Anticipated synchronization in human EEG data: unidirectional causality with negative phase-lag
Francisco-Leandro P. Carlos, Maciel-Monteiro Ubirakitan, Marcelo Cairrão Araújo Rodrigues, Moisés Aguilar-Domingo, Eva Herrera-Gutiérrez, Jesús Gómez-Amor, Mauro Copelli, Pedro V. Carelli, Fernanda S. Matias
aa r X i v : . [ q - b i o . N C ] A ug Anticipated synchronization in human EEG data: unidirectional causality withnegative phase-lag
Francisco-Leandro P. Carlos, Maciel-Monteiro Ubirakitan,
2, 3
Marcelo Cairr˜aoAra´ujo Rodrigues, Mois´es Aguilar-Domingo,
3, 4
Eva Herrera-Guti´errez, Jes´usG´omez-Amor, ∗ Mauro Copelli, Pedro V. Carelli, and Fernanda S. Matias † Instituto de F´ısica, Universidade Federal de Alagoas, Macei´o, Alagoas 57072-970 Brazil. Grupo de Neurodinˆamica, Departamento de Fisiologia e Farmacologia,Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil. Spanish Foundation for Neurometrics Development,Department of Psychophysics and Psychophysiology, 30100, Murcia, Spain. Department of Human Anatomy and Psychobiology, Faculty of Psychology,University of Murcia, 30100 Espinardo Campus, Murcia, Spain. Department of Developmental and Educational Psychology, Faculty of Psychology,University of Murcia, 30100 Espinardo Campus, Murcia, Spain. Departamento de F´ısica, Universidade Federal de Pernambuco, Recife PE 50670-901, Brazil.
Understanding the functional connectivity of the brain has become a major goal of neuroscience.In many situations the relative phase difference, together with coherence patterns, have been em-ployed to infer the direction of the information flow. However, it has been recently shown in localfield potential data from monkeys the existence of a synchronized regime in which unidirectionallycoupled areas can present both positive and negative phase differences. During the counterintuitiveregime, called anticipated synchronization (AS), the phase difference does not reflect the causality.Here we investigate coherence and causality at the alpha frequency band ( f ∼
10 Hz) between pairsof electroencephalogram (EEG) electrodes in humans during a GO/NO-GO task. We show thathuman EEG signals can exhibit anticipated synchronization, which is characterized by a unidirec-tional influence from an electrode A to an electrode B, but the electrode B leads the electrode Ain time. To the best of our knowledge, this is the first verification of AS in EEG signals and inthe human brain. The usual delayed synchronization (DS) regime is also present between manypairs. DS is characterized by a unidirectional influence from an electrode A to an electrode B anda positive phase difference between A and B which indicates that the electrode A leads the elec-trode B in time. Moreover we show that EEG signals exhibit diversity in the phase relations: thepairs of electrodes can present in-phase, anti-phase, or out-of-phase synchronization with a similardistribution of positive and negative phase differences.
PACS numbers:
Introduction
The extraordinary ability of humans to model and pre-dict facts are one of the prerequisites for both actionand cognition. These capacities emerge from the vari-ous synchronous rhythms generated by the brain [1, 2],which represent a core mechanism for neuronal commu-nication [3]. In particular, phase synchronization [4] hasbeen related to selective attention [5, 6], large-scale in-formation integration [7] and memory processes [8, 9].Despite huge evidence of zero-lag synchronization in thebrain [2], there is a growing number of studies reportingnon-zero phase differences between synchronized brainareas [6, 9, 10, 11, 12, 13]. It has been assumed thatphase diversity plays an important role in fast cognitiveprocesses [14].In many situations the phase, together with coherencepatterns, have been employed to infer the direction of the ∗ Deceased † fernanda@fis.ufal.br information flow [10, 15, 16, 17, 18, 19]. The assumptionis typically that the phase difference reflects the transmis-sion time of neural activity. However, this assumed re-lationship is not theoretically justified [20]. Particularly,during special synchronized regimes, the phase differencedoes not reflect the causality [21, 22, 23, 24, 25].It has been shown that a monkey performing a cog-nitive task can present unidirectional influence from acortical region A to another region B with a negativephase difference between the two areas [21, 22, 23]. Thismeans that the receiver region B can lead the activityof A. For example, it has been observed that during thewaiting period of a GO/NO-GO task, a macaque monkeypresent unidirectional causality from the somatosensorycortex to the motor cortex with a negative phase [21, 23].A similar apparent incongruence has been verified be-tween PreFrontal Cortex (PFC) and Posterior ParietalCortex (PPC) in monkeys performing a working mem-ory task [22]. The information flows from the PPC tothe PFC but the activity of the PFC leads the activityof the PPC by 2 . . S = f ( S ( t )) , (1)˙ R = f ( R ( t )) + K [ S ( t ) − R ( t − t d )] . S and R ∈ R n are dynamical variables respectively repre-senting the sender and the receiver systems. f is a vectorfunction which defines each autonomous dynamical sys-tem, K is the coupling matrix and t d > R ( t ) = S ( t + t d ) is a solution of the system, which canbe easily verified by direct substitution in Eq. 1. AShas been observed in excitable models driven by whitenoise [35], chaotic systems [28, 31], as well as in ex-perimental setups with semiconductor lasers [36, 37] andelectronic circuits [38].AS has also been observed when the self-feedback wasreplaced by parameter mismatches [39, 40, 41, 42, 43],inhibitory dynamical loops [23, 44, 45, 46] and noise atthe receiver [26]. It has been suggested that AS canemerge when the receiver dynamics is faster than thesenders [26, 46, 47, 48]. Furthermore, unidirectionallycoupled lasers reported both regimes: AS and the usualdelayed synchronization (DS, in which the sender pre-dicts the activity of the receiver), depending on the dif-ference between the transmission time and the feedbackdelay time [37, 49]. The two regimes were observedto have the same stability of the synchronization man-ifold in the presence of small perturbations due to noiseor parameter mismatches [37]. Neuron models can alsopresent a transition from positive to negative phase dif-ferences (from DS to AS) depending on coupling parame-ters [23, 26, 44, 45]. Therefore, the study of anticipatoryregimes in biological systems (not man-made) is receivingmore attention in the last years [50, 51, 52, 53].Here we employ spectral coherence and Grangercausality (GC) measures to infer the direction of influ-ence, as well as the phase difference between electrodesof the EEG from 11 subjects. We verify, for all sub-jects, the existence of coherent activity in the alpha band( f ∼
10 Hz) between pairs of electrodes. We also showthat many of these pairs exhibit a unidirectional influ- ence from one electrode to another and a phase differ-ence that can be positive or negative. In Sec. I and IIIwe describe the experimental paradigm and EEG pro-cessing and analysis. In Sec. I, we report our results,showing that when we consider all the unidirectionallycoupled pairs we verify that there is a diversity in thephase relation: they exhibit in-phase, anti-phase, or out-of-phase synchronization with similar distribution of pos-itive and negative phase differences (DS and AS, respec-tively). Concluding remarks and brief discussion of thesignificance of our findings for neuroscience are presentedin Sec. II.
I. RESULTS
The experiment consists in 400 trials of a GO/NO-GOtask. In each trial a pair of stimuli were presented aftera waiting window of 300 ms, which is the important in-terval for our analysis (see the green arrow in Fig. 1(b)).Depending on the combination of stimuli, participantsshould press a button or not. Oscillatory main frequency,synchronized activity and directional influence were es-timated by the power, coherence, phase difference andGranger causality spectra as reported in Matias et al. [23](see more details in Sec. III). (a) F P1 F P2 F F F z F F T C C z C T T P P z P T O O (a) (b) GONO-GOIGNORENOVEL 3000ms ∆ t (ms) A
100 1000 100
A AAPPP H + (b) FIG. 1:
Experimental paradigm. (a) 10/20 System ofEEG electrodes placement employed in the experiments. (b)GO/NO-GO task based on three types of stimulus with im-ages of animals (A), plants (P), and people (H + ). After awaiting window of 300 ms, two stimulus were presented for100 milliseconds, with a 1000 ms inter-stimulus-interval. Ifboth stimulus are animals (AA) the participant should pressa button as quickly as possible (see Sec. III for more details).Here we analyzed the 300 ms before the stimulus onset. Synchronization between electrodes l and k can becharacterized by a peak in the coherence spectrum C lk ( f peak ). The phase difference ∆Φ l − k at the peak fre-quency f peak provides the time delay τ lk between theelectrodes. The direction of influence is given by theGranger causality spectrum. Whenever an electrode l strongly and asymmetrically G-causes k , we refer to l asthe sender (S) and to k as the receiver (R) and the linkbetween l and k is considered a unidirectional couplingfrom l to k (S → R). After determining which electrode isthe sender and which one is the receiver we analyze thesign of ∆Φ S − R to determine the synchronized regime. P o w e r F P1 F C ohe r en c e Frequency(Hz) G r ange r C au s a li t y F → F P1 F P1 → F Frequency(Hz) - π π φ F - F P τ = 2.4ms FIG. 2:
Unidirectional causality with positive phase-lag characterizes the delayed synchronization regime(DS).
Power, coherence, Granger causality and phase spectra between electrodes F and F P for volunteer 439. The pairis synchronized with main frequency f peak = 11 . f peak reveals a directional influence from site F to F P and the phase difference at the main frequency∆Φ F − F P ( f peak ) = 0 . F leads F P (with an equivalent time delay τ = 2 . Unless otherwise stated we analyze only the unidirection-ally connected pairs.
Delayed synchronization (DS): unidirectionalcausality with positive phase-lag
Typically when a directional influence is verified fromA to B, a positive time delay is expected, indicating thatA’s activity temporally precedes that of B [10, 54]. Thispositive time delay characterizes the intuitive regimecalled delayed synchronization (DS, or also retarded syn-chronization) in which the sender is also the leader [37].In neuronal models the time delay between A and B canreflect the characteristic time scale of the synapses be-tween A and B but can also be modulated by local prop-erties of the receiver region B [23, 26].In Fig. 2 we show an example of DS between thesites F and F P for volunteer 439. Power and coher-ence spectra present a peak at f peak = 11 . G-causes F P , but notthe other way around. The positive sign of the phase∆Φ F − F P ( f peak ) = 0 . leads the receiver electrode F P with a pos-itive time delay τ = 2 . Anticipated synchronization (AS): unidirectionalcausality with negative phase-lag
Despite the fact that phase differences and coherencepatterns, have been employed to infer the direction of the information flux [10, 15, 16, 17, 18, 19], our results implythat if we consider only the coherence and phase-lag wecould infer the wrong direction of influence between theinvolved pairs. Such counter-intuitive regime exhibitingunidirectionally causality with negative phase differencehas first been reported in the brain as a mismatch be-tween causality and the sign of the phase difference in lo-cal field potential of macaque monkeys during cognitivetasks [21, 22]. Afterwards, it has been reported that theapparent paradox could be explained in the light of an-ticipated synchronization ideas [23]. Here we show thathuman EEG signals can also present unidirectional influ-ence with negative phase-lag. As far as we know, this isthe first evidence of AS in human EEG data.An example of anticipated synchronization betweenEEG electrodes is shown in Fig. 3. The sites F Z and F P exhibit a peak at alpha band in the power and coherencespectra for f peak = 10 . F Z to F P but not in the opposite direction, indicating that F Z G-causes F P at f peak = 10 . F Z − F P ( f peak ) = − . Z lags behind the activityof F P . The time delay associated to ∆Φ F Z − F P ( f peak )is τ = − . P o w e r F Z F P1 C ohe r en c e Frequency(Hz) G r ange r C au s a li t y F Z → F P1 F P1 → F Z Frequency(Hz) - π π φ F Z - F P τ = -2.9ms FIG. 3:
Unidirectional causality with negative phase-lag characterizes anticipated synchronization (AS).
Power,coherence, Granger causality and phase spectra between sites F Z and F P for volunteer 439. The electrodes are synchronizedwith main frequency f peak = 10 . f peak reveals a directional influence from site F Z to F P . F Z G-causes F P , but the negative phase difference at themain frequency ∆Φ F Z − F P ( f peak ) = − . τ = − . F P leads F Z in time. frequency band, the group delay could be useful to es-timate the time difference between the signals. Indeed,a negative group delay has been associated with antici-patory dynamics [55, 56, 57] and it is comparable to thetime difference obtained by the cross-correlation func-tion [55]. Here, we verified that some AS pairs presentboth negative phase delay and negative group delay (asin the example shown in Fig. 3). However, this is notthe case for all AS pairs in the analyzed data. We havefound all possible combinations for the signs of phase andgroup delays for both DS and AS. A further investigationof the relation between phase delay and group delay inbrain signals is out of the scope of this paper and shouldbe done elsewhere. Zero-lag synchronization (ZL)
Zero-lag (ZL) synchronization has been widely docu-mented in experimental data since its first report in thecat visual cortex [58]. It has been related to differentcognitive functions such as perceptual integration and theexecution of coordinated motor behaviours [3, 7, 59, 60].Despite many models showing that bidirectional couplingbetween areas promotes zero-lag synchronization [61, 62],it is also possible to have ZL between unidirectional con-nected populations [23, 26, 45]. In these systems, nonlin-ear properties of the receiver region can compesate char-acteristic synaptics delays and the two systems synchro-nize at zero phase.We consider zero-lag whenever | ∆Φ S − R ( f peak ) | < . F and F P for volunteer 439. These sites are synchronized withmain frequency f peak = 10 . F − F P ( f peak ) = − . τ = − . Anti-phase synchronization
Participants can also exhibit anti-phase synchroniza-tion between electrodes. We define anti-phase synchro-nization (AP) when π − . < | ∆Φ S − R ( f peak ) | < π +0 . O and C for volunteer 439. The site O G-causes C and thetime delay between them is τ = 47 . f peak = 10 . TABLE I:
Number of unidirectionally connectedpairs for all subjects together: separated by phase-synchronization regime along the lines and by the directionof influence along the columns.Unidirectional Back-to-Front Lateral Front-to-BackTotal 686 430 90 166ZL 93 39 25 29DS(1) 77 25 14 38AS(1) 99 51 27 21AP 174 135 11 28DS(2) 108 83 4 21AS(2) 135 97 9 29 P o w e r F P2 F C ohe r en c e Frequency(Hz) G r ange r C au s a li t y F → F P2 F P2 → F Frequency(Hz) - π π φ F - F P τ = -0.2ms FIG. 4:
Unidirectional causality with zero-lag synchronization (ZL, defined by ∆Φ ≃ ). Power, coherence, Grangercausality and phase spectra between electrodes F and F P for volunteer 439. Sites are synchronized with main frequency (givenby the peak of the coherence, brown dashed lines) f peak = 10 . f peak indicates that site F unidirectionally influences F P . The time delay between both is almost zero τ = − . F − F P ( f peak ) = − . P o w e r C O C ohe r en c e Frequency(Hz) G r ange r C au s a li t y O → C C → O Frequency(Hz) - π π φ O - C τ = 47.5 ms FIG. 5:
Unidirectional causality with anti-phase synchronization (AP, defined by ∆Φ ≃ ± π ). Power, coherence,Granger causality and phase spectra between electrodes O and C for volunteer 439. The activity of the electrodes aresynchronized with main frequency f peak = 10 . f peak revealsa directional influence from O to C and the phase spectrum shows that ∆Φ O − C ( f peak ) = 3 . τ = 47 . Phase relation diversity across pairs and subjects
Reliable phase relation diversity is a general propertyof brain oscillations. It has been reported on multi- ple spatial scales, ranging from very small spatial scale(inter-electrode distance <
900 mm) in macaque [6, 9],to a large spatial scale (using magnetoencephalography)
FIG. 6:
Circular phase differences distribution.
Thepairs are separated into six groups relative to their phase-synchronization regime: zero-lag (ZL, dark gray), anti-phase(AP, light gray), delayed synchronization in the first quad-rant (DS(1),dark blue), delayed synchronization in the secondquadrant (DS(2), light blue), anticipated synchronization inthe fourth quadrant (AS(1), dark red), anticipated synchro-nization in the third quadrant (AS(2), light red). (a) Phase ofall 686 unidirectionally connected pairs: (b) 430 pairs show-ing back-to-front influence, (c) 90 pairs within lateral flux, (d)166 pairs presenting front-to-back influence. in humans [63]. However, the functional significance ofphase relations in neuronal signals is not well defined.It has been hypothesized that it may support effectiveneuronal communication by enhancing neuronal selectiv-ity and promoting segregation of multiple informationstreams [14].Considering the 19 electrodes per subject, the numberof analyzed pairs is 171 for each volunteer which corre-sponds to 1881 pairs in total. Among these pairs, 1394presented a peak in the coherence spectrum at the alphaband. Regarding the Granger causality spectra, 686 pairspresented an unidirectional influence and 358 a bidirec-tional influence. In Fig. 6(a) we show the phase-differencedistribution of all 686 unidirectionally connected pairs forall volunteers in a circular plot. In Figs. 6(b),(c),(d) weshow all the pairs separated by the direction of influ-ence: from the back to the front (430), lateral flux (90)and from the front to the back (166), respectively. Thecolors represent the four different synchronized regimesmentioned before: DS (blue for positive phase: 0 . < ∆Φ S − R ( f peak ) < π − . − π + 0 . < ∆Φ S − R ( f peak ) < − . | ∆Φ S − R ( f peak ) | < . ± π : π − . < | ∆Φ S − R ( f peak ) | < π + 0 . FIG. 7:
Histograms for number of pairs ineach synchronized regime.
The colors indicate phase-synchronization regime. (a) Electrode pairs are separated bydirection of influence: all unidirectional pairs, back-to-frontinfluence, front-to-back and lateral direction. (b) All unidi-rectional pairs separated per volunteer.
The total number of synchronized and unidirection-ally connected pairs varies among volunteers, as well asthe distribution of phases. All subjects present DS, AS,ZL and AP pairs (see Fig. 7(b)). However, one subjectdoes not present AS(1). All subjects present back-to-front, lateral and front-to-back influence and more pairswith back-to-front than front-to-back direction of influ-ence. Considering only the back-to-front pairs, there aremore AP than ZL synchronized regimes. This is also trueif we compare all pairs in the second and third quadrant(AP, DS(2) and AS(2)) with the ones in the first andfourth (ZL, DS(1), AS(1)).As illustrative examples, in Fig. 8 we show the direc-tion of influence between some pairs that have the sameunidirectional back-to-front Granger for at least 4 sub-jects and their respective phases. Almost all pairs thathave the electrodes P Z , P and P as the sender presentphases close to anti-phase (AP, DS(2), AS(2)), whereasalmost all the pairs in which the sender is F Z , T or T are synchronized close to zero-lag (ZL, DS(1), AS(1)).Regarding back-to-front influences, no pair presentedthe same Granger causal relation for 9 or more subjects.Three pairs exhibited same unidirectional relation for 8volunteers: P Z → F , P → F P , O → F ; other 3 pairspresented the same unidirectional relation for 7 subjects: P → F , P → F , O → F P . Ten pairs had sameGranger causal relation for 6 volunteers: F Z → F P , P → F P , P → F , C Z → F , C Z → T , C → F P , C → F , C → F , O → F P , O → F . All these 16pairs had none or only one other subject presenting theopposite direction of the Granger causality. Out of these16 pairs, only F Z → F P is mostly synchronized close doZL as shown in Figs. 6(a) and (b), all others are mostlysynchronized close to AP as in Figs. 6(c)-(f). FIG. 8:
Illustrative examples of unidirectionally con-nected pairs and their phase relations. (a) and (b) Ex-ample of pairs with the majority of phase differences in thefirst and the fourth quadrants (ZL, DS(1), AS(1)): F Z → F P , F Z → F P , T → F P and T → F P . (c) to (f) Example ofpairs with the majority of phase differences in the second andthe third quadrants (AP,DS(2),AS(2)). P Z , P and P arewell connected senders. All the chosen pairs are synchronizedwith same direction of influence for at least 4 subjects. II. CONCLUSION
We show that human EEG can simultaneously presentunidirectional causality and diverse phase relations be-tween electrodes. Our findings suggest that the human brain can operate in a dynamical regime where the infor-mation flow and relative phase-lag have opposite signs.To the best of our knowledge this is the first evidence ofunidirectional influence accompanied by negative phasedifferences in EEG data. This counter-intuitive phe-nomena have been previously reported as anticipatedsynchronization in monkey LFP [21, 22, 23], in neu-ronal models [34, 35, 41, 43, 44] and in physical sys-tems [36, 37, 38, 39, 40]. Therefore, we propose that thisis the first verification of anticipated synchronization inEEG signals and in human brains.Studies estimating the actual brain connectivity usingdata from EEG signals should consider many relevant is-sues such as [64]: the importance of common reference inEEG to estimate phase differences [20] and the effects ofvolume conduction for source localization [65, 66]. Ourfindings suggest that it is also important to take into ac-count the possible existence of AS in connectivity studiesand separately analyze causality and phase relations. It isworth mentioning that, it has been shown that for enoughdata points the Granger causality is able to distinguishAS and DS regimes [24]. However, for very well behavedtime series the reconstruction of the connectivity can beconfused by the phase [25].Our results open important avenues for investigatinghow neural oscillations contribute to the neural imple-mentation of cognition and behavior as well as for study-ing the functional significance of phase diversity [6, 14].Future works could investigate the relation between an-ticipated synchronzation in brain signals and antici-patory behaviors [51] such as anticipation in human-machine interaction [52] and during synchronized rhyth-mic action [53]. It is also possible to explore the relationbetween consistent phase differences and behavioral datasuch as learning rate, reaction time and task performanceduring different cognitive tasks . Neuronal models haveshown that spike-timing dependent plasticity and the DS-AS transition together could determine the phase differ-ences between cortical-like populations [45]. However, anexperimental evidence for the relation between learningand negative phase differences is still lacking.We also suggest that our study can be potentially in-teresting to future researches on the relation betweeninhibitory coupling, oscillations and communication be-tween brain areas. On one hand, inhibition is consid-ered to play an important role to establish the oscilla-tory alpha activity, in particular, allowing selective infor-mation processes [67]. On the other hand, according tothe anticipated synchronization in neuronal populationsmodel presented in Ref. [23], a modification of the in-hibitory synaptic conductance at the receiver populationcan modulate the phase relation between sender and re-ceiver, eventually promoting a transition from DS to AS.Therefore, we suggest that the inhibition at the receiverregion can control the phase difference between corticalareas, which has been hypothesized to control the effi-ciency of the information exchange between these areas,via communication through coherence [3, 12].
III. APPENDIX: METHODS
Subjects
We analyzed data from 11 volunteers (10 women, 1man, all right-handed) who signed to indicate informedconsent to participate in the experiment. The youngestwas 32 years old and the oldest 55 years old (average 45.7and standard deviation 7.8). All subjects were evaluatedby both psychiatrist and psychologist. Exclusion crite-ria were: perinatal problems, cranial injuries with loss ofconsciousness and neurological deficit, history of seizures,medication or other drugs 24 hours before the recording,presence of psychotic symptoms in 6 months prior thestudy and the presence of systemic and neurological dis-eases. The experiment was not specifically designed toinvestigate the phenomena of anticipated synchronizationin humans and the data analyzed here were first analyzedin Ref. [68]. The entire experimental protocol was ap-proved by the Commission of Bioethics of the Universityof Murcia (UMU, project: Subtipos electrofisiolgicos ymediante estimulacin elctrica transcraneal del Trastornopor Dficit de Atencin con o sin Hiperactividad).
EEG recording
The electroencephalographic data recordings were car-ried out at the Spanish Foundation for Neuromet-rics Development (Murcia, Spain) center using a Mit-sar 201M amplifier (Mitsar Ltd), a system of 19channels with auricular reference. Data were dig-itized at a frequency of 250 Hz. The electrodeswere positioned according to the international 10-20 system using conductive paste (ECI ELECTRO-GEL). Electrode impedance was kept < Z ,C Z and P Z ) and eight sites over each hemisphere(F P /F P ,F /F ,F /F ,T /T ,C /C ,P /P ,T /T andO /O ). The acquisition was realized by WinEEG soft-ware (Version 2.92.56). EEG epochs with excessive am-plitude ( > µ V) were automatically deleted. Finally,the EEG was analyzed by a specialist in neurophysiologyto reject epochs with artifacts.
Experimental task
The EEG data were recorded while subjects performeda GO/NO-GO task (also called visual continuous perfor-mance task, VCPT). Participants sat in an ergonomicchair 1.5 meters away from a 17 ′′ plasma screen. Psy-task software (Mitsar Systems) was used to present theimages. The VCPT consists of three types of stim-uli: twenty images of animals (A), twenty images ofplants (P), twenty images of people of different profes-sions (H + ). Whenever H + was presented, a 20 ms-long artificial sound tone frequency was simultaneously pro-duced. The tone frequencies range from 500 to 2500 Hz,in intervals of 500 Hz. All stimuli were of equal size andbrightness.In each trial a pair of stimuli were presented after awaiting window of 300 ms, which is the important inter-val for our analysis (see the green arrow in Fig. 1(b)).Each stimulus remains on the screen for 100 ms, with a1000 ms inter-stimulus-interval. Four different kinds ofpairs of stimuli were employed: AA, AP, PP and PH + .The entire experiment consists in 400 trials (the fourkinds of pairs were randomly distributed and each oneappeared 100 times). The continuous set occurs when Ais presented as the first stimulus, so the subject neededto prepare to respond. An AA pair corresponds to a GOtask and the participants are supposed to press a buttonas quickly as possible. An AP pair corresponds to a NO-GO task and the participants should suppress the actionof pressing the button. The discontinuous set, in which Pis first presented, indicates that one should not respond(independently of the second stimuli). IGNORE task oc-curred with PP pairs and NOVEL when PH + pairs ap-peared. Participants were trained for about five minutesbefore beginning the experimental trials. They rested fora few minutes when they reached the halfway point of thetask. The experimental session lasted ∼
30 min.
EEG processing and analysis
The Power, Coherence, Granger causality and phasedifference spectra were calculated following the method-ology reported in Matias et al. [23] using the auto-regressive modeling method (MVAR) implemented in theMVGC Matlab toolbox [69]. Data were acquired whileparticipants were performing the GO/NO-GO visual pat-tern discrimination described before. Our analysis fo-cuses on 30000 points representing the waiting windowof 400 trials ending with the visual stimulus onset (greenarrow in Fig. 1(b)). This means that in each trial, the300-ms pre-stimulus interval consists of 75 points with a250-Hz sample rate.The preprocess of the multi-trial EEG time series con-sists in detrending, demeaning and normalization of eachtrial. Respectively, it means to subtract from the timeseries the best-fitting line, the ensemble mean and divideit by the temporal standard deviation. After these pro-cesses each single trial can be considered as producedfrom a zero-mean stochastic process. In order to de-termine an optimal order for the MVAR model we ob-tained the minimum of the Akaike Information Crite-rion (AIC) [70] as a function of model order. The AICdropped monotonically with increasing model order upto 30.For each pair of sites ( l, k ) we calculated the spectralmatrix element S lk ( f ) [21, 71], from which the coherencespectrum C lk ( f ) = | S lk | / [ S ll ( f ) S kk ( f )] and the phasespectrum ∆Φ l − k ( f ) = tan − [Im( S lk ) / Re( S lk )] were cal-culated. A peak of C lk ( f ) indicates synchronized oscil-latory activity at the peak frequency f peak , with a timedelay τ lk = ∆Φ lk ( f peak ) / (2 πf peak ). We only consider7 < f peak <
13 Hz and we use the terms time delayand phase difference interchangeably. It is worth men-tioning that ∆Φ l − k = − ∆Φ k − l and − π < ∆Φ l − k π .Directional influence from site l to site k was assessedvia the Granger causality spectrum I l → k ( f ) [21, 23, 71].When the I l → k ( f ) has a peak around the f peak obtainedfrom the coherence spectrum, we consider that l G-causes k . In order to define back-to-front, lateral or front-to-back influence we separated the electrodes in 5 lines (seeFig. 1(a)): F P and F P ; F , F , F Z , F and F ; T , C , C Z , C and T ; T , P , P Z , P , and T ; O and O . Acknowledgments
The authors thank CNPq (grants 432429/2016-6, 425329/2018-6, 301744/2018-1), CAPES (grants88881.120309/2016-01, 23038.003382/2018-39),FACEPE (grants APQ-0642-1.05/18, APQ-0826-1.05/15), FAPEAL, UFAL and UFPE for financialsupport. This paper was produced as part of theactivities of Research, Innovation and DisseminationCenter for Neuromathematics (grant No. 2013/07699-0,S. Paulo Research Foundation FAPESP). [1] G. Buzsaki,