Increased information transmission during scientific hypothesis generation: Mutual information analysis of multichannel EEG

International Journal of Psychophysiology 62 (2006) 337 – 344 www.elsevier.com/locate/ijpsycho

Increased information transmission during scientific hypothesis generation: Mutual information analysis of multichannel EEG Seung-Hyun Jin a , Yong-Ju Kwon b,⁎, Jin-Su Jeong b , Suk Won Kwon b , Dong-Hoon Shin b a

b

Bio-signal Research Laboratory, Korea Research Institute of Standards and Science, Daejeon, 305-600, Korea Department of Biology Education, Korea National University of Education, Chungbuk, 363-791, Republic of Korea Received 23 November 2004; received in revised form 15 March 2006; accepted 15 June 2006 Available online 22 August 2006

Abstract Hypothesis generation has been regarded as one of the core reasoning processes in creative thinking and scientific discovery. To investigate changes in the amount of information transmission during scientific hypothesis generation, the averaged cross-mutual-information (A-CMI) of EEGs was estimated. Twenty-five 5th grade students were sampled in this study. EEG signals from 16 electrodes on each subject's scalp were recorded using a 32-channel EEG system. In order to generate hypotheses, the students were asked to observe 20 quail eggs that gave rise to questions such as: Why do different sizes and shapes of patterns appear on the surface of the eggs? After the observation, they were asked to generate a scientific hypothesis—a tentative causal explanation for the evoked question. The results of experimentation indicated several distinct brain activities during hypothesis generation interacting between different local brain regions. In addition, it was observed that the amount of information transmission during hypothesis generation increased in a large part of the brain region encompassing the temporal, parietal, and occipital cortexes, which implies the use of declarative and procedural memory systems. Furthermore, this study suggested the possibility that neuropsychological approaches may be potential tools to investigate the neuronal activity of EEGs during hypothesis generation. © 2006 Elsevier B.V. All rights reserved. Keywords: Mutual information; Hypothesis generation; EEG; Information transmission; Declarative memory; Procedural memory

1. Introduction A hypothesis is a proposition or a set of propositions proposed as a tentative causal explanation for an observed situation (Enger and Ross, 2003; Lawson, 1995; Uno et al., 2001). Generating and testing scientific hypotheses are key components of the modern scientific method (McPherson, 2001). Specifically, hypothesis generation has been regarded as one of the core reasoning processes in creative thinking and scientific discovery (Lawson, 1995). In the context of cognitive psychology, hypothesis generation may be defined as the procedure of interaction between declarative and procedural memory. Declarative memory refers to accessible conscious knowledge which includes personal (episodic memory) and world knowledge (semantic memory). Procedural memory, in contrast, is one form of nondeclarative memory that involves the learning of a ⁎ Corresponding author. Tel.: +82 43 230 3763; fax: +82 43 232 7176. E-mail address: [email protected] (Y.-J. Kwon). 0167-8760/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpsycho.2006.06.003

variety of motor skills, cognitive skills and cognitive reasoning (Gazzaniga et al., 2002). For example, if one is confronted with a questioning situation, he/she might attempt to generate a hypothesis in order to explain the evoked question. Hypothetical explanation for questioning phenomena arises from the adoption of experienced phenomena. This is in accordance with the opinions that abduction involves sensing ways in which a new situation is somewhat similar to other known situations and using this similarity to make hypotheses about the new situation (Lawson, 1995, 2000; Moore and Vodopich, 1998). In the process of hypothesis generation, evoking a questioning situation and retrieving an experienced situation similar to the questioning situation correspond to the declarative memory processes and comparing the questioning situation with the experienced situation and drawing on experienced phenomena as questioning phenomena correspond to procedural memory processes. Thus, hypothesis generation may be defined as the procedure of interaction between declarative and procedural memory. Philosophical and cognitive psychological research has

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done much for scientific hypothesis and hypothesis generation (Lawson, 1995; McPherson, 2001); however, despite their importance, neuropsychological approaches have been largely ignored in scientific hypothesis generation. Therefore, the aim of the present study is to investigate whether different brain activities in multi-channel electroencephalography (EEG) can be observed during hypothesis generation. In the context of information theory, linear properties depend on second-order statistics and nonlinear properties include higher-order statistics of the probability distribution function that describes a certain signal. If the probability distribution function of a signal is not a simple Gaussian process, having only second-order statistics, nonlinear properties appear along with linear activities. Multi-dimensional EEGs are usually considered signals drawn from higher-order statistics, and EEGs are composed of linear and nonlinear activities (Jin et al., 2003). Linear analysis has been used for detecting changes between EEGs from different brain states during various cognitive processes (Harmony et al., 2004; Jaušovec and Jaušovec, 2000). The application of tools for characterizing a time series generated by nonlinear dynamical systems may provide a more complete description of the EEG recordings (Van der Heyden et al., 1999). Practically, nonlinear dynamical analysis such as correlation dimension has been used to investigate the information processed during cognitive tasks (Kirsch et al., 2000). These measures provide useful tools to estimate linear or nonlinear properties; however, more information could be provided from measures that determine the functional connectivity between different areas, other than just the level of activity in different areas (Jaušovec, 2000). Coherence has been used to study the functional connectivity between, and within, brain hemispheres using EEG data (Anokhin et al., 1999; Schack et al., 1999). However, EEG coherence measures only linear dependencies in the electrical potentials across those regions (Na et al., 2002). In the present study, to wholly investigate the linear and nonlinear properties of functional connectivity between a pair of electrodes, investigators applied the measure of mutual information. Mutual information detects linear and nonlinear statistical dependencies between two time series (Vastano and Swinney, 1988). It has a maximum value when the two time series are completely identical, whereas it has a zero value when one system is completely independent of the other. The transmission of information was estimated among the different cortical areas in the wake and sleep states using mutual information from eight EEG electrodes (Xu et al., 1997). In a clinical environment, Jeong et al. (2001) assessed the transmission of information between different cortical areas of patients suffering from Alzheimer's disease, and Na et al. (2002) applied the same measure to schizophrenic patients. They discussed the results in terms of the cortico-cortical connection and the transmission of information between different cortical areas. In addition, Min et al. (2003) showed different changes in cortico-cortical connectivity during odor stimulation of normal subjects classified by occupation by means of the mutual information content of EEGs. Thus, the aim of this study is to investigate whether different brain activities in EEG can be observed during hypothesis gen-

eration and which cognitive systems are related to this process by means of the averaged cross-mutual-information (A-CMI) between EEG electrodes. Section 2 presents the experimental procedure and data acquisition of this study and briefly explains the algorithm for estimating the A-CMI from a time series, whereas Section 3 discusses independent component analysis (ICA) used for artifact removal. A-CMI changes in EEG before and during hypothesis generation are presented in Section 4. Lastly, discussions of study results are provided in Section 5. 2. Materials and methods 2.1. Subjects EEG recordings were obtained from 25 normal right-handed 5th grade students (age: 11.04 ± 0.35 years, 12 males and 13 females) who were selected from a group of volunteers with no history of psychiatric or neurological diseases. Their intelligence quotient (IQ) score was 99.95 ± 16.70 and their school achievement score was more or less the same. The level of school achievement was determined by school grades and teacher reports. Tests of statistical significances (t-test for equality) between the two scores (IQ and school achievement) and gender were nonsignificant with means of P = 0.154 and 0.238, respectively. All subjects and their parents were fully informed and consented to participate in the study, and the local ethical committee approved this study. 2.2. Experimental procedure Before the actual experiment, all subjects participated in a pilot experiment, which was representative of the experimental procedure they would later encounter with only different hypothesis generation matter. Through this preparatory experiment procedure, students came to fully comprehend the entire experiment, subsequently enabling smooth execution of the real experiment. Fig. 1 presents a schematic display of the entire experimental procedure. In Step1, experimenter thoroughly explains the experiment procedure and points out cautionary behaviour while attaching electrodes to the subject's scalp. EEG recordings were attained from students seated in comfortable chairs in an electrically shielded room. Students were informed that their EEG would be recorded while at rest as well as during hypothesis generation. After the electrodes had been attached by the experimenter, a 5-min adaptation period was observed before the first recording (Step2). Following the adaptation period, student EEGs were recorded over a 30-s stimulus-free period as students looked at a sheet of white paper on the desk (Step3). Subjects were asked to keep their mind during the resting condition free of other thoughts. For the hypothesis generation task, this study employed the ‘Quail Egg Task,’ designed by four experts in science education, taking into account the difficulty of the task. The 20 eggs obtained from a quail differed in size and surface patterns. The experimenter displayed the 20 quail eggs in front of the students.

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Fig. 1. Schematic display of experimental procedure.

Then, the students would observe them for 30 s (Step4). In general, student observation should raise the interesting question, “Why do the eggs differ in size and surface pattern?” or something similar. After the experimenter verified the evoked question (Step5), students were asked to generate a scientific hypothesis, a tentative causal explanation for the question (Step6). Hypotheses generation from a silent cognitive process produces a signal that is apparently greater than when the task is verbalized (Yetkin et al., 1995; Schlösser et al., 1998) because verbalization decreases significance owing to the amplification of noise interference (Friston et al., 1996). Hence, as a precaution, the experimenter advised students to concentrate solely on generating a hypothesis. After data collection, the experimenter checked the subjects' hypotheses through an indepth interview (Step7). As it is virtually impossible to determine if students concentrated solely on the task at hand or if they performed other cognitive activities, the experimenter had to make an inference from students' answers during the indepth interview process at to whether the results were related to hypothesis generation per se or some other cognitive activity. If subjects were unable to generate a hypothesis, the experiment was repeated until generation was achieved. Even though prior to the task the procedure for generating a hypothesis was explained to the participants, two female and three male subjects failed to generate a hypothesis on the first try. However, they all successfully managed to generate a hypothesis on the second try. According to several studies (Kwon et al., in press, 2003), children have been shown to possess a considerable amount of cognitive capacity in hypothesis generation without previous training. Kwon and his colleagues found that 89 out of 138 6th graders successfully generated hypothesis in a vapor condensation task without explanatory instruction about how to generate a hypothesis. In the like manner, Kwon and his colleagues also found that 281 out of 290 5th graders could generate hypothesis in a pendulum task without prior conditioning about the process of hypothesis generation. Nonetheless, a large number of these hypotheses had no scientific grounding. Even so, from these studies, it may be presumed that 5th grade children possess the cognitive ability to generate hypotheses.

2.3. EEG acquisition EEG activities were recorded from 16 scalp locations (Fp1/2, F3/4, C3/4, P3/4, O1/2, F7/8, T3/4, T5/6) according to the international 10–20 system. EEG signals were acquired with a sampling frequency of 256 Hz and digitized using a 12-bit analog–digital converter on an IBM PC. Contact resistances were kept below 5 kΩ. The EEGs from 16 channels against linked earlobes were amplified on a COMPUMEDICS system (Australia) with a time constant of 0.1 s. All EEG signals were recorded for durations of 30 s and digitally filtered with a band pass of 0.3 Hz to 60 Hz. For all conditions 16 s of data were used (4096 data points) for mutual information analysis. 3. EEG analysis methods 3.1. Artifact removal Artifact removal, especially eye movement and blinks, needed to be performed because EEG data was collected while subjects' eyes were open. In order to accomplish this, the “infomax” algorithm proposed by Bell and Sejnowski (1995) was chosen from all available ICA methods and employed. Rejecting EEG segments with artifacts larger than an arbitrarily preset value is the most commonly used method for dealing with artifacts in research settings. However, when limited data are available, or blinks and muscle movements occur too frequently, the amount of data lost to artifact rejection may be intolerable (Lee, 1998). To overcome this disadvantage, ICA can determine applicability and effectiveness for removing a wide variety of artifacts from EEG recordings (Jung et al., 1998, 2000a,b; Lee, 1998). It has several advantages. ICA is computationally efficient and no arbitrary thresholds are needed to determine when regression should be performed. Separate analyses are not required to remove different classes of artifacts because once ICA training is complete, artifact-free EEG records in all channels can be derived by simultaneously eliminating the contributions of various identified artifactual sources in the EEG record (Lee, 1998). The function of the ICA algorithm is to find a matrix W which makes the elements u(t) = [u1(t),…uN (t)]T of the linear transform u(t) = Wx(t) with data vector x(t) = [x1(t),…xN (t)]T statistically

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independent. ICA imposes the stronger criterion that the multivariate probability density function (p.d.f) of u factors as: N

fu ðuÞ ¼ ∏ fui ðui Þ. Additionally, ICA assumes that each of the i¼1 unknown independent components ui has the same form of cumulative density function (CDF), denoted as Fu (u) after scaling and shifting. ICA can then maximize the entropy H (y) of a nonlinearly transformed vector to minimize the mutual information between ui: y = Fu(u). This yields the following stochastic gradient ascent rule for adjusting W:
 AHðyÞ T W W ¼ e I−/ðuÞuT W DW ¼ e AW where ε is the learning rate (normally less than 0.01) and ϕ(u) is the gradient vector of the log likelihood called the ‘score function’ (Amari, 1998) :     A Ayi /ðui Þ ¼ ln Aui Aui Lee (1998) showed that the logistic function yi = Fui(ui) = (1 + exp(− ui))− 1 generated comparable results to other known CDFs. In the case of ϕ(ui) = 2yi − 1, the algorithm has a very simple form. For further details of the theory and practical algorithm of ICA consult research by the Sejnowski group (Bell and Sejnowski, 1995; Makeig et al., 1996; Lee, 1998; Lee et al., 2000). ICA appears to be very effective for performing source separation in domains where the number of sources is greater or equal to the number of sensors, i.e., N sensors used in the ICA algorithm can separate a maximum of N sources. Accordingly, the EEG of each subject was separated into 16 independent components since 16 channels had been used as a measure of EEG. The 16-dimensional vectors were presented to a 16→16 ICA network one at a time; criteria specified by Makeig and his colleagues (1996). Fig. 2(a) shows a subject's unedited EEG recording from 16 channels. The eye blinks near the 4, 10 and 15 s time coordinates contaminate all channels. Fig. 2(b) displays ICA components relative to their contribution to the raw data. From the time course of an individual independent component and its scalp map, it is possible to determine which artifact should be removed from the raw data. In Fig. 2(b), the ICA component 1 reflects a pure eye blink signal so the corrected EEG signals will appear as shown in Fig. 2(c). This process was repeated for all EEG data, and the A-CMI value was calculated with the artifact removed from the EEG signals. Because ICA removed the artifact, corrected EEG signals can be viewed as artifact-free data reflecting other meaningful brain activities. This, in turn, implies there is no ICA influence on mutual information measures. 3.2. Mutual information Mutual information is a measure of the amount of information gained about one system from the measurement of another. Let U be the whole set composed of an element of possible messages u1,u2,u3,…un and probability PU(u1),PU(u2),PU(u3),…

PU(un). The average amount of information gained from the measurement of U is the entropy H of the system, X PU ðui ÞlogPU ðui Þ HðU Þ ¼ − ui aU

where PU(ui) is the associated probability that an isolated measurement will find the system in the ith element. Also, PU(ui) is the normalized histogram of the distribution of values observed for the measurement u. These probabilities were evaluated via a histogram of the variations of the measurement u. It is here that the mutual information can be achieved as the amount by which the measurement of U reduces the uncertainty of V. Mutual information I(V,U) is as follows: IðV ; U Þ ¼ HðV Þ−HðV jU Þ ¼ HðV Þ þ HðU Þ−HðV ; U Þ ¼ IðU ; V Þ It can, then, be rewritten as: I ðV ; U Þ ¼ −

X

  PVU ðvi ; uj Þ PVU vi ; uj log : PV ðvi ÞPU ðuj Þ

Mutual information has a maximum value when the two time series are completely identical, whereas the mutual information value is zero when one system is completely independent of the other. Time-delayed mutual information was computed using the following equation (Jeong et al., 2001; Min et al., 2003; Na et al., 2002). I ðV ðt Þ; U ðt þ sÞÞ X ¼− PV ðtÞU ðtþsÞ ðvðt Þ; uðt þ sÞÞ vðtÞaV ; uðtþsÞaU

 log

PV ðtÞU ðtþsÞ ðvðtÞ; uðt þ sÞÞ PV ðtÞ ðvðtÞÞPU ðtþsÞ ðuðt þ sÞÞ

The time-delayed CMI, I(V(t),U(t + τ)), which represents the mutual information of the EEG between different electrodes as a function of time delay, along with A-CMI values were used as a measure for mutual coupling or for information transmission between different cortical areas. Detailed derivation of these equations and factual descriptions are presented in Cover and Thomas (1991), Fraser and Swinney (1986), and Jeong et al. (2001). 64 bins were utilized to construct a histogram from the experimental data in order to estimate the probability density PVU(v,u). This process provided stable estimates of probability. To investigate brain functional connectivity, the CMI of each EEG as a function of time delay between two different electrodes over time delays of 0 ms to 500 ms were estimated, and the CMI values were averaged to attain a A-CMI value over time delays. 240 pairs of A-CMI values were obtained because 16 pairs corresponding to auto-mutual information were excluded. The t-test for statistical significances in equality

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Fig. 2. (a) 16-channel EEG data set—near the coordinates of 4, 10 and 15 s artifacts from eye blinks contaminate the data set, (b) ICA components separated from the EEG data in (a)—eye blinks are clearly concentrated in ICA component 1, (c) edited EEG signals—removal of the ICA artifact component 1.

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between A-CMI values and gender were found to be nonsignificant. The results of the A-CMI value calculations were examined statistically using a repeated measure analysis of variance (ANOVA) with a condition factor (CONDITION: resting/generating a hypothesis, 2 levels) and with a subject factor (ELECTRODE: 240 pairs of electrodes). In order to evaluate all possible single A-CMI differences between resting and generating a hypothesis within gifted and normal children, group comparisons were performed using a paired student's t-test (SPSS version 12.0). Multiple comparisons necessitate the correction of significance levels to avoid the risk of increase in type I error which arises from testing repeatedly. However, because of the large number of variables, these corrections would lead to extremely low probabilities for rejecting false null hypotheses, so any possible EEG effects

would be cancelled out. Therefore, the statistical procedure has to be considered a statistical filter and the obtained error probabilities purely descriptive and not used to confirm or reject the null hypotheses (Weiss and Rappelsberger, 2000). Test results were converted to error probabilities (P b 0.05) and presented as lines between the electrodes in schematic drawings of the brain (Fig. 4), and of course, had to be considered purely descriptive. 4. Results Fig. 3(a) and (b) show the distribution of A-CMI values between all pairs of channels for both resting and hypothesis generating conditions. ANOVA yielded significant main effects for CONDITION (F(1, 11520) = 272.400, P = 0.000) and for ELECTRODE (F(239, 11520) = 463.400, P = 0.0000). No significant interaction for CONDITION × ELECTRODE was found (F(239, 11520) = 0.8975, P = NS; not significant). A higher A-CMI value suggests mutually stronger functional coupling and increases information transmission between the two different time series. Fig. 4 highlights the pairs where higher A-CMI values (P b 0.05) were observed in the hypothesis generation condition. The higher A-CMI values were observed in the left temporo-centro-occipital brain regions (C3–O1, T3–O1, T5–O1) during hypothesis generation. For the distant right A-CMI between pairs of electrodes across the central line, the right hemispheric pairs in F4–P4 generated higher values during hypothesis generation than during the resting condition. This study also found increased A-CMI values between the left posterior and the right anterior brain regions (O1–F4, T5–F4, O1–F8) as well as between the left posterior and the right posterior brain regions (O1–C4, O1–P4, O1–T4, T5–C4, T5–P4) during hypothesis generation. 5. Discussion

Fig. 3. Distribution of the A-CMI values between all pairs of channels in the (a) resting and (b) generating hypothesis conditions. Although CMI is not a symmetric quantity with time delay, A-CMI across the time delay is, to all intents and purposes, the same irrespective of a time delay in one of the electrodes in a pair of electrodes. In general, A-CMI values are higher during hypothesis generation than the resting condition.

In the present work, analysis of the A-CMI from the EEGs demonstrated a significant increase in A-CMI values during hypothesis generation. Although A-CMI does not directly estimate axonal connection or cortico-cortical communication, it is possible to quantify the transmission of information statistically from one site in a time series to another (Jeong et al., 2001). EEG coherence and A-CMI both quantify information transmission among different areas of the brain. However, the difference between the two measurements is that EEG coherence measures only the linear dependencies in the electrical potentials across those regions, whereas A-CMI considers both the linear and nonlinear dependencies of information transmission among those brain regions (Na et al., 2002). Findings showed increased A-CMI values for distant information transmission within the right hemisphere and for the interhemispheric transmission of information between the left posterior and the right hemisphere. As such, this result confirmed that distinct brain activities operate during hypothesis generation, especially, there appears to be increased information transmission between the different local brain regions as compared to the resting condition.

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Fig. 4. t-map featuring all pairs where higher A-CMI values (paired t-test, P b 0.05) are observed in the hypothesis generation condition.

There is growing evidence that no single region of the brain is responsible for all memory and that each region makes a specific contribution, that is, the brain systems that support various memory processes differ, depending on the type of information to be retained and also on how it is encoded and retrieved (Gazzaniga et al., 2002; Kolb and Whishaw, 2003). For example, the lateral and anterior regions of the temporal lobe may be particularly important for the retrieval of information from the storage of long-term declarative memories (Gazzaniga et al., 2002; Kandal et al., 1995). The increased information transmission between the temporal cortex and the other brain regions may suggest the need for explicit long-term memory systems during hypothesis generation in accordance with prior research. Cortical injuries in the parietal, posterior temporal, and possibly occipital cortexes sometimes produce specific longterm memory difficulties, and the posterior parietal cortex in both hemispheres are active during memory retrieval (Kolb and Whishaw, 2003). In addition, the memories of experienced events contain sensory-perceptual episodic knowledge stored in occipital networks (Conway et al., 2003), and the posterior regions contribute to explicit attentional and visuoconstructional abilities (Luerding et al., 2004). Results from this study showed increased inter- and intra-hemispheric information transmission not only in the temporal cortex but also parietal and occipital cortexes. Taken together, these results seem to suggest that the cognitive processes during hypothesis generation involve part of the declarative memory system. On the other hand, procedural knowledge, an implicit memory system, concerns knowledge on how to do something such as analyzing, searching, and confirming. Key structures in implicit memory processes are the neocortex and basal ganglia. Basal ganglia structures have been implicated in motor and cognitive skills (Gazzaniga et al., 2002). In addition, they are part of a cortical–subcortical motor loop (Kandal et al., 1995). As such, they receive projections from all regions of the neocortex and send projections through the globus pallidus and ventral thalamus to the premotor cortex (Gazzaniga et al., 2002; Kolb and Whishaw, 2003), which corresponds to the central region in this study. The increased interhemispheric transmis-

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sion of information between the right central and the left occipital and temporal regions, and the intrahemispheric transmission of information between the left central and occipital regions may be the result of procedural memory intervention during hypothesis generation. Lawson (1995) emphasized the important role of abduction in hypothesis generation. According to Lawson, abduction involves sensing the ways in which the current situation is somehow similar to other known situations and using this similarity as a source of hypotheses in the present situation. In addition, abduction involves representing available information and searching for an explanation to the given situation. Because these acts are related to personal wisdom, autobiographical memory, world knowledge, and cognitive skills such as analyzing, searching, and confirming, abduction is presumed to be relevant to both declarative and procedural memory. Therefore, results of the present study provide neuropsychological support for the proposal that hypothesis generation reflects abduction as implicated by declarative and procedural memory. In conclusion, the distinct brain activities found during hypothesis generation, especially the increased information transmission between different local brain regions, reflects the use of declarative and procedural memory systems. Furthermore, this study raises the possibility that neuropsychological approaches can be potential tools to investigate the neuronal activity of EEGs during scientific hypothesis generation. Acknowledgements This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund (R05-2004-12069-0) and KRF2004-216-B00004). References Amari, S., 1998. Natural gradient works efficiently in learning. Neural Comput. 10 (2), 251–276. Anokhin, A.P., Lutzenberger, W., Birbaumer, N., 1999. Spatiotemporal organization of brain dynamics and intelligence: an EEG study in adolescents. Int. J. Psychophysiol. 33 (3), 259–273. Bell, A.J., Sejnowski, T.J., 1995. An information maximization approach to blind separation and blind deconvolution. Neural Comput. 7, 1129–1159. Conway, M.A., Pleydell-Pearce, C.W., Whitecross, S.E., Sharpe, H., 2003. Neurophysiological correlates of memory for experienced and imagined events. Neuropsychologia 41, 334–340. Cover, T.M., Thomas, J.A., 1991. Elements of Information Theory. John Wiley & Sons, New York, pp. 12–22. Enger, E.D., Ross, F.C., 2003. Concepts in Biology, 10th eds. The McGraw-Hill Compaines, Inc., New York, NY, pp. 2–8. Fraser, A.M., Swinney, H.L., 1986. Independent coordinates for strange attractors from mutual information. Phys. Rev., A 33, 1134–1140. Friston, K.J., Willians, S., Howard, R., Frackowiak, R.S., Turner, R., 1996. Movement-related effects in fMRI time-series. Magn. Reson. Med. 35, 346–355. Gazzaniga, M.S., Ivry, R.B., Mangun, G.R., 2002. Cognitive Neuroscience, The biology of the mind, 2nd eds. W.W. Norton and Company, Inc., New York, London, pp. 82–84, 313–350. Harmony, T., Fernández, T., Gersenowies, J., Galán, L., Fernández-Bouzas, A., Aubert, E., Díaz-Comas, L., 2004. Specific EEG frequencies signal general

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