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Given the hard problem of consciousness, there are no brain

electrophysiological correlates of the subjective experience

(the felt quality of redness or the redness of red, the experience of dark and light, the quality of depth in a visual field, the sound of a clarinet, the smell of mothball, bodily sensations from pains to orgasms, mental images that are conjured up internally, the felt quality of emotion, the experience of a stream of conscious

thought, or the phenomenology of thought).

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However, there are brain occipital (Oz)

electrophysiological correlates of the

subjective experience [1].

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The relevant computation to the effect of the occipital (Oz) correlates of

the distinction between access and phenomenology [1] is the

computation of the high degree of visibility "4" and "5" assigned by the

participants in both experiments to the correctly identified stimuli

(and what there are more in the second experiment is more incorrect

answers than in the first experiment), because to distinguish

electrophysiologically the access from phenomenology we need that

access and phenomenology will be cognitively consciousness of

something and we need that access will be the same for all participants in the two experiments [1 : 337-339].

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Notwithstanding, as evoked signal, the change in event-related brain

potentials (ERPs) phase (frequency is the change in phase over time) is

instantaneous, that is, the frequency will transiently be infinite:

a transient peak in frequency (positive or negative), if any, is

instantaneous in electroencephalogram (EEG) averaging or filtering

that the ERPs required and the underlying structure of the ERPs in

the frequency domain cannot be accounted, for example, by the

Wavelet Transform (WT) or the Fast Fourier Transform (FFT) analysis,

because they require that frequency is derived by convolution (frequency are pre-defined and constant over time) rather than by differentiation (without predefining frequency and accounted that frequency may

vary over time).

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Despite the fact that the Wavelet or the Fourier

Transform are the methods most widely used for

analysing the linear (proportionality or additivity)

and stationary

(the signal and the time series representing it have the same mean and variance throughout)

properties of the EEG signal,

the EEG signal has nonlinear (nonproportionality or nonadditivity) and nonstationary (the signal's

statistical characteristics change with time)

properties.

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However, one suitable method for analysing the

instantaneous change in event-related brain

potentials (ERPs) phase and accounting for a

transient peak in frequency (positive or negative), if any, in the underlying structure of the ERPs is

the Empirical Mode Decomposition (EMD) with

post-processing [2] Ensemble Empirical Mode Decomposition (postEEMD).

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The Wavelet or the Fourier Transform analyse the

signal in time-frequency-energy (Wavelet) and

frequency-energy (Fourier) domains without

discrete feature extraction

(Wavelet, with continuous feature extraction) or

without discrete or continuous feature extraction

(Fourier).

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However, the Hilbert-Huang Transform (HHT) analyses the signal in

the time-frequency-energy domain for feature extraction.

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For example, either the Fourier functions or

the EMD functions are oscillations with zero mean derived from the decomposition of a

signal (for example, ERPs) that, when

summed together, reconstitute the original

signal.

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However, whereas the Fourier functions are

called harmonic functions, meaning that their amplitude and frequency are constant over

time, the EMD functions are called Intrinsic

Mode Functions (IMFs), meaning that their

amplitude and frequency may vary over time.

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Once the Intrinsic Mode Functions have been extracted and post-processed [2],

the Hilbert-Huang Transform can be used to

display the underlying structure in the

amplitude and frequency domain of the grand average occipital and left temporal electrical activity characterised in [1].

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To evaluate the presumed excessive

correlation among variables (i.e., colinearity), we calculated the variance inflation factor (VIF) for each variable by vif_fun.r [5].

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If the VIF calculated for each variable is more

than 10 (values in the range of 5-10 are commonly used as thresholds), colinearity is

strongly suggested and the variable is

removed.

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If we set 59 as the seed, the partial least squares regression (PLSR) [6] , [7] , [8], cross-validated using 10 random segments, returned the _____ as the minimal root mean squared error of prediction (RMSEP) for

Oz instantaneous amplitude and or frequency.

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Minimal value that we can use to measure

with less error of prediction the propagation of the remaining Oz amplitude and or

frequency values around the variability

between the two experiments.

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The partial least squares regression (PLSR)

Oz instantaneous amplitude

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Fig. 1. The postIMF 3 combined Diamond Pseudo is the Oz instantaneous

amplitude minimal value that we can use to measure with less error of prediction

the propagation of the remaining Oz instantaneous amplitude values around the variability between the two experiments.

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An independent-sample t-test was conducted to compare

postIMF 3 combined Diamond Pseudo (Ozp3cDP) between the two experiments in

Oz instantaneous amplitude.

Equal variances not assumed, there was a significant difference in the

postIMF 3 combined Diamond Pseudo Oz instantaneous amplitude for experiment II

(M= 250.08, SD= 221. 24) and experiment I

(M=141.85, SD = 116. 99),

t (347.796)= 6.559, p < 0.001, 95% CI [75.78, 140.69], g [ 95 % CI] = 0.61 [ 0.42 , 0.8 ].

The Common Language Effect Size (CLES) indicates that the chance that for a randomly

selected pair of Ozp3cDP instantaneous amplitude values, the Ozp3cDP instantaneous

amplitude values from experiment II are higher than the Ozp3cDP instantaneous amplitude

values from experiment I is 66.7% [9].

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The partial least squares regression (PLSR)

Oz instantaneous frequency

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Fig. 2. The postIMF 1 Mask is the Oz instantaneous frequency minimal value that we can use to measure with less error of prediction the propagation of the remaining Oz instantaneous frequency values around the variability between the two

experiments.

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An independent-sample t-test was conducted to compare postIMF 1 Mask (Ozp1M) between the two experiments in Oz instantaneous frequency.

Equal variances not assumed, there was a significant difference in the postIMF 1 Mask Oz

instantaneous frequency for experiment II (M= 0.29, SD= 0.14) and

experiment I (M=0.23, SD = 0.15),

t (457.061)= 4.737, p < 0.001, 95% CI [0.03, 0.09], g [ 95 % CI] = 0.44 [ 0.26 , 0.63 ].

The Common Language Effect Size (CLES) indicates that the chance that for a randomly selected pair of Ozp1M instantaneous frequency values, the Ozp1M instantaneous frequency values

from experiment II are higher than the Ozp1M instantaneous frequency values from

experiment I is 62.24% [9].

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Notwithstanding, what variables are important

for the variability between the two experiments

remained to be assessed.

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　Given the calculated minimal value that we can use to measure with less error of prediction (namely, 23 variables in

Oz instantaneous amplitude and, 40 variables in Oz instantaneous frequency), the propagation of the

remaining values around the variability between the two

experiments, which variables are important for the variability

between the two experiments, is assessed by the significance

multivariate correlation (sMC) statistic ([10] and, e.g., [11]) of the partial least squares regression (PLSR) results (figs. 1-2),

cross-validated using 10 random segments

(setting 59 as the seed).

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　In other words, which variables are important for the

variability between the two experiments [1] are assessed by

comparing the ratios between the variable-wise

Mean Squared Errors (MSE) and the mean squared of its

residuals to an F-test with 1 and N - 2 degrees of freedom

(the cut-off is based on the F-test, because appeared that the

cut-off based on the mean was influencing negatively the

predictions):

the variables that exceed the F-test threshold are selected.

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　If we set 59 as the seed, the significance

multivariate correlation (sMC) statistic,

with a correction of 1st order auto-correlation in the residuals, "out-of-bag" (OOB) validation and with 1000 cross-validation bootstrap samples,

selected the following variables as important for the variability between the two experiments [1] in Oz instantaneous amplitude and in Oz instantaneous

frequency.

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Significance multivariate correlation (sMC) statistic

Oz instantaneous amplitude

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　　　Related to Oz instantaneous amplitude,

the 4 variables postIMF 6 SquarePseudo,

postIMF 7 diamo, postIMF 4 SquareMask,

postIMF 4 DiamondMask, empirically decomposed

and post-processed [2] from Oz event-related

changes [1], are selected as important for the

variability between the two experiments in

instantaneous amplitude.

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The repeated measures analysis of variance (ANOVA) with

the experiment I and experiment II [1] as a between-subjects factors and the postIMF variables selected as important by significance multivariate correlation (sMC) statistic as a

within-subject factors gave the following significant

(Greenhouse-Geisser correction for violations of the sphericity) results for Oz instantaneous amplitude [F(1.197,548.082)= 146.612, p < 0.001, ηp² = 0.24249, 90% CI [0.96 , 1.29], ηG² = 0.14940]. See [12], for

calculating and reporting effect sizes.

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Significance multivariate correlation (sMC) statistic

Oz instantaneous frequency

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Related to Oz instantaneous frequency, the 6

variables postIMF 7 Pseudomask,

postIMF 6 SquarePseudo, postIMF 5 SquarePseudo, postIMF 5 SquareMask,

postIMF 6 DiamondPseudo, and postIMF 7 diamo,

empirically decomposed and post-processed [2]

from Oz event-related changes [1], are selected as

important for the variability between the two

experiments in instantaneous frequency.

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The repeated measures analysis of variance (ANOVA) with the

experiment I and experiment II

[1] as a between-subjects factors and the postIMF variables

selected as important by significance multivariate correlation (sMC) statistic as a within-subject factors gave the following significant

(Greenhouse-Geisser correction for violations of the

sphericity) results for Oz instantaneous frequency,

the repeated measures ANOVA results are [F(3.111,1424.755)= 73.586,

p < 0.001, ηp² = 0.13843, 90% CI [0.64 , 0.96], ηG² = 0.08082].

See [12], for calculating and reporting

effect sizes.

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Contrast in access for Oz instantaneous

amplitude

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Fig. 3. The statistically significant contrast in the variability of intrinsic mode functions between the two experiments correlated with a contrast in access is for the

instantaneous amplitude within the 3 variables postIMF 4 SquareMask,

postIMF 6 SquarePseudo, postIMF 4 DiamondMask (Oz).

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Contrast in access for Oz instantaneous

frequency

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Fig. 4. The statistically significant contrast in the variability of intrinsic mode

functions between the two experiments correlated with a contrast in access is

for instantaneous frequency within the 4 variables postIMF 5 SquarePseudo, postIMF 5 SquareMak, postIMF 6 DiamondPseudo and postIMF 6 SquarePseudo (Oz).

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　Remind that the trials that are the same in the second

block in both experiments for the same high degree of

visibility "4" and "5" (they also, access) and for the same

correct answers (stimulus’s discrimination doesn’t contrast

in correct and incorrect responses between the two

experiments) are the isolated presentations of square or

diamond and of mask or pseudo-mask.

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Contrast in phenomenology for

Oz instantaneous amplitude

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Fig. 5. The statistically significant variability between the two experiments correlated

with a contrast in phenomenology is for the instantaneous amplitude within the

1 variables postIMF 7 diamo (Oz).

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Contrast in phenomenology for

Oz instantaneous frequency

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Fig. 6. The statistically significant variability between the two

experiments correlated with a contrast in phenomenology is for the

instantaneous frequency within the 1 variables postIMF 7 diamo (Oz).

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References

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