Subliminal visual oddball stimuli evoke a P300 component

Edward Bernat*, Howard Shevrin, Michael Snodgrass

Psychology Department, University of Minnesota, Elliot Hall, 75 East River Road, Minneapolis, MN 55455, USA

Accepted 18 August 2000

Abstract

Objective: To provide evidence that a P300 component can be elicited by subliminal stimuli in an oddball paradigm.

Methods: The words LEFT and RIGHT were presented in a frequent-rare ratio (80±20%), counterbalanced between subjects. Stimuli were

presented at the objective detection threshold (d 0 � 0, via unmasked 1 ms presentations), a stringent measure for detecting any conscious

perception.

Results: A signi®cantly larger amplitude component was found for rare vs. frequent stimulus presentations across electrodes Fz, Cz, and

Pz using both a broad 200±900 ms window (F�1; 27� � 5:75, P , 0:012, h2 � 0:18; one-tailed), and a more narrow 400±760 ms window

de®ned using principal component analysis (F�1; 27� � 10:10, P , 0:002, h2 � 0:27; one-tailed). No signi®cant component latency effects

were found. An analysis of the conscious perception index (d 0) and the oddball effect (rare-frequent amplitude difference) revealed a negative

relationship, further supporting the contention that conscious perception does not account for the ®nding, and suggesting that any conscious

stimulus detection may inhibit this subliminal effect.

Conclusions: Results provide evidence that an endogenous component can be elicited by undetectable subliminal stimuli in an oddball

paradigm. Implications are discussed for comparing conscious and unconscious information processing, unconscious learning, and the

measurement of ERPs to subliminal stimuli. q 2001 Elsevier Science Ireland Ltd. All rights reserved.

Keywords: Event-related potential; Oddball; P300; Subthreshold; Subliminal; Unconscious; Nonconscious

1. Introduction

A substantial body of work is now available supporting

the notion that considerable mental activity can happen

without conscious awareness (Bunce et al., 1999; Esteves

et al., 1994; Fox, 1991; Izard, 1993; LeDoux, 1995; Murphy

et al., 1995; Ohman et al., 1995; Shevrin and Fritzler, 1968;

Shevrin et al., 1996; Wong et al., 1994, 1997). This is

consistent with a broader understanding developing in

psychology that a great many mental processes must

occur outside conscious awareness (Kihlstrom, 1987;

Miller, 1996; LeDoux, 1995; Shevrin and Dickman,

1980). The current study was designed to determine whether

a subliminal event-related potential (ERP) could be

obtained in one of the most commonly investigated and

replicated ERP procedures, the oddball paradigm. Speci®-

cally, would an enhanced P300 component at an appropriate

location be found to rare stimuli when both frequent and

rare stimuli are presented entirely outside of consciousness?

The importance of demonstrating a subliminal oddball

P300 has not escaped the interest of other investigators.

Brazdil et al. (1998) presented stimuli in a supra- and

subliminal oddball design and reported ®nding an enhanced

oddball P300 in response to rare relative to frequent sublim-

inal stimuli. On methodological grounds (which will be

discussed in more detail below) their result remains ques-

tionable because conscious perception of the stimuli can not

be ruled out. Devrim et al. (1997) compared P300 responses

to supraliminal rare (target) stimuli in conditions using

either subliminal frequent stimuli or no frequent stimuli

(single-stimulus oddball design, e.g. Polich, 1996), and

reported an enhanced P300 in the subliminal frequent stimu-

lus condition relative to no frequent stimuli, suggesting that

the processing of subliminal frequent stimuli enhanced rare

P300 responses. However, like Brazdil et al., problems with

their subliminal methodology complicate and weaken their

®ndings (which will also be discussed in more detail below).

In the experiment to be reported, the method for establishing

an absence of awareness is based on a standard signal detec-

tion theory (SDT; Green and Swets, 1966) forced-choice

discrimination task, and stimuli meet the most stringent

criterion for subliminality, the objective detection threshold.

Clinical Neurophysiology 112 (2001) 159±171

1388-2457/01/$ - see front matter q 2001 Elsevier Science Ireland Ltd. All rights reserved.

PII: S1388-2457(00)00445-4

www.elsevier.com/locate/clinph

CLINPH 99183

* Corresponding author. Tel.: 11-612-624-5063; fax: 11-612-626-2079.

E-mail address: ebernat@umn.edu (E. Bernat).

1.1. Establishing subliminality

Establishing subliminality (absence of stimulus aware-

ness) must be based on sound methodological grounds.

Thus, it is important to explain the methodology of the

current study in the broader context of subliminal research,

and to de®ne some terms and issues. We will ®rst summar-

ize the approach to measuring subliminal thresholds

employed in this study, then review some important issues

about these methods, and ®nally discuss the recent attempts

to investigate subliminal oddball P300 responses in this

context.

In this study, an inference of unconscious perception is

made by assessing activity on a direct measure of conscious

perception (forced-choice stimulus discrimination,

expressed as d 0) and an indirect measure of unconscious

perception (P300 amplitude from subliminal rare vs.

frequent stimuli) using a form of the classic dissociation

paradigm (CDP; e.g. Dagenbach et al., 1989; Greenwald

et al., 1995; Holender, 1986; Snodgrass, 2000). The premise

of the CDP is that if null sensitivity can be demonstrated on

a direct measure (i.e. d 0 � 0), while signi®cant effects are

present on an indirect measure (e.g. greater P300 to rare vs.

frequent amplitude), this would be evidence for activation

without phenomenal awareness, or unconscious perception.

Relevant to understanding CDP approaches, SDT has

offered an important distinction between a participant's

subjective criterion to report a stimulus (b; response bias)

and their sensitivity to discriminate stimuli (d 0). While d 0

re¯ects a participant's more fundamental sensitivity to

discriminate two stimulus states, the criterion re¯ects a

non-sensory decision process that participants apply to

their sensory experience in order to select a response

(Macmillan and Creelman, 1991; Snodgrass, 2000). These

SDT parameters correspond closely to the subjective thresh-

old and objective threshold approaches (Cheesman and

Merikle, 1986) commonly used in subliminal research. In

subjective threshold approaches, participants are asked to

indicate when they have a phenomenal awareness of stimu-

lus discrimination, and stimuli are arranged such that parti-

cipants achieve null sensitivity with regard to their

subjective criterion for phenomenal awareness. For objec-

tive threshold approaches, participants complete a forced-

choice discrimination task, and stimuli are arranged such

that participants achieve null sensitivity on the d 0 measure.

Discrimination in either approach can be either an identi®-

cation-based task (discriminations of one stimulus from

another) or a detection-based task (discriminations of the

presence or absence of a stimulus). Subjective thresholds

and identi®cation tasks generally correspond to higher d 0

values than objective thresholds and detection tasks respec-

tively; that is, they involve more conscious perception. For

example, it is easier to discriminate whether or not any

stimulus was presented (detection task) than to discriminate

whether stimulus A or B was presented (identi®cation task).

Similarly for thresholds, in varying the intensity of a stimu-

lus presentation from maximum to zero (e.g. no stimulus

presented), participants will report being `unable to see' a

stimulus (subjective threshold) with higher intensities than

those required for participants to perform at chance on a

forced-choice discrimination task (objective threshold). In

this hierarchy, the objective detection threshold is the most

stringent criterion for subliminality. An important dif®culty

of the subjective threshold approach is that the subjective

criterion (b) is confounded with the participant's sensitivity

(d 0). This confound, often called the `criterion artifact,'

served as the basis for fundamental criticisms against

early subliminal work using subjective threshold

approaches in which null sensitivity was incorrectly inferred

from subjective threshold methods (Cheesman and Merikle,

1986; Eriksen, 1960; Goldiamond, 1958; Macmillan, 1986;

Ohman, 1999; Snodgrass, 2000). Objective threshold

approaches, on the other hand, make it possible to determine

a true null discrimination sensitivity for the direct measure

of conscious perception.

Although many researchers subscribe to the logic of the

CDP (e.g. Greenwald et al., 1989; Dagenbach et al., 1989;

Groeger, 1988; Snodgrass, 2000), Reingold and Merikle

(Reingold and Merikle, 1988, 1990; Merikle and Reingold,

1998) have suggested that even objective detection tasks

may not `exhaustively' measure all task-relevant conscious

perception. The essence of Reingold and Merikle's concern

(see also Jacoby, 1991) is that whenever different tasks are

used to index conscious (direct measure, e.g. d 0) and uncon-

scious perception (indirect measure, e.g. subliminal priming

in their work), task differences and process differences are

confounded. Thus, even if null discrimination sensitivity

were satisfactorily attained, effects on the indirect measure

might merely re¯ect aspects of conscious perception not

indexed by the direct measure, rather than truly unconscious

effects.

However, there are substantial reasons to think that detec-

tion is exhaustively sensitive to any conscious perception

that might account for the target indirect effects (see Snod-

grass, 2000 for a full treatment of these issues, which are

summarized here). First, the subliminal effects of interest

usually require that the stimuli be semantically analyzed

(e.g. semantic priming). For such semantic analysis to

occur, in turn, requires at least partial stimulus identi®cation

(differentiating one stimulus from another). Second, and

crucially, SDT models identi®cation as multidimensional

detection (see, e.g. Green and Birdsall, 1978; Macmillan

and Creelman, 1991). Speci®cally, identi®cation is

conceived of as the multidimensional distance between

the individual detection sensitivities. That is, SDT regards

each stimulus as having its own detection dimension, and

identi®cation between two stimuli is represented as the third

leg of the triangle connecting the two individual detection

dimensions (see Fig. 1). In this way, identi®cation arises

from, depends on, and cannot occur without non-zero detec-

tion. In short, given the SDT framework, detection is

exhaustively sensitive to all identi®cation-relevant informa-

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171160

tion. In particular, when the objective detection threshold is

attained, identi®cation should be impossible (presuming

that there is only one, presumably conscious, perceptual

process at work). Thus, when effects requiring some degree

of stimulus identi®cation are nonetheless obtained on the

indirect measure, this is strong evidence for unconscious

perception. As Macmillan (1986), p. 39) concluded,

ªAbove-chance recognition (i.e. identi®cation) performance

(or other evidence of activation) when detection d 0 � 0

would be, for almost everyone, persuasive evidence for

unconscious perception.º

Next we will review recent advances in subliminal

research methods which advocate modeling the relationship

between d 0 and the indirect measure, providing additional

testable hypotheses for putatively unconscious effects. First,

a direct implication of the SDT model is that it predicts a

positive relationship between detection and identi®cation

(Snodgrass, 2000). Using the geometric model described

above (Fig. 1), as the detection dimensions get larger, the

identi®cation dimension becomes larger as well. With this

in mind, a single-process (e.g. conscious perception only)

SDT model predicts that the (identi®cation-dependent)

indirect effects should correlate positively with the direct

detection measure, and that if null detection sensitivity is

attained, the indirect effects should be greatly reduced or

completely eliminated (Fig. 2, top). Notably, Reingold and

Merikle (Reingold and Merikle, 1988, 1990; Merikle and

Reingold, 1998; Cheesman and Merikle, 1984) have repeat-

edly stressed just this idea ± that indirect effects should

decline to zero as d 0 approaches zero. Pritchard (1981) has

similarly suggested, in a review of signal detection related

P300 ®ndings, that P300 is absent until d 0 is greater than

zero.

Several researchers have begun to examine this idea by

investigating the relationship between d 0 for various direct

measures and indirect effects using subliminal priming para-

digms. Greenwald et al. (1995) found using a regression

analysis that under some conditions when the direct measure

(d 0) was zero the intercept on the indirect measure was

signi®cantly above zero. They suggest that this is strong

evidence that indirect effects do not approach zero as the

detection d 0 approaches zero, thus supporting the inference

that unconscious processing is present. Dagenbach et al.

(1989) found that the relationship between the direct and

indirect measures can be non-monotonic, and suggest that

such irregularities indicate a single conscious process can

not explain the ®ndings. Greenwald et al. (1995) similarly

suggested such a non-monotonic relationship, proposing

that any degree of conscious perception may actually reduce

subliminal effects on the indirect measure above the objec-

tive detection threshold (d 0 slightly above zero), which will

then recover when the objective detection threshold is

achieved (d 0 � 0).

Drawing on the ideas suggested by Greenwald et al.

(1995) and Dagenbach et al. (1989), Snodgrass (2000) has

proposed a non-monotonic model of the relationship

between direct (conscious) and indirect (unconscious)

effects, conceptualized in the hierarchical terms of SDT

discrimination tasks (see Fig. 2, bottom). The relationship

is hypothesized to be strongly positive from full conscious

awareness to somewhere below the subjective identi®cation

threshold. Then the indirect effect is hypothesized to bottom

out and become non-signi®cant somewhere above the

objective detection threshold (due to interference of slight

conscious perception on unconscious processing), but that

as the stimuli meet more stringent threshold criteria

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171 161

Fig. 1. Signal detection theory (SDT) model of identi®cation between two

stimuli as a function of ability to detect each of the stimuli independently.

Fig. 2. Comparison of a single-process model (e.g. conscious perception

only) (top), in which the direct and indirect measures are simply positively

correlated, to the proposed non-monotonic relationship (bottom) which

makes the opposite negative correlation prediction in the range of data

obtained from data in this study (gray part, top and bottom).

(towards the objective detection threshold of d 0 � 0), the

indirect effect will begin to recover (due to the disappear-

ance of even slight bits of interfering conscious perception).

Data in this study occupy this lowest end of possible of d 0

values (not different from objective detection d 0 of zero).

Thus, for data in this study, the single-process and non-

monotonic models of this relationship make exactly oppo-

site predictions (Fig. 2, gray part top and bottom); the

single-process model predicts a positive relationship while

Snodgrass's non-monotonic model predicts a negative rela-

tionship. We thus hypothesized that (1) a negative relation-

ship would be found between d 0 on an objective detection

task and the indirect subliminal oddball P300 effects, and (2)

at d 0 � 0 these indirect subliminal effects will be present as

indicated by a regression y-intercept term signi®cantly

above zero. In this study we will test both parts of this

hypothesis in seeking to demonstrate that an oddball P300

effect will be found at the objective detection threshold.

1.2. Studies of P300 and subliminal stimuli

Finally, here we will assess the P300 studies discussed

earlier in the context of more general subliminal research

methods. Brazdil et al. (1998) reported an increased P300

response to rare versus frequent subliminal stimuli using a

CDP design. However, stimulus conditions were manipu-

lated to meet only the subjective identi®cation threshold, the

weakest of subliminal criteria. As discussed earlier, the

subjective method for establishing subliminality confounds

sensitivity (d 0) with a subjective criterion for consciousness,

the `criterion artifact' problem. For example, the partici-

pants in the Brazdil et al. (1998) study may simply have

had a high subjective criterion for reporting awareness even

though some awareness was present. There is thus no way to

assure that while participants may have reported no aware-

ness of the stimulus, that they were additionally unable to

discriminate the stimuli above chance.

Devrim et al. (1997) reported an enhanced rare (target)

P300 in a subliminal frequent stimulus condition relative to

no frequent stimuli, suggesting that the processing of

subliminal frequent stimuli contributed to the rare P300

responses. However, their study also suffers from some

methodological limitations. First, the study does not address

(and it was not their aim) whether the entire process of

context updating, including the rare stimuli, can happen

without conscious awareness. Secondly, like Brazdil et al.

(1998), their method for establishing subliminality is

problematic. First, in the detection series, participants did

not discriminate between stimulus-plus-noise (SN) and

noise-only (N) stimuli, as would be the case for standard

SDT procedures. Rather, using an approach resembling the

classical method of limits, stimulus intensities were gradu-

ally reduced and participants were simply required to indi-

cate when they perceived that a stimulus had been

presented. This was done in two separate, blocked condi-

tions ± no subliminal stimuli (false alarm condition), or with

subliminal stimuli (hit condition). Accordingly, Devrim et

al.'s procedures did not allow computation of true d 0. Addi-

tionally, the hit and false alarm measures they did obtain

were substantially undersampled. Of the 30 presentations in

each condition, both mean hit and false alarm rates were 1.6,

suggesting a severe response bias (a more balanced response

selection would be 15). Even if their non-standard d 0 proce-

dures were reasonable, this response bias renders hit and

false alarm estimates unstable, making their claim of no

difference between them problematic. As in the Brazdil et

al. (1998) study, serious questions remain as to whether

conscious perception was in fact ruled out, and thus whether

the enhanced oddball P300 could have resulted from

conscious perception of the stimuli.

1.3. Hypotheses

1. The rare stimuli will evoke greater amplitude than

frequent stimuli in the de®ned component window

when all stimuli are presented at the objective detection

threshold

2. The relationship between d 0 and the oddball effect will be

negative

3. The y-intercept of a regression between d 0 and the

oddball effect will be signi®cantly above zero.

2. Method

2.1. Participants

Thirty-two right handed paid participants took part in the

study, although 4 were excluded due to equipment failure

during data collection. The remaining 28 participants had a

mean age of 21.7 years (SD 2.49), 18 were female, all had

vision correctable to 20/20 and all reported no history of

neurological or mental abnormalities. Participants were

recruited using a classi®ed advertisement in the student

newspaper at the University of Michigan.

2.2. Passive oddball paradigm

Because stimuli were presented below the objective

detection threshold, and participants were thus not

conscious of what had been presented, a passive oddball-

type paradigm was used in which participants are not asked

to respond in any way to the stimulus presentations. Polich

(1989) directly compared passive and active auditory

oddball paradigms, with no additional tasks. He reported

that compared to the active paradigm, the passive oddball

paradigm generated a P300 which was lower in amplitude

overall, and had a decreased, but present, parietal maxi-

mum. Polich cites a number of other studies which have

evidenced a frontally maximal P300 in a passive auditory

oddball paradigm, but contends that because such studies

generally use some other active task (e.g. the no-go part of a

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171162

go/no-go paradigm), the passive paradigm and the addi-

tional active task are confounded in any interpretation of

the source of the frontal maximum. Thus, the P300 topo-

graphic distribution in the passive paradigm employed here

is likely to be parietally maximal to a lesser degree than an

active paradigm. A frontally maximal effect, however,

cannot be entirely ruled out.

The words LEFT and RIGHT served as the frequent and

rare stimuli, counterbalanced between participants. Stimuli

were presented in 60 blocks containing 5 stimulus presenta-

tions (one frequent and 4 rare) in an 80±20 frequent-rare

ratio. The rare stimulus occurred randomly in position 3, 4,

or 5 in the block. Participants were told nothing about the

content of the stimulus presentations, including the block

structure of the presentations and the frequent-rare ratio of

the stimuli. During debrie®ng, participants uniformly

described being unable to see the stimuli and reported no

awareness of the content of the stimuli or the organization of

stimulus presentations.

The interstimulus interval (ISI) in this study was variable

(routinely between 5 and 15 s, and infrequently as long as a

minute) and was not directly measured or analyzed. There

are two sources of the variable ISI: our use of a tachisto-

scope for stimulus presentations which required a person to

be in the recording booth with the participant changing the

stimulus card before each trial, and the logistical procedure

for stimulus delivery (a more detailed accounting of the

procedure for stimulus delivery is included below). Our

reason for using a tachistoscope was its ability to deliver

stimuli at a 1 ms duration, thus making it possible to reach

the objective detection threshold. It is important to note that

both the experimenter in the booth and the experimenter

monitoring the EEG machine (where individual trials were

triggered) were blind to the content of all trials. A longer ISI

has been shown to reduce P300 frequent-rare differences

(Donchin et al., 1986). Thus, to the degree our method

differs from many oddball studies in this respect, the differ-

ences should work against positive ®ndings.

2.3. Stimulus presentation

The stimuli were printed in Adobe 18 pt. Helvetica light

centered on 4 £ 6 inch white cards and presented in a 3-®eld

Gerbrands Model T3-8 tachistoscope. One ®eld of the

tachistoscope was used for all stimulus presentations. A

second ®eld was used for a ®xation point, visible at all

times except during the moments of stimulus presentations.

The distance from the stimulus ®eld to the eyepiece was 76

cm. The printed stimulus words LEFT and RIGHT were 14

and 19 mm wide, respectively, within the 58 visual angle for

foveal vision (Polyak, 1957). Field brightness was tested for

luminance level and pulse width and equated for both ®elds.

Luminance levels for the stimulus and ®xation ®elds, as well

as the ambient light levels in the booth, were set at 5

footlamberts. Stimuli were rendered subliminal by being

presented at 1 ms duration. Because the tachistoscopically

presented subliminal 1 ms stimuli (black print on a white

background) were preceded and followed by a ®xation ®eld

(black dot on a white background) of equal luminance, there

was very little disturbance in the visual ®eld.1 Presumably,

this contributed substantially to the small amplitude of the

observed ERPs.

2.4. Experimental procedure

After a brief introduction to the laboratory, participants

completed an informed consent statement. All electrodes

were attached prior to seating participants in a sound-

proof, electrically shielded, temperature-controlled booth.

Participants were instructed that during each stimulus

presentation they were to remain as still as possible, to

focus on the ®xation point, to pay attention, and to keep

eye blinks to a minimum. This instruction was repeated

periodically during the experiment. They were told that

the stimulus presentations were very brief so that they

may or may not be able to see them. After experiencing a

few practice trials, participants were reassured that some-

thing was being presented, and that we were interested in

their brain responses to the stimuli even though they may

not experience seeing something. Participants were

instructed that they were not required to respond in any

way to the stimuli, just to stay attentive, still, and keep

eye blinks to a minimum during the stimulus delivery and

ERP recording for each trial.

The stimulus delivery sequence was as follows. First

participants heard a single `ready' tone indicating that the

experimenters were ready to present a trial. Participants

would then respond by stating the number of the current

trial followed by the word ready (i.e. `one-ready,' `two-

ready,' and so on). After that verbal response, stimulus

delivery was triggered by an experimenter monitoring the

EEG record, who was blind to the stimulus content. After

the stimulus was presented and the 1 s of ERP activity was

recorded, a double tone signaled the end of that trial. Parti-

cipants were told they could move, blink, and relax between

that double tone and the next single ready tone. During the

time between the double tone and the next single ready tone,

the data from that trial was written to disk, and an experi-

menter in the booth, who was blind to the content, changed

the stimulus card.

Several time epochs in this sequence were variable,

constituting the variable ISI discussed earlier. The time

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171 163

1 Our method differs from `energy' masking in which the stimulus is

rendered subliminal by following it with a much brighter stimulus.

Andreassi et al. (1976) have reported on the use of energy masking and

its results. In the studies described the index for subliminality was based on

the patient's failure to report the masked stimulus, thus amounting to a

subjective threshold. Our method also differs from pattern masking insofar

as our stimuli are exposed for a very brief duration (1 ms) and are not

followed by a conscious pattern mask. The shortest stimulus duration

generally used in pattern making is one screen refresh of a computer moni-

tor (generally not faster than 10 ms), and stimuli are rendered subliminal by

being followed with a supraliminally presented pattern.

between the single ready tone and participant's `trial

number-ready' response was controlled by the participant.

While most often this response immediately followed the

single tone, sometimes participants would take several

seconds to prepare for a trial. In rare instances participants

took 10 or 15 s. The time between the participants `trial-

number ready' response and the initiation of stimulus deliv-

ery was controlled by the experimenter at the EEG machine.

This time most frequently was within a few seconds, but

sometimes was longer if the EEG re¯ected eye blinking or

excessive muscle movement at which point time was

allowed to elapse until the record appeared free of such

artifacts. Records which were contaminated with artifacts

(from an online visual inspection) were rejected and the trial

presented again in the next cycle. Our reason for being care-

ful to collect artifact free individual ERP trials is that the

stimulus delivery process was slow relative to many compu-

ter based stimulus delivery mechanisms (due to the use of a

tachistoscope needed for 1 ms stimulus durations). This

limited the number of stimulus presentations and thus

made it more important for each trial to be as free of error

as possible. The ®nal source of variance in the ISI was the

time between the double tone and the next single ready tone.

Most frequently this was about 5 s (the time it took for the

card to be changed in the booth).

A 64-item forced-choice detection task was administered

at the end of the experiment under the same 1 ms and 5

footlambert conditions (due to time constraints, one partici-

pant of the 28 did not complete the detection task). Of the 64

stimuli, 16 were the word LEFT, 16 were the word RIGHT,

and 32 were blank. Participants were told that either a word

or a blank card would be presented an equal number of times

in random order. They were asked to state after each presen-

tation whether a word or blank card had been presented, and

to keep their responses approximately equally divided

between the two choices. Sensitivity (d 0) did not differ

from zero (mean � 0:07, SD � 0:344; (t�26� � 1:06,

P , 0:30). These same conditions have been shown to

preclude conscious recognition of stimuli in other studies

(Bernat et al., 2000; Snodgrass et al., 1993; Shevrin et al.,

1996; Wong et al., 1997).

2.5. Physiological measurement apparatus

Recording sites were Fz, Cz, and Pz referenced to linked

ears. Standard Grass instrument silver-silver chloride elec-

trodes were used with impedance kept to less than 5 kV. Eye

activity was monitored by electrodes placed on the outer

canthus and suborbital ridge of the right eye, referenced to

each other (EOG). All signals were collected utilizing a

Grass Model 8-24D polygraph linked to a Macintosh

computer. Signals were digitized at 500 Hz, then stored in

computer ®les for off-line analysis. Signals were analog

®ltered online with a low-pass frequency of 200 Hz, and a

high-pass frequency of 0.1 Hz. ERPs were sampled for 1400

ms, including a 400 ms prestimulus interval. As discussed

earlier, the lack of a conscious visual stimulus, and the

passive oddball design, resulted in small amplitude ERPs

which also tended to contain more alpha. For these reasons,

a digital ®lter at 7 Hz was applied to the raw data before

component peak selection using a 5th order Chebychev

®lter, ripple parameter of 20 dB down, applied using the

Matlab ®lt®lt command.

2.6. Component measure

We used a P300 window based on windows reported in

supraliminal studies. Time windows for measuring the P300

in supraliminal studies have varied substantially. Latencies

have been reported as early as 210 ms and ended as late as

900 ms (Pritchard, 1981; Gehring et al., 1992; Cacioppo et

al., 1994; Coles and Rugg, 1995). Donchin et al. (1986)

suggest that endogenous components often occur between

500 and 1000 ms, depending on the experimental task. The

P300 window used in this study was the difference between

baseline and the largest positive going peak between 200

and 900 ms post-stimulus. Component measures were

applied to averages within electrode and participant. Each

participant's 300 ERPs were broken into 5 averages of 60

each (20% of total): one average for the rare stimuli, while

the 240 frequent stimuli were broken down into 4 random

groups of 60 each. This was done to select components from

ERP subaverages with equal numbers of trials.

3. Results

The grand average ERP pro®les are presented for rare and

frequent stimuli in Fig. 3 (frequent curve is the average of

the 4 frequent subaverages used for component selection).

The most obvious difference is a positive going peak

between 500 and 600 ms apparent in all 3 electrodes for

the rare average which is larger than the corresponding

positivity for the frequent average. Statistical analyses to

be presented below will con®rm these impressions.

First, we measured the amplitude and latency of the

largest positive peak between 200 and 900 ms (means

presented in Table 1), and subjected those values to a 2

(oddball: frequent, rare� £ 3 (electrode: Fz, Cz, Pz) analysis

of variance (ANOVA). The hypothesized main oddball

effect was signi®cant for the amplitude measure

(F�1; 27� � 5:75, P , 0:012, h 2 � 0:18; one-tailed2)

where rare stimuli evoked larger amplitudes than did

frequent stimuli. The main effect of electrode was signi®-

cant for amplitude as well (F�2; 54� � 3:72, P , 0:031,

h2 � 0:12), driven by larger frontal values. The interaction

of the oddball and electrode factors for amplitude was non-

signi®cant (F�2; 54� , 1), indicating that even though there

appears to be a greater difference in the amplitude of the

frontal region, the oddball effect does not signi®cantly differ

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171164

2 One-tailed criteria are used for comparisons based on a priori direc-

tional hypotheses (e.g. rare . frequent P300 peak amplitude values).

by region. We then subjected amplitudes and latencies from

each of the 3 electrodes separately to an ANOVA compar-

ing the frequent to rare component values. The rare compo-

nents were signi®cantly greater than the frequent for each of

3 electrodes separately (Fz: F�1; 27� � 4:04, P , 0:027,

h2 � 0:13; Cz: F�1; 27� � 5:21, P , 0:016, h2 � 0:16;

Pz: F�1; 27� � 3:87, P , 0:030, h2 � 0:13; one-tailed).

Analysis of P300 latencies yielded no signi®cant results.

We also assessed activity recorded from the EOG using

the same 200±900 ms window which did show a trend level

difference between the rare and frequent stimuli

(F�1; 27� � 2:90, P , 0:10, h2 � 0:10). This difference

was less signi®cant than ®ndings for the midline electrodes,

suggesting that this activity is more likely a re¯ection than a

source of the component observed at the midline electrodes.

Additionally, results at midline electrodes, do not decrease

in signi®cance in a linear fashion at sites further away from

the EOG (i.e. from frontal to parietal). Finally, the only

observable rare peak in the EOG grand average is near

700 ms, later than the observed rare peak in the midline

electrodes (near 550 ms), suggesting that activity at the

EOG is not the source of the peak observed at the midline

electrodes.

3.1. Principal components analysis

To ®nd convergent validation for the signi®cant oddball

peak in the 200±900 ms window, we conducted a varimax

rotated principal components analysis (PCA). The analysis

was based on a data matrix of 420 averages (3 electrodes £ 5

averages (one rare and 4 frequent� £ 28 participants) by 50

(the 1 s of raw data downsampled to 50 data points using the

Matlab resample function to handle ®ltering before down-

sampling). We did not apply additional ®ltering to the data

in this analysis (i.e. 7 Hz) to allow a closer look at the peaks

and troughs in the individual weighting vectors. Based on a

scree plot, we extracted 3 principal components which

accounted for 76% of the variance (Fig. 4). The ®rst compo-

nent (PC1) corresponded to the late part of the 1 s epoch,

and most closely resembled a late positivity or a slow wave.

The second principal component (PC2) was most clearly

like the P300 component window we had used; it had

minima at 240 ms and 900 ms, indicating that it corre-

sponded closely to the original 200±900 ms P300 window

we started with. The third principal component (PC3) corre-

sponded to the early part of the 1 s epoch, and is a gross

measure across the entire early epoch. Given the absence of

clearly identi®able peaks in this early time region, we felt a

gross measure was appropriate for representing this early

time epoch in this data.

We then separately multiplied the 3 principal components

by each of the 420 subaverages used to generate the princi-

pal components (Chapman and McCrary, 1995), and used

the mean (component or factor score) from the resulting

curves as data for analysis. We additionally measured the

peak in addition to the mean because P300 is conventionally

measured as a peak. We separately submitted the mean and

peak values to the same 2 (oddball: frequent, rare� £ 3 (elec-

trode: Fz, Cz, Pz) analysis of variance (ANOVA) as we had

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171 165

Table 1

Means and standard deviations for rare and frequent P300 peak amplitudes

and latencies (200±900 ms window) for individual electrodes and the aver-

age across electrodes

P300

Amplitude Latency

Rare Frequent Rare Frequent

Mean SD Mean SD Mean SD Mean SD

Fz 1.96 (2.33) 1.47 (1.81) 552 (210) 556 (184)

Cz 1.35 (1.86) 0.78 (1.24) 552 (206) 488 (142)

Pz 1.30 (1.86) 0.86 (1.39) 578 (206) 530 (142)

Average 1.54 (2.03) 1.04 (1.51) 560 (206) 524 (158)

Fig. 3. Rare (solid line) versus frequent (dashed line) grand averages for

electrodes Fz, Cz, and Pz, digitally ®ltered at 7 Hz..

the 200±900 ms window measures. The numerical statistical

results are presented in Table 2 and summarized below.

First, PC2 (P300) evidences signi®cant frequent-rare

differences, in an omnibus analyses across the electrodes,

for both the peak and the mean measures. As with the 200±

900 ms measure, the oddball effect does not signi®cantly

interact with electrode in this omnibus analysis, while the

main effect of electrode does show trend level differences.

Analysis of individual electrodes con®rms that each of the 3

electrodes evidence signi®cant frequent-rare differentiation

independently. The signi®cance level using the PC2 (P300)

peak measure are stronger than the 200±900 ms peak P300

measure, suggesting that the epoch weighted by the PC2

(P300) component contains more of the differentiating

activity. Second, for the PC1 (late) component the main

oddball effect is signi®cant for the mean and trend level

for the peak. For the individual electrode analyses, Cz

shows signi®cant differentiation for the peak and mean,

while Fz shows trend level for the peak and mean and Pz

show only trend level for the mean measure (Table 2).

Lastly, the PC3 (early) component does not approach signif-

icance for frequent-rare differences, and does show an elec-

trode main effect for the mean measure.

From an examination of the grand average plots, the

observed rare P300 component rises from a negative in¯ec-

tion after 300 ms to a peak after 500 ms, which appears to be

more narrow in time than our broad 200±900 ms window.

The shape of the PC2 (P300) also supports the conclusion of

a component centered on this peak, particularly in view of

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171166

Table 2

Signi®cant F ratios, P values, and h 2 values for omnibus and individual electrode analyses for the peak and mean of each of the 3 extracted principal

componentsa

Effect d.f. Principal component

Early (PC3) P300 (PC2) Late (PC1)

F P h 2 F P h 2 F P h 2

Peak

Omnibus analysis

Oddball 1,27 9.48 0.003 0.26 3.87 0.060 0.13

Electrode 2,54

Oddball £ Electrode 2,54

Electrodes separately

Oddball (Fz) 1,27 7.44 0.006 0.22 2.93 0.098 0.10

Oddball (Cz) 1,27 7.04 0.007 0.21 4.67 0.040 0.15

Oddball (Pz) 1,27 8.64 0.004 0.24

Mean

Omnibus analysis

Oddball 1,27 4.23 0.025 0.14 4.43 0.045 0.14

Electrode 2,54 5.07 0.010 0.16 2.82 0.069 0.09 2.73 0.075 0.09

Oddball £ Electrode 2,54

Electrodes separately

Oddball (Fz) 1,27 3.96 0.029 0.13 3.05 0.092 0.10

Oddball (Cz) 1,27 3.14 0.044 0.10 4.41 0.045 0.14

Oddball (Pz) 1,27 3.33 0.040 0.11 3.71 0.065 0.12

a Oddball main effect P values for P300 (PCA2) in omnibus and individual electrode analyses are one-tailed.

Fig. 4. Principal components derived using data from electrodes Fz, Cz, and

Pz.

the fact that ®ndings for the PC2 (P300) peak measure were

stronger than the 200±900 ms peak measure. However, the

grand average of the frequent stimuli, because an obvious

peak is lacking, offers little guidance for the rational selec-

tion of a more narrow component window to apply

uniformly to both rare and frequent stimulus responses.

Perhaps the amplitude of the responses to frequent stimuli

was too small to be detected, variability was too great,

substantial habituation occurred, or there simply was no

measurable response to subliminal frequent stimuli. The

dif®culty in ®nding a P300 peak for subliminal frequent

stimuli was also reported by Devrim et al. (1997), as well

as for supraliminal frequent auditory stimuli when using a

passive oddball design (Polich, 1989).

To further investigate whether a closer ®t for the P300

component could be found, we selected a more narrow

window based on the PC2 (P300) component, using the

local minima at 400 ms and 760 ms as a window de®nition

(Fig. 4). These minima were chosen as window boundaries

because they included the strongest weightings in the center

portion of the principal component and excluded the parts

which overlapped with the strongest portions of the other

two principal components. We then applied this more

narrow window to the raw ERPs (not ERPs transformed

by PCA weighting vectors) in the same manner as the

200±900 ms windows (same level of subaveraging, 7 Hz

®ltering, etc.). Results from analysis of the peak amplitude

in this 400±760 ms window were considerably stronger than

those from the 200±900 ms window both for the main effect

of oddball in the omnibus analysis including electrode as a

factor (oddball (one-tailed): F�1; 27� � 10:10, P , 0:002,

h2 � 0:27; electrode: F�1; 27� � 2:35, P , 0:105,

h2 � 0:08; oddball by electrode: F , 1), and the oddball

effect in the electrodes separately (Fz: F�1; 27� � 6:73,

P , 0:008, h2 � 0:20; Cz: F�1; 27� � 7:37, P , 0:006,

h2 � 0:21; Pz: F�1; 27� � 11:42, P , 0:001, h2 � 0:30;

one-tailed). These ®ndings provide further supportive

evidence that indeed more of the differential activity

happens in a this narrow window, which is more similar

in latency and duration to many P300 components evoked

with supraliminal stimuli than the 200±900 ms window.

3.2. Relationship between d 0 and the oddball effect

As discussed above, a skeptical conscious perception

explanation of putatively subliminal ®ndings makes several

testable predictions. First, it predicts that participants should

be able to detect the stimuli above chance; this was not the

case in the current experiment. However, because the grand

detection mean was numerically above chance, one might

wonder if the current non-signi®cant results might have

been due to insuf®cient power. Fortunately, further tests

are possible to test the alternative conscious perception

hypothesis. Recall that (1) a conscious perception explana-

tion would predict a positive relationship between detection

and the experimental effect, and relatedly (2) that no experi-

mental effect should be present when detection d 0 � 0. In

contrast, we predicted that (1) the oddball effect would

correlate negatively with detection, and (2) that the experi-

mental effect would not only be present at d 0 � 0 but at or

near its maximum.

To test these predictions, we employed Greenwald and

associates' regression approach (e.g. Greenwald et al.,

1995). In this method, the experimental effect (i.e. the

oddball effect in this study) is regressed onto direct measure

performance (detection d 0). Of primary interest to us was

not only the y-intercept (which estimates the oddball effect

when d 0 � 0, and which was Greenwald's primary interest),

but the direction of the relationship (i.e. positive or negative

slope). A potential problem with the regression approach is

bias in estimating the y-intercept. There is good reason to

expect such bias because regression assumes perfect

measurement of the predictor(s), whereas experimentally

measured detection performance clearly possesses some

measurement error. It is well-known (see, e.g. Dosher,

1998; Klauer et al., 1998a,b) that such measurement error

will systematically decrease the absolute value of the slope

estimate, which will in turn systematically bias the y-inter-

cept estimate. Crucially, however, the direction of this bias

is different depending on whether the slope is positive or

negative. If the true slope is positive, the `¯attening' effect

of measurement error will bias y-intercept estimates

upward, thus potentially producing artifactually signi®cant

above-zero y-intercepts. Importantly, however, if the true

slope is negative, measurement error will bias the y-inter-

cept estimate downward producing a conservative bias.

Measurement error is only problematic for the regression

approach, then, when positive slopes are obtained (Snod-

grass, 2000). If our prediction of a negative slope was

con®rmed, then, the associated y-intercepts will be conser-

vative estimates of the true oddball effect when d 0 � 0.

For the regression, the oddball effect was measured as the

difference between the P300 amplitude to the rare stimuli

and the frequent stimuli, using the narrow component

window (400±760 ms) based on the PCA. Separately for

each electrode, and again for the average of the 3 electrodes,

we computed a regression analyses between the oddball

effect and d 0. A discordancy test for single outliers (Barnett,

1994) indicated that all P300 difference and d 0 scores were

within an expectable chance distribution (individual parti-

cipant's P300 and d 0 scores are listed in Table 3). Scatter

plots of this relationship for the 3 electrodes are presented in

Fig. 5, with a linear regression line displayed. As hypothe-

sized, the regression b coef®cient and the corresponding

correlation are negative for the average across the 3 electro-

des (b � 21:61, r � 20:44, t�25� � 22:45, P , 0:011;

one-tailed) and for all 3 electrode locations separately (Fz:

b � 22:03, r � 20:48, t�25� � 22:73, P , 0:006; Cz:

b � 21:50, r � 20:34, t�25� � 21:79, P , 0:043; Pz:

b � 21:30, r � 20:37, t�25� � 22:01, P , 0:028; one-

tailed). Thus, the extent to which a participant is above d 0 �0 is associated with a decreased oddball effect. Interpreted

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171 167

in accord with the Snodgrass hypothesis, this ®nding means

that the more a participant might have detected (been

conscious of), the less the subliminal oddball effect, a coun-

terintuitive result based on a single process (conscious)

explanation.

Perhaps more important, however, in establishing subli-

minality at the objective threshold is to determine what is

happening when d 0 � 0. As discussed earlier, a signi®cant

effect when d 0 � 0 (i.e. the y-intercept) would support the

presence of unconscious processing (Greenwald et al., 1995;

Snodgrass, 2000). As hypothesized, the y-intercept is signif-

icantly above zero for the average of the 3 electrodes

(t�25� � 4:08, P , 0:0002, one-tailed), and at all 3 electro-

des separately (Fz: t�25� � 3:72, P , 0:0005; Cz:

t�25� � 3:16, P , 0:002; Pz: t�25� � 4:02, P , 0:0003;

one-tailed).

4. Discussion

Our results provide evidence that a late endogenous

component can be elicited by subliminal stimuli presented

in an oddball paradigm with all stimuli meeting criteria for

the objective detection threshold. Although Brazdil et al.

(1998) used a design similar to ours, they could not rule

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171168

Fig. 5. Scatter plot of d 0 versus rare-frequent peak amplitude difference

(400±760 ms window), for the average amplitude across electrodes Fz,

Cz, and Pz (top), and separately for each electrode, with a linear regression

line displayed in each plot.

Table 3

Listing of individual participant d 0 scores and P300 peak amplitude values

(400±760 ms window) averaged across Fz, Cz, and Pz for rare, frequent,

and the rare-frequent difference, sorted by rare-frequent difference

Rare-freq. Rare Freq. d 0

2.92 0.78 22.14 20.39

2.91 4.20 1.29 0.24

2.34 3.90 1.55 0.16

2.20 2.89 0.68 0.00

1.74 3.12 1.38 20.47

1.72 4.06 2.34 20.16

1.71 3.18 1.47 20.16

1.52 2.98 1.46 0.00

1.45 2.97 1.51 20.16

1.36 3.20 1.84 0.16

1.21 3.70 2.49 0.08

1.12 0.86 20.26 0.24

1.07 21.20 22.27 20.75

1.05 0.39 20.65 20.16

0.97 2.89 1.92 0.4

0.67 0.38 20.29 0.00

0.66 1.10 0.44 0.16

0.44 0.75 0.31 20.24

0.34 21.08 21.42 0.64

0.26 0.97 0.71 0.39

0.20 1.06 0.86 0.00

0.10 1.47 1.37 0.4

20.05 1.14 1.19 Not available

20.38 0.73 1.12 0.39

20.91 21.91 21.00 0.00

21.32 22.00 21.00 0.24

21.76 21.00 0.53 0.00

21.77 21.49 0.28 0.91

out conscious perception as an explanatory factor because of

their use of a subjective threshold. Devrim et al. (1997)

found that subliminal frequent stimuli increased P300

amplitude to a supraliminal rare stimulus in an oddball

task, although it should also be reiterated that their study

relied on a problematic implementation of signal detection

theory procedures and thus conscious perception of the

stimuli can not be ruled out. Our design made it possible

to obtain a P300 to the rare stimuli presented without

conscious awareness. Notably, some have theorized that

P300 is directly associated with conscious registration.

Libet (1977) has suggested that the later ERP components

(after 100 ms in his research) might be directly associated

with consciousness. Similarly, Posner and Boies (1971)

have suggested that P300 might be a marker for conscious-

ness, as has Pritchard (1981) who cites evidence suggesting

that the P300 is absent until d 0 exceeds zero. Our results do

not support this understanding of P300. Based on much

®rmer methodological grounds for ruling out consciousness,

our results strongly suggest that ERPs to subthreshold

stimuli are markers for some of the same functional proper-

ties as ERPs to above threshold stimuli, and thus linking

®ndings on subliminal ERPs to a considerable body of

ERP research and theory.

Our results show no signi®cant electrode differences for

the frequent-rare comparisons, although the Fz amplitude is

greater than Cz and Pz. Whether a P300 component is fron-

tally or parietally maximal has been an important considera-

tion in P300 studies. Perhaps the clearest examples are the

functional differences found for P3a and P3b. The more

frequently observed P3b shows a parietal maximum while

P3a shows a frontal maximum (Polich and Kok, 1995). The

failure to ®nd a clear frontal or parietal maximum is consis-

tent with the ®ndings of Polich (1989) showing decreased

parietal maximum, or less difference between these regions,

using a passive auditory paradigm. It is worth speculating

that a number of factors might have reduced any frontal

effect, given the smaller amplitude of the subliminal

ERPs, and the resulting greater contribution of any level

of artifact such as any eye movement or muscle potentials.

While the question of frontal or parietal maximum will go

without a de®nitive answer in this report, the critical main

®nding is the signi®cantly higher amplitude for a late endo-

genous component occurring within the P300 window to the

rare as compared to the frequent stimuli when objective

detection d 0 is at zero.

The negative relationship between values of d 0 (equal to

or above zero) and the oddball effect is a powerful argument

against the hypothesis that consciousness can account for

the effect. Interestingly, a non-signi®cant relationship would

also argue against the consciousness hypothesis, but a nega-

tive relationship raises the provocative possibility,

suggested by the Snodgrass hypothesis, that some conscious

awareness of the stimuli counteracts subliminal in¯uences

(Snodgrass, 2000). In that sense, a little conscious percep-

tion may actually inhibit a strong subliminal effect. If d 0

were considerably above zero and the stimuli were all

clearly in consciousness then an oddball effect would be

obtained (as it has been many times), but the correlation

between d 0 and the oddball effect would be positive. It is

this type of reversal in direction of the correlation which

Snodgrass (2000; see also Dagenbach et al., 1989) refers to

as the non-monotonicity of the relationship between detec-

tion d 0 and the subliminal effect.

As a ®nal consideration, one could argue that because

direct detection measures are often measured with fewer

trials than indirect subliminal measures, indirect-without-

direct effects may simply be an artifact of undersampling

the direct measure. Our study could be subject to this criti-

cism because we did sample d 0 with fewer trials than the

oddball effect (64 vs. 300 trials, respectively). In this

scenario, if enough trials were administered the true extent

of consciousness on the direct measure would be revealed.

The underlying logic in this argument, however, is that the

true relationship is positive and that if detection were

adequately sampled a positive correlation would be found

between d 0 and the apparent subliminal effect, thus under-

mining the claim that the indirect task was eliciting an

unconscious effect. However, in our case the sampling

size proved suf®cient to ®nd a relationship, but as hypothe-

sized it was negative (and not positive or non-signi®cant). It

would be hard to account for this ®nding with a hypothesis

based solely on undersampling which would predict no rela-

tionship. The ®nding of a negative correlation also applies to

criticisms that detection tasks may simply be less sensitive

to even the same conscious processes than other measures

(e.g. physiological measures may be intrinsically more

sensitive than verbal report), even if well sampled (e.g.

Eriksen, 1960). This criticism would again predict no rela-

tionship, not a signi®cant negative relationship.

A demonstrable P300 component to subliminal stimuli is

a potentially important contribution to the study of

consciousness and P300 related information processing.

First, we can begin to speculate about the role of conscious

awareness in the context updating processes. Sommer and

Matt (1996) have provided evidence suggesting that parti-

cipants can have a conscious index of the amplitude of their

P300 when evoked in a standard supraliminal oddball para-

digm. Devrim et al. (1997) offer suggestive evidence that

subliminal frequent stimuli enhance P300 responses to

supraliminal rare stimuli in an oddball paradigm. Results

from this study now suggest that a P300 response can be

evoked even when both rare and frequent stimuli are

presented outside conscious awareness. Indeed, the P300

phenomenon appears to span the range from unconscious

processes to conscious awareness. Because subjective prob-

ability is given fundamental importance in interpreting P300

®ndings (Donchin et al., 1986), we are left to speculate that

either subjective probability is somehow not fundamental to

the current ®ndings (e.g. perhaps unconscious processes

operate under qualitatively different rules), or perhaps

subjective probabilities can occur without conscious aware-

E. Bernat et al. / Clinical Neurophysiology 112 (2001) 159±171 169

ness. This would suggest that expectancies can be both

modi®ed and evoked without conscious awareness. In

other words, a mental process which is dynamically inter-

active with the environment can happen without the bene®t

of consciousness. This is compatible with a growing body of

literature demonstrating that learning in the form of aversive

conditioning can occur without bene®t of conscious aware-

ness (Ohman et al., 1995; Wong et al., 1997). There may

well be other such processes operating without bene®t of

conscious awareness, the presence and nature of which

remain for future research to investigate.

Acknowledgements

Portions of this data were presented at the third meeting

of the Association for the Scienti®c Study of Consciousness,

in London, Ontario, Canada, June, 1999. The research

reported in this study was supported in part by gifts from

Robert H. Berry, the Department of Psychiatry, Department

of Psychology, and the Rackham Graduate School of the

University of Michigan. We thank William Williams,

William Gehring, and Philip Wong for assistance and feed-

back on many aspects of this manuscript.

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