrees of fine tuning to the picture you are drawing.

bnsin nt

BUT WAIT! What the heck do the an and bn terms do?

Referring back to the Fourier Series Generator, these terms are the same as the slides in the generator. They increase or decrease the amplitude of the waves.

When we are trying to ANALYZE a complicated wave, rather than build one, these an and bn thingies are just what we need to find. They are called the

FOURIER COEFFICIENTS

When you find the Fourier coefficients for a complicated wave, you have all the information you need to do all the analyzing tricks you want.

So this is Fourier’s second trick.

The first one we already learned:

A complicated wave is the sum of simple waves!

Now remember this one:

We can analyze any complicated wave by finding the coefficients of each simple wave that makes it up.

We are not going to go through in detail the technique of how to do this. It involves a kind of mathematical filter. But we want you to have these tools in your tool box so that you can refer to them if you want to learn about them later. You can find a very clear discussion of how these tools are applied in Chapter 3 of the introductory book mentioned above - Who is fourier? A mathematical adventure. So here they are

THE a0 FINDER

This tells us that to find the Fourier Coefficient a0, we find the area from 0 to T (one period) for complicated wave f(t), then divide by T.

THE SINE WAVE AMPLITUDE FINDER

This tells us that to find the sine wave coefficient bn, multiply the complicated wave f(t) by sin nt, find the area from 0 to T (one period), then divide by T/2.

THE COSINE WAVE AMPLITUDE FINDER

This tells us to find the cosine wave coefficient an, multiply the complicated wave f(t) by cos nt, find the area from 0 to T (one period), then divide by T/2.

Now we have a method for getting all the Fourier coefficients. So what?

Well, we have a way of completely specifying any complicated wave. We have the wave’s signature, if you like. In Mathspeak, the wave signature is called its

SPECTRUM.

By putting our Fourier coefficients into a spectrum, we can tell at a glance which sine and cosine waves make up the complicated wave and in what quantity. We use a coordinate system with the AMPLITUDE (an ) on the vertical or y axis, and FREQUENCY (nt) on the horizontal or x axis).

Let’s pretend we have a special device called a Spectrum Analyzer. (These exist, but we are going to use an imaginary one because it’s easier.) The spectrum analyzer is a box that takes an EEG signal as input, and outputs the EEG spectrum.

Spectrum Analyzer

EEG signal

A M

P L

I T

U D

E

frequency

THE EEG SPECTRUM

Earlier, we discussed the three characteristics of the wave that carry information. Which one does the spectrum leave out?

There is one more way of writing the Fourier formulas that is good to know about. It’s handy. It’s used in calculations. So here we will present the Radiant Radian Recipe for the Fourier formulas.

The Radiant Radian Recipe

First, assemble the following ingredients –

1 circle1 piece of string1 scissors1 pencil1 straight edgeThe formula for the circumference of a circle

Lay the circle on a table top and roll until flat.

Voilá

Stretch the string along a radius of the circle, and cut it so it is the same length as the radius:

Take the cut piece of string and lay it along the circumference of the circle -(Imagine that the string is stretched around the circumference so it makes a smooth line.

Draw a line from each end of the string to the center of the circle –

The angle created by the two lines you have drawn is called 1 radianA radian is a unit of measure, just like the degree.

If we want to – and we do want to – we can find how many radians make up the circumference of a circle.

No kidding, 1 radian = 57.2958 degrees.

One way is to divide the circumference in degrees by radians in degrees –

What are we to make of the number 6.2831830605384687882881467751563? Does this number mean anything to you? How could we find out?

OOOhhhh, I know! Let’s ask GOOGLE!

And GOOGLE responds: Your search - 6.2831830605384687882881467751563 - did not match any documents.

Now what?

Well, recall that the equation for the circumference of a circle is

C = d

C = 2r2r = 2r

And the number of radians in 1 circle is the circumference r

So then

2r = 2r r r

2 r = 2 r r r

C = 2

360 = 2 RADIANS !!!!!!

SIXTH APPENDIX

Fast Fourier Transform

SEVENTH APPENDIX

EEG frequencies

Normal Activity

One second of EEG signal

The EEG typically described in terms of (1) rhythmic activity and (2) transients. The rhythmic activity is divided into bands by frequency. To some degree, these frequency bands are a matter of nomenclature (i.e., any rhythmic activity between 8-12 Hz can be described as "alpha"), but these designations arose because rhythmic activity within a certain frequency range was noted to have a certain distribution over the scalp or a certain biological significance.

Most of the cerebral signal observed in the scalp EEG comes falls in the range of 1-20 Hz (activity below or above this range is likely to be artifactual, under standard clinical recording techniques):

delta waves. Delta is the frequency range up to 3 Hz. It tends to be the highest in amplitude and the slowest waves. It is seen normally in

adults in slow wave sleep. It is also seen normally in babies. It may occur focally with subcortical lesions and in general distribution with diffuse lesions, metabolic encephalopathy hydrocephalus or deep midline lesions. It is usually most prominent frontally in adults (e.g. FIRDA - Frontal Intermittent Rhythmic Delta) and posteriorly in chilldren e.g. OIRDA - Occipital Intermittent Rhythmic Delta).

theta waves. Theta is the frequency range from 4 Hz to 7 Hz. Theta is seen normally in young children. It may be seen in drowsiness or

arousal in older children and adults; it can also be seen in meditation. Excess theta for age represents abnormal activity. It can be seen as a focal disturbance in focal subcortical lesions; it can be seen in generalized distribution in diffuse in diffuse disorder or metabolic encephalopathy or deep midline disorders or some instances of hydrocephalus.

alpha waves. Alpha is the frequency range from 8 Hz to 12 Hz. Hans Berger named the first rhythmic EEG activity he saw, the "alpha

wave." This is activity in the 8-12 Hz range seen in the posterior regions of the head on both sides, being higher in amplitude on the dominant side. It is brought out by closing the eyes and by relaxation. It was noted to attenuate with eye opening or

mental exertion. This activity is now referred to as "posterior basic rhythm," the "posterior dominant rhythm" or the "posterior alpha rhythm." The posterior basic rhythm is actually slower than 8 Hz in young children (therefore technically in the theta range). In addition to the posterior basic rhythm, there are two other normal alpha rhythms that are typically discussed: the mu rhythm and a temporal "third rhythm". Alpha can be abnormal; for example, an EEG that has diffuse alpha occurring in coma and is not responsive to external stimuli is referred to as "alpha coma".

smr waves. mu rhythm is alpha-range activity that is seen over the sensorimotor cortex. It characteristically attenuates with movement of

the contralateral arm (or mental imagery of movement of the contralateral arm).

beta waves. Beta is the frequency range from 12 Hz to about 30 Hz. It is seen usually on both sides in symmetrical distribution and is most

evident frontally. Low amplitude beta with multiple and varying frequencies is often associated with active, busy or anxious thinking and active concentration. Rhythmic beta with a dominant set of frequencies is associated with various pathologies and drug effects, especially benzodiazepines. Activity over about 25 Hz seen in the scalp EEG is rarely cerebral (i.e., it is most often artifactual). It may be absent or reduced in areas of cortical damage. It is the dominant rhythm in patients who are alert or anxious or who have their eyes open.

gamma waves. Gamma is the frequency range approximately 26–100 Hz. Because of the filtering properties of the skull and scalp, gamma

rhythms can only be recorded from electrocorticography or possibly with magnetoencephalography. Gamma rhythms are thought to represent binding of different populations of neurons together into a network for the purpose of carrying out a certain cognitive or motor function.

"Ultra-slow" or "near-DC" activity is recorded using DC amplifiers in some research contexts. It is not typically recorded in a clinical context because the signal at these frequencies is susceptible to a number of artifacts.

Some features of the EEG are transient rather than rhythmic. Spikes and sharp waves may represent seizure activity or interictal activity in individuals with epilepsy or a predisposition toward epilepsy. Other transient features are normal: vertex waves and sleep spindles are transient events which are seen in normal sleep.

It should also be noted that there are types of activity which are statistically uncommon but are not associated with dysfunction or disease. These are often referred to as "normal variants." The mu rhythm is an example of a normal variant.

The normal EEG varies by age. The neonatal EEG is quite different from the adult EEG. The EEG in childhood is generally comprised of slower frequency oscillations than the adult EEG.

The normal EEG also varies depending on state. The EEG is used along with other measurements (EOG, EMG)to define sleep stages in polysomnography. Stage I sleep (equivalent to drowsiness in some systems) appears on the EEG as drop-out of the posterior basic rhythm. There can be an increase in theta frequencies. Santamaria and Chiappa cataloged a number of the variety of patterns associated with drowsiness. Stage II sleep is characterized by sleep spindles--transient runs of rhythmic activity in the 12-14 Hz range (sometimes referred to as the "sigma" band) that have a frontal-central maximum. Most of the activity in Stage II is in the 3-6 Hz range. Stage III and IV sleep are defined by the presence of delta frequences and are often referred to collectively as "slow-wave sleep." Stages I-IV are comprise non-REM (or "NREM") sleep. The EEG in REM (rapid eye movement) sleep appears somewhat similar to the awake EEG.

EEG under general anesthesia depends on the type of anesthetic employed. With halogenated anesthetics, such as halothane or intravenous agents, such as propofol, a rapid (alpha or low beta), nonreactive EEG pattern is seen over most of the scalp, especially anteriorly; in some older terminology this was known as a WAR (widespread anterior rapid) pattern, contrasted with a WAIS (widespread slow) pattern associated with high doses of opiates. Anesthetic effects on EEG signals are beginning to be understood at the level of drug actions on different kinds of synapses and the circuits that allow synchronized neuronal activity (see: http://www.stanford.edu/group/maciverlab/).

Artifacts

Biological artifacts

Signals in the EEG that are of non-cerebral origin are called artifacts. The EEG is nearly always contaminated by such signals. This is one of the reasons why it takes considerable experience to interpret EEGs clinically. The most common types of artifacts are:

Eye artifacts (including eyeball, ocular muscles and eyelid)

EKG artifacts EMG artifacts Glossokinetic artifacts

Eyeball artifacts are caused by the potential difference between the cornea and retina, which is quite large compared to cerebral potentials. When the eye is completely still, this is not a problem. But there are nearly always small or large reflexive eye movements, which generates a potential which is picked up in the frontopolar and frontal leads. Eye movements - whether vertical or horizontal [saccades] - are caused by ocular muscles, which also generate electromyographic potentials. Purposeful or reflexive eye blinking also generates electromyographic potentials, but more importantly there is reflexive movement of the eyeball during blinking which gives a characteristic artefactual appearance of the EEG (see Bell's phenomenon).

Eyelid fluttering artifacts of a characteristic type were previously called Kappa rhythm (or Kappa waves). It is usually seen in the prefrontal leads, that is, just over the eyes. Sometimes they are seen with mental activity. They are usually in the Theta (4–7 Hz) or Alpha (8–13 Hz) range. They were named because they were believed to originate from the brain. Later study revealed they were generated by rapid fluttering of the eyelids, sometimes so minute that it was difficult to see. They are in fact noise or "artifact" in the EEG reading, and should not technically be called a rhythm or wave. Therefore, the term Kappa rhythm (or wave) is no longer used in electroencephalography. It should be described as eyelid fluttering artifact.[7]

Some of these artifacts are useful. Eye movements are very important in polysomnography, and is also useful in conventional EEG for assessing possible changes in alertness, drowsiness or sleep.

EKG artifacts are quite common and can be mistaken for spike activity. Because of this, modern EEG acquisition commonly includes a one-channel EKG from the extremities. This also allows the EEG to identify cardiac arrythmias that are an important differential diagnosis to syncope or other episodic/attack disorders. Glossokinetic artifacts are caused by the potential difference between the base and the tip of the tongue. Minor tongue movements can contaminate the EEG, especially in parkinsonian and tremor disorders.

External artifacts

In addition to internal artifacts, there are many artifacts which originate from outside the patient. Movement by the patient, or even just settling of the electrodes, may cause electrode pops, spikes originating from a momentary change in the impedance of a given electrode. Poor grounding of the EEG electrodes can cause significant 50 or 60Hz artifact, depending on the local power system's

frequency. A third source of possible interference can be the presence of an IV drip; such devices can cause rhythmic, fast, low-voltage bursts, which may be confused for spikes.

Artifact correction

Recently, source decomposition techniques have been used to correct or remove EEG contaminates. These techniques attempt to "unmix" the EEG signals into some number of underlying components. There are many source separation algorithms, often assuming various behaviors or natures of EEG. Regardless, the principle behind any particular method usually allow "remixing" only those components that would result in "clean" EEG by nullifying (zeroing) the weight of unwanted components.

Eighth Appendix

Complex number representation of Fourier series and Fourier coefficients – “i, e, you, and sometimes, Why?”

Holy haystack, what a mouthful!

In this context, ‘complex number’ does not mean ‘complicated number’, it means a special kind of number called a ‘complex number’.

A good site to refresh your learning on complex numbers is: http://www.clarku.edu/~djoyce/complex/

Complex numbers make the whole business of Fourier analysis easier.

Oh yeah? Well I’d like to see you prove it!

Which reminds me of a joke.

A mathematician and her boyfriend were having an argument.Boyfriend: I think you love your mathematics more than you love me.

Mathemaician: I do not!Boyfriend: Prove it!Mathematician: Let W be the set of all loveable objects…

Complex numbers are used a great deal in complex signal analysis (aka quadrature signals). The main reason for this is they make the whole topic of analyzing and understanding alternating signals much easier. The problem is understanding what they 'mean' and how to use them in the first place.

To help you get a clear picture of how they're used and what they mean we can look at a mechanical example...

The above animation shows a rotating wheel. On the wheel there is a blue blob which goes round and round. When viewed 'flat on' we can see that the blob is moving around in a circle at a steady rate.

However, if we look at the wheel from the side we get a very different picture. From the side the blob seems to be oscillating up and down. If we plot a graph of the blob's position (viewed from the side) against time we find that it traces out a sinewave shape which oscillates through one cycle each time the wheel completes a rotation. Here, the sine-wave

behavior we see when looking from the side 'hides' the underlying behavior which is a continuous rotation.

We can now reverse the above argument when considering EEG (sinewave) oscillations in electroencephalography. Here we can regard the oscillating voltages as 'side views' of something which is actually 'rotating' at a steady rate. We can only see the 'real' part of this, of course, so we have to 'imagine' the changes in the other direction.

This leads us to the idea that what the oscillation voltage that we see is just the 'real' portion' of a 'complex' quantity that also has an 'imaginary' part. At any instant what we see is determined by a phase angle which varies smoothly with time.

  

In other words, complex Fourier analysis lets us handle the sine functions AND the cosine functions AND the phase together in one expression.

When it comes time to calculate, even a computer can go a lot faster using this version.

OK. That’s the general idea. Let’s see how we got there.

Once upon a time there was a really smart cookie named Leonhard Euler (Euler pronounced OILER).

He was funny looking.But nobody cared because he was really, really smart.

NOTE: By “really smart cookie” I mean the greatest mathematician of the 18th century.

Euler bequeathed us a great gift, aptly named for him –

Euler equation

What is a Euler equation and why would anyone want one?

Well, to appreciate it, recall thatin the Fifth Appendix we got four tools for our Maths toolbox:

FOURIER SERIES GENERATOR

f(t) = a0 + a1cos t + b1sin t + a2cos 2t + b2sin 2t

+ ………………………

+ ancos nt + bnsin nt

THE a0 FINDER

THE SINE WAVE AMPLITUDE FINDER

THE COSINE WAVE AMPLITUDE FINDER

Euler’s great act of prestidigitation was to find a way to tie these together with the natural logarithms and imaginary numbers. This equation contains everything there is to know about classical mathematics

BUT WAIT! It also let’s us do Fourier math tricks really, really fast.

The best introductory discussion of how to derive this formula is in: Transnational College of Lex, 1998, Who is Fourier? A mathematical adventure.

An even more detailed approach from the perspective of “embodied cognition” is George Lakoff and Rafael Núñez, 2000, Where mathematics comes from.

Slightly more advanced, from the Master, is Richard Feynman, 1963, volume I of The Feynman Lectures in Physics.

So here it is, the most elegant and useful of your maths tools

THE FAST FOURIER TRANSFORM MAKER

Using some maths tricks that this formula shows us, we can produce a way of doing Fourier transforms that is

FAST

and that’s a good thing because it means we can analyze gigabits of data and still have time for the rest of life.

And if it’s one thing the brain oscillations do, is produce

megabits 1,000,000

gigabits 1,000,000,000

terabits1,000,000,000,000petabits 1,000,000,000,000,000

exabits1,000,000,000 000,000,000

zettabits

1,000,000,000,000,000,000,000

vottabits

1,000,000,000,000,000,000,000,000and beyond of data.

Power/Name/Symbol10^1 deka da10^2 hecto h10^3 kilo k10^6 mega M10^9 giga G10^12 tera T10^15 peta P

10^18 exa E10^21 zetta Z10^24 yotta Y10^27 xona X10^30 weka W10^33 vunda V10^36 uda U10^39 treda TD10^42 sorta S10^45 rinta R10^48 quexa Q10^51 pepta PP10^54 ocha O10^57 nena N10^60 minga MI10^63 luma L

There are some pretty big amounts of data named here.

What are the limits of the brain’s computational abilities?

We don’t know for sure, but big enough to figure out the complex number representation of the Fourier series and the Fourier coefficients.

So without further ado, here they are

COMPLEX NUMBER REPRESENTATION OF FOURIER SERIES

COMPLEX NUMBER REPRESENTATION OF FOURIER COEFFICIENTS

We are not going to do anything more with these formulas at this time. We really just want you to know that they exist.

NINTH APPENDIX

Getting the info from the Complex Number Representations

We will march through this algorithm in short order.

1. Calculate the complex Fourier coefficients for each frequency of interest for each time.2. To find the amplitude, square the real Fourier coefficient and the imaginary Fourier coefficient, add them together,

and take the square root.3. To find the phase, divide the arctangent of the imaginary Fourier coefficient by the arctangent of the real Fourier

coefficient.

Let’s get a sense of how the steps of the algorithm dance actually work.

1. Calculate the complex Fourier coefficients for each frequency of interest for each time.

Recall that when we used the old formulas (see the Fifth Appendix) we found the coefficients we wanted by using a

kind of mathematical filter. Basically, this involves multiplying f(t)* by the wave that had the amplitude we were

trying to find.

*f(t) being

a0 + a1cos t + b1sin t + a2cos 2t + b2sin 2t

+ ………………………

+ ancos nt + bnsin nt

It turns out that if we want to find the coefficient a1, we multiply the expression above by cost. All the other terms are then zero, and we find a1 by using THE COSINE WAVE AMPLITUDE FINDER.

In the complex number representation of the Fourier coefficients, f(t) is multiplied by e-int to find Cn.

Here’s how it goes. We want to find the Fourier coefficient Cm

Recall from the Fifth Appendix that this is the equation

for the complex number representation

of the Fourier coefficient

As we did with the original representation of the Fourier series, we want to have a way to pick out one coefficient from the set of coefficients in the Fourier series. We are given the idea that we can do that by multiplying the Fourier series f(t) by the term

Cm 1T

0

T n

Cneint eimtdt

Now, we can apply the integration rule of addition or subtraction and move and Cn outside of the portion being integrated:

Cm 1T

n

Cn

0

T

eint eimtdt

Now take a look at the part to the right of the integration sign.

We can think about this part with the same logic as we use in telling time from a stopped clock. We know that a stopped clock will give the correct time two times each day.

In the portion of the equation we are considering, as n changes from -1 to 1, then

n = m one time only. At all other values, n K m.

What happens when n K m?

To see this more clearly, let’s first rewrite the portion of the equation making use of the exponent rule:

0

T

eint eimtdt 0

T

ein mt dt

By Euler’s equation, we can write the equation above in the form of the cosine and sine functions:

ein mt cosn mt isinn mtRecall that when we integrate cos and sin from 0 to T, we get zero for both of them:

0

T

ein mt dt 0 i 0 0

So, when n K m, the result is always 0.

What happens when n = m ???????????????????????????????

0

T

ein mt dt 0

T

ei0t dt

0

T

e0 dt 0

T

1dt T

We can go back to our original formula, Cn = Cm, so:

Cm 1T

CnT Cn Cm

2. To find the amplitude, square the real Fourier coefficient and the

imaginary Fourier coefficient, add them together, and take the square root.

The Reader says, “Wait just a gol darn minute! I thought the coefficient and the amplitude were the same????” The owl says, “Not quite. Here’s why. When we were looking into the mathematical tools for finding the sine and cosine coefficients for a periodic wave, the wave we considered had some period T. Therefore, whenever we calculated the amplitudes a1, a2, b1, b2 and so on, we always finished by dividing the area by 2/T. In Fourier coefficients, period T is always fixed, so we always divide by the same number to finish. As long as we know the area of each component wave, we don’t really have to calculate the respective amplitudes. The relative amplitude of a wave compared to any other wave is always the same. The Fourier transform does not provide us with the actual amplitudes expressed in the Fourier series. It provides us with the relationship among the amplitudes of the component waves.

For the sake of simplicity, let’s say that we are evaluating a signal with a period of 2.

Recall: 2 = 360 = one period of a wave.

Here we have the complex form of the Fourier series expansion of the function f(x) with period T.

The formula for the complex Fourier coefficients is thus

The complex numbers Cn form an infinite sequence Cnn

which is the spectrum of the periodic function.

In the world of Fourier, whenever we have a complex exponent, we can always rewrite the expression using Euler’s formula, thus separating the real and imaginary parts:

Cn 1T

T2

T2

ftncost insintdt

We can then calculate the amplitude as:

AfRealf2 Imaginaryf2where f is the frequency for which we calculate the amplitude.

3. To find the phase, divide the arctangent of the imaginary Fourier coefficient by the arctangent of the real Fourier coefficient.

arctan 2

Imaginary CnRealCnn