## 3 Analysis and Results
### Analysis of Realistic EEG in Mental Arithmetic Tasks  
In order to demonstrate the performance of the proposed CBTN method on realistic experimental data, the EEG signals of mental arithmetic tasks-dataset were used to distinguish the difference between the resting and the arithmetic states of the brain [41]. The dataset can be downloaded freely from the website: [[https://physionet.org/content/eegmat/1.0.0/](https://physionet.org/content/eegmat/1.0.0/)]([https://physionet.org/content/eegmat/1.0.0/](https://physionet.org/content/eegmat/1.0.0/)), accessed on 23 January 2022. Electrodes were placed according to the international 10/20 scheme and the equipment used was the Neurocom monopolar EEG 23-channel system (Ukraine, XAI-MEDICA). The placement of the silver/silver chloride electrodes on the scalp was prefrontal (Fp1 and Fp2), frontal (F3, F4, Fz, F7, and F8), central (C3, C4, and Cz), parietal (P3, P4, and Pz), occipital (O1 and O2), and temporal (T3, T4, T5, and T6), all referenced to an interconnected ear reference electrode. The impedance between the electrodes and the scalp was less than 5 k\(\Omega\), and the sampling rate for each channel was 500 Hz. The acquired EEG signals were filtered using a high-pass filter with a cut-off frequency of 0.5 Hz, a low-pass filter with a cut-off frequency of 45 Hz, and a power line notch filter (50 Hz). The EEG data from 36 subjects (9 males and 27 females, aged 16-26 years) met the requirements for analysis, after a visual inspection of the filtered signals by neuroelectrophysiologists to remove data with poor signal quality. Subject 31 was not included because the length of the recordings was different from that of other subjects. The experiments involved mental arithmetic tasks and each experiment trial was divided into three phases: an adaptation  
Figure 4: Coupling analysis results for the CBTN-based unidirectional coupled Henon model when the sliding time window is fixed at 2000 samples and the coupling strength \(C\) is varied in steps of 0.05 in the range [0, 0.9]. The values of the ordinate are \(H_{NOTE}\). The blue curve is the NOTE between \(x_{1}\) and \(x_{2}\) and the red curve is the NOTE between \(x_{1}\) and \(x_{2}^{surrogate}\). \(x_{2}^{surrogate}\) can be obtained by surrogating \(x_{2}\) using the iAAFT method (all values in the graph are the result of 30 repeated calculations). **(a)** The results of coupling analysis using CBTN. **(b)** The results of coupling analysis using CPE, \(d=5\), \(\tau=2\). period, a resting state and an arithmetic state. First, the subjects were acclimatized to the experimental conditions for 3 min. Afterwards, the subjects relaxed for 3 min with their eyes closed in the resting state. Finally, the subjects were asked to perform a succession of subtractions in 4 min, each consisting of a four-digit (subtracted number) and two-digit (subtracted number) succession. The two digits were given to the subject verbally and the arithmetic task was not allowed to be performed verbally, but finger movements were allowed. In order to minimize the effect of emotional fluctuations caused by the increased cognitive load of the subjects during intensive cognitive activity on the results of the EEG analysis, the last minute of the resting state and the first minute of the arithmetic state were selected for analysis. Neuroimaging studies showed that the prefrontal and frontal regions were significantly activated during the performance of arithmetic or cognitive tasks [42; 43]. Therefore, EEG data collected from seven channels (FP1, FP2, F3, Fz, F4, F7, and F8) in the prefrontal and frontal lobes were used in this study, and the NOTE between any two channels was calculated using the CBTN method to construct an undirected weighted network with the NOTE as the edge weight. Network parameters were extracted from the constructed complex network as a quantitative evaluation indicator of cognitive load.