Complexity and Non-Predictability in Neurodynamic: Gender-Specific EEG Dynamics Uncovered via Hidden Markov Models

Complexity and Non-Predictability in Neurodynamic: Gender-Specific EEG Dynamics Uncovered via Hidden Markov Models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Complexity and Non-Predictability in Neurodynamic: Gender-Specific EEG Dynamics Uncovered via Hidden Markov Models Fatemeh Zareayan Jahromy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6332401/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 Jun, 2025 Read the published version in Cognitive Neurodynamics → Version 1 posted 9 You are reading this latest preprint version Abstract One area of interest in neuroscience is the study of differences between male and female brains, encompassing structural, physiological, and neural activity, as well as their implications for behavioral traits and functional capabilities. In this study, we investigate the differences in the complexity of EEG signals between men and women and propose hidden Markov model (HMM) method for measuring complexity which significantly improves the accuracy of gender-based classification compared to conventional signal complexity measures. Using this method to measure complexity of signal, we enhanced the results by reaching to 86% decoding accuracy. Additionally, we demonstrated that the observed effect is particularly dominant in the parietal, frontal and central regions of the brain. Through signal filtering, we observed that differences in signal complexity between men and women are present across most of frequency bins with high rate of enhancement. It is also noteworthy that the level of complexity in women's brain activity is higher than in men's. The results of HMM method showed higher classification accuracy across most frequency bins compared to conventional methods for measuring signal complexity and nonlinearity, such as entropy, Lyapunov and Hurst exponent. Importantly, the performance improvement rate was significantly higher than that of other conventional methods. Additionally, our finding of higher signal complexity in female was entirely consistent with previous studies. Overall, the results demonstrated that using a Hidden Markov Model can more effectively extract signal complexity, significantly enhancing the accuracy of EEG-based gender classification. EEG complexity gender classification hidden Markov model emotion Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction One intriguing application of electroencephalograph (EEG) signal analysis is classification of individuals based on their gender according to their brain activity. Understanding this difference is critical in neuroscience studies [ 1 ] because Many aspects of mind abilities are demonstrated to be different between genders which is related to either structural [ 2 , 3 ], and networking[ 4 , 5 ] of brain’s circuit and also some epigenetic mechanisms[ 6 , 7 ]. Given these well-documented differences between male and female, predicting this difference in many neuroscience studies can help us to improve the precision of signal analyzing algorithms. As we know, in neuroscience studies, EEG can serve as a non-invasive and precise tool for detecting mystery of brain function in different task. So detecting the aspects of gender difference in EEG signal is a beneficial finding either as a classification approach for gender-based classification of subjects or as a tool to enhance the accuracy of EEG studies by alignment of data from different genders. For instance, gender-specific brainwave patterns could help tailor medical treatments, improve BCI adaptability, and enhance diagnostic tools for neurological disorders. Analysis of EEG signals has been traditionally based on linear methods such as power, which, while useful, often fail to capture the nonlinearity of brain activity which is a main part of non-stationary nature of EEG signal. Recent advancements in introducing signal processing algorithms for measuring signal complexity have clarify the importance of nonlinear features and signal complexity in analyzing EEG data[ 8 ]. Complexity and nonlinear measures such commonly used entropy, fractal dimension, Lyapunov exponents and skewness provide a quantitative assessment of the irregularity and unpredictability of brain signals. By measuring the amount of complexity of EEG signals in each experiment, researchers can detect state-specific patterns that are hidden in the signal. One of the most widely used complexity measures is entropy, which quantifies the amount of randomness in a signal. Approximate Entropy (ApEn) and Sample Entropy (SampEn) have been extensively applied to EEG data to study various mental states such as different emotions, [ 9 – 11 ] or brain abnormalities such as epilepsy [ 12 ], Alzheimer's disease [ 13 ], autism [ 14 ] and sleep disorders [ 15 ]. Fractal dimension (FD) is another prominent measure of signal complexity, reflecting the self-similarity and structural intricacy of EEG time series. Different methods including Higuchi’s fractal dimension and Katz's fractal dimension have been utilized to analyze EEG signals in various domain relating to brain activity [ 15 – 18 ]. These studies have shown that fractal dimension can serve as a reliable indicator of the statues of brain activity. Lyapunov exponents, is a measure of complexity which quantifies the rate of divergence of nearby trajectories in a dynamical system. This measure can be applied to EEG signals to assess its chaotic behavior. Lyapunov exponent (LLE) can effectively characterize the stability and predictability of brain activity, introducing it as a method to distinguish between different mental and brain states [ 19 – 21 ]. This paper aims to investigate the role of nonlinear features and signal complexity in the classification of EEG signals based on gender. There are some previous studies that have focused on finding the different of EEG complexity and nonlinearity between genders. In many of these papers, nonlinearity measures (as explained above) were extracted to indicate the degree of randomness and predictivity of signals. Research indicates that male and female brains exhibit distinct patterns in terms of signal complexity, entropy, and fractal dimensions and Hurst exponent [ 22 – 25 ], which can be effectively captured using nonlinear metrics. For instance, entropy-based measures have revealed gender-specific differences in the regularity and predictability of EEG signals, with females often showing higher entropy values, suggesting greater complexity and randomness in their brain activity [ 23 – 24 ]. Similarly, fractal dimension analysis has demonstrated that male EEG signals tend to exhibit more structured and predictable patterns compared to females, and so women often display higher fractal complexity [ 25 ]. Because of this gender-specific pattern of complexity, these features can be used as an effective input for gender classification with EEG signal in resting state or task state. In our dataset in this research, popular measures of EEG complexity in average lead to decoding accuracy of about 60% that while significant, but is not a high accuracy. We seek to find a measure to quantify EEG complexity and predictability that give us a higher gender-classification accuracy. Hidden Markov Models (HMMs) have emerged as a powerful algorithm for characterizing the dynamics of EEG signals by analyzing the probability of hidden states underlying observed data. By representing EEG signals as a sequence of states with probabilistic transitions, HMMs can capture the temporal structure and variability of brain activity, so that we can calculate the complexity and predictability of neural processes. This study investigates the application of HMMs to quantify the complexity of EEG signals and assess their predictability, offering a novel framework for understanding brain dynamics and its implications for cognitive research. So, we used HMM to measure the predictability of EEG based on the accuracy of its fitted model for its hidden state in each single trial and we could reach to about 84% performance which is significantly higher performance relative to other measures of complexity. We controlled the effect of noise on this finding and demonstrated that this is a genuine feature of brain activity that differentiate between genders, not a noise effect. Although this is consistent with previous findings on the dependency between gender and signal complexity, but shows this distinction with greater accuracy. In addition, the greater signal complexity in female was also confirmed by the proposed method. Methods Dataset and preprocessing The SEED (SJTU Emotion EEG Dataset) is a publicly available dataset that is recorded for emotion recognition research using EEG signals. It was developed by the BCMI Laboratory at Shanghai Jiao Tong University. The dataset contains EEG recordings from 15 participants (7 males and 8 females, although we used 7 males and 7 females for balancing the number of participants in each category) who were watching film clips to arouse different emotional states. These clips were carefully selected to elicit three primary emotional states: positive, neutral, and negative. Each participant performed 15 trials, with each trial consisting of a video stimulus followed by a self-assessment of their emotional state. The EEG signals were recorded using a 62-channel ESI Neuroscan system at a sampling rate of 1000 Hz, ensuring high temporal resolution. Preprocessing steps, such as down sampling to 200 Hz and bandpass filtering (0.5 Hz to 75 Hz), were applied to enhance signal quality and reduce noise. Additionally, artifacts like eye movements and muscle were removed from signal manually (EOG has been recorded to identify blink artifacts) [ 28 , 29 ]. In addition to the initial preprocessing steps, some channels still contained high-amplitude noise. To examine these channels, each channel was labeled with the maximum signal amplitude. Then, for each channel, the number of trials where this label exceeded the mean plus two times the standard deviation of the labels in that same channel was counted. If more than 10% of the trials in a channel exceeded the threshold value, that channel was identified as noisy and removed from further calculations. To maintain a balance between the two datasets (male and female), common channels were removed from the total set of channels, resulting in the removal of 8 channels in total. Following this stage, given the critical role of signal amplitude and its variations in data classification, we normalized the data using z-score standardization. This process aligned the mean of all trials across both genders to zero and their variance to one. The calculation was performed individually for each trial across all 54 remaining channels, resulting in a 54-dimensional feature space per trial. Subsequently, we applied Independent Component Analysis (ICA) to identify and remove noise components unrelated to neural activity. Through systematic evaluation of all components, artifactual elements were eliminated, yielding denoised signals for subsequent analysis stages. Furthermore, as detailed in later sections, we validated our approach across multiple frequency bands. The consistent performance of our method across all bands not only demonstrates its robustness but also confirms the methodological integrity of our proposed framework, as it remains unaffected by noise or band-specific artifacts. This multi-band verification underscores the reliability and novelty of our technique in capturing genuine neurodynamic features. HMM method Hidden Markov Models (HMMs) are probabilistic models used to describe systems that transition between a finite set of hidden states, where each state generates observable outputs according to a probability distribution. For EEG analysis, the hidden states represent underlying neural dynamics, while the observed outputs correspond to the recorded EEG signals. An HMM is characterized by three main components: (1) the transition probability matrix, which defines the likelihood of moving from one state to another; (2) the emission probability matrix, which describes the probability of observing a particular EEG pattern given the current state; and (3) the initial state distribution, which specifies the starting probabilities of the hidden states. [ 26 , 27 ] By training the HMM on EEG data using algorithms such as the Baum-Welch algorithm, the model learns the optimal parameters that best explain the observed signal dynamics. After training the model, we tested the model by decoding each single trial. while testing the model for each trial, the probability of that trial to be consistent with the model by a trained transition matrix is evaluated. The log of this probability is in each trial for each channel separately, is selected as the feature space element, so the features are negative quantities because the probabilities are between 0 and 1. If the time series (signal of single trial) is so complex and non-predictable, the model will not be responsible for the trial that is used for decoding and so the probability will be more negative. So, this approach provides a robust framework for capturing the non-stationary and stochastic nature of brain activity. One of the critical steps in implementing the hidden Markov model (HMM) is signal quantization, which prepares the data for model training. Quantization assigns each signal level to a specific state, enabling the creation of a model that represents the input signal. This step significantly influences the model's accuracy, making it essential to carefully determine the quantization levels. In this study, we utilized the Bayesian Information Criterion (BIC) to identify the optimal number of quantization levels. BIC is a widely used statistical measure that balances model fit and complexity, penalizing excessive parameters to prevent overfitting. In the context of EEG signal quantization, BIC helps determine the most suitable number of clusters by minimizing the criterion, ensuring that the model captures the signal's essential features while maintaining computational efficiency. After applying BIC, we identified 10 clusters as the optimal number, leading us to quantize the EEG signal amplitude into 10 distinct levels. The result is illustrated in Fig. 1 . Nonlinear features As we explained above, nonlinear feature captures the complex and dynamic nature of brain activity. Here we proposed that we can extract nonlinearity and complexity of EEG signal with HMM to use it as a feature for gender-based classification. To examine the advantages of proposed method, we compared its results with the results of classification using other common methods of nonlinear feature extraction. Several methods are commonly employed to quantify nonlinear characteristics. Skewness measures the asymmetry of the probability distribution of the signal, calculated as the third standardized moment. In EEG analysis, skewness helps identify deviations from a normal distribution, which may reflect asymmetrical neural activity or the presence of artifacts. Entropy is another nonlinear measure which quantifies the irregularity or unpredictability of the signal. Mathematically, Shannon Entropy is defined as H(X)=−∑p(x)log p(x)H(X)=−∑p(x) log p(x), where p(x) is the probability distribution of the signal. In EEG, entropy reflects the complexity of neural processes, with higher entropy values often associated with more complex brain states. The Hurst Exponent evaluates the long-term memory or persistence in a signal, computed using rescaled range analysis or detrended fluctuation analysis. For EEG signals, H > 0.5 indicates persistent behavior, H < 0.5 suggests anti-persistence, and H = 0.5 corresponds to random behavior, providing insights into the temporal organization of neural activity. he Lyapunov exponent is a nonlinear dynamic measure used to quantify the sensitivity of a system to initial conditions, often applied to chaotic systems. In the context of EEG signal analysis, the Lyapunov exponent can be utilized as a feature to characterize the complexity and stability of brain activity. Specifically, it measures the average exponential divergence or convergence of nearby trajectories in the phase space of the EEG signal. A positive Lyapunov exponent indicates chaotic behavior, reflecting higher complexity and unpredictability in the signal, while a negative value suggests stability and regularity. Together, these methods provide a comprehensive framework for analyzing the nonlinear dynamics of EEG signals, enabling deeper insights into brain function, cognitive states, and neurological disorders. Classification After producing feature space (62D space), we trained a SVM classifier for each nonlinear feature separately. We used 5-fold cross validation, the trials of two groups were balanced at the first step. We repeated classification 100 time, so we obtained 500 accuracies for each analysis, the reported accuracies are just on test data. Statistical analysis was performed using ttest(p < 0.01). Results Compare between emotion states The algorithm proposed in this study, based on the Hidden Markov Model (HMM), was initially designed to enhance the accuracy of gender classification using brain signals. Similar to other methods for measuring signal complexity, the Hidden Markov Model can predict the degree of randomness in a signal. The prediction rate of signal occurrences in this method is estimated based on how well the HMM fits the target signal. It is claimed that the efficiency of this approach is superior to other signal complexity measurement methods, a claim that will be substantiated in the following sections. At first, to evaluate the effectiveness of the proposed model, we utilized seed data, which consists of data related to emotions. In this dataset, three emotional states—neutral, positive, and negative—were defined across various trials. A key question in gender classification is whether there are differences in brain activity between men and women across different emotional states. Specifically, can the same level of gender classification accuracy be achieved in one emotional state as in others? If the classification accuracy decreases in a particular emotional state, it suggests that brain activity between men and women becomes more similar in that state. For instance, in the method proposed in this article, a significant drop in classification accuracy in a specific emotional state would imply that the signal complexity levels between men and women are converging in that state. However, as shown in the results presented in Fig. 2 , changing the emotional state does not lead to a significant difference in gender classification accuracy based on signal complexity. Two conclusions can be drawn from this finding. One is that emotions do not generally cause brain activity states to become closer or further apart between men and women, and the other is a more correct understanding that the complexity of brain signals measured by the method presented in this article is not a function of the individual's emotional state. Of course, this understanding requires more detailed examination in future studies. Effective brain regions In this dataset, we used 62-channel data. In this section, we will examine the role of signal complexity in which part of the brain has the greatest effect on distinguishing between the sexes of individuals. To do this by using chi-square method we sorted the features for gender classification (62 features for 62 electrodes) and selected the 15 electrodes as the most effective ones. For each time of cross-validation procedure we sorted the features separately, so we repeated this for 500 times. At last, we counted the repetition of each electrodes in 500 iteration. Number of repetitions was used as a marker of its importance. Figure 3 shows that this effect is not a global effect, but a concentrated effect, which is more pronounced in the parietal and central region and also frontal region. We will discuss the relationship between these regions and gender differences in more detail in the Discussion section. The accuracy of the results presented from this brain map will be examined in the control methods discussed in the following sections. Controls: Filtering One of the issues that may affect the accuracy of our results is the effect of noise on the signal. If the increase in noise in some data affects the predictability of the signal, it cannot be said with certainty that the accuracy obtained is due to a genuine difference in the complexity of the brain signal between men and women. To ensure this, we first used signal filtering. In this method, we filtered the data with a Butterworth band-pass filter in 5 Hz frequency windows. If there is noise in a specific frequency spectrum and the effect of this noise on increasing the classification accuracy, the classification accuracy should increase only in that frequency band and we should face a decrease in the classification accuracy in the remaining frequencies. As shown in Fig. 4 , after applying the filter, the classification accuracy is higher than chance in all frequency bands, although in some frequency band performance is significantly higher. This indicates that noise does not affect the increase in the classification accuracy with the proposed method based on the predictability of the signal. On the other hand, it can be said that the difference in signal complexity between men and women is not specific to a specific frequency band and is visible in all bands. After investigating the impact of frequency on the decoding power of the proposed method, we decided to compare the results of this method with those of conventional approaches for extracting nonlinear features and measuring signal complexity. Here, the proposed method is evaluated alongside entropy, skewness, Hurst exponent, and Lyapunov exponent, which are among the most widely used methods for calculating signal complexity. As shown in Fig. 5 .A and 5.B, the HMM-based method demonstrates significantly higher classification accuracy in 43% of frequency bands (3 from 7) compared to other methods, but it is important that the summation of performance enhancement for best features relative to the second best feature in all frequency bands is significantly higher for HMM method. This finding demonstrates that the proposed method significantly and effectively improves the accuracy of gender-based classification compared to other methods. This effect is observed not only at low frequencies but also at high frequencies. Alongside the noise removal techniques explained earlier, this indicates that the obtained results reflect a genuine phenomenon in the brain, rather than being an outcome of noise. Furthermore, in the discussion section, we will elaborate on how our findings regarding the difference in signal predictability between males and females are entirely consistent with previous studies and in this paper, we have proposed a method that measures this difference with high precision and utilizes it to classify signals based on gender SNR: In the next control stage, we focus on examining the effective electrodes. Has the difference in SNR in this electrode compared to other electrodes caused the classification accuracy in this electrode to be higher than others? To investigate this issue, the time course of the signal amplitude distribution in consecutive time intervals is plotted in Fig. 6 . If there is a decrease or increase in SNR in the introduced effective area, this difference should be noticeable in all time intervals. While in this time course, we see that at each time point, a specific area of ​​the brain had the most positive or negative activity and in the next time step, the location of the maximum has changed. This figure shows that the introduced area does not have any special characteristics in terms of SNR compared to other areas, and as a result, its effect on signal classification based on gender is significant. Complexity different between male and female As discussed in the review of previous studies in the introduction section, previous studies have shown that the complexity of brain signals is different between men and women, and if we measure this complexity with criteria such as entropy and fractal, we will see that the level of complexity in women's brain signals is higher than that of men. This issue can be examined and compared from a structural and mental characteristics perspective, which we will discuss in detail in the discussion section. Now we want to know whether the signal complexity in women is still higher than that in men with the currently presented method, which had a much higher gender classification accuracy than other criteria. Figure 7 shows the brain map of the difference in model output between men and women, so that positive values ​​indicate that this value is higher for men. As we can see, the model output, which indicates the level of signal predictability, is higher in men than in women, which indicates the greater complexity and unpredictability of brain activity in women. As expected, this difference increased in electrodes with higher classification accuracy. Discussion The aim of this study is to explore the differences in brain function between men and women. Using machine learning techniques, we sought to classify single trials related to males and females by leveraging various features extracted from EEG-recorded brain activity. Our primary focus is on the complexity and predictability of EEG signals. Previous research has indicated that the complexity of brain signals in women tends to be higher than in men, as assessed through criteria that measure signal predictability or irregularity. For instance, entropy, a measure rooted in information theory, has been used to quantify the irregularity of brain signals. These studies suggest that utilizing nonlinear features of EEG signals to construct a feature space for classifier input can be an effective approach for gender-based classification of brain signals. In this context, we aimed to develop a method that enhances the accuracy of EEG-based gender classification by evaluating signal complexity and irregularity. Our proposed approach involves the use of a hidden Markov model (HMM). This model is trained to describe spatial signals based on their temporal changes, incorporating several hidden states that we hypothesize underlie the observed brain activities. The trained model is then employed to decode the signals. The model's responsiveness to the input signal during the decoding phase serves as an indicator of signal complexity: the more complex and unpredictable the signal, the lower the likelihood of the model being responsive. In this study, this probability during the decoding phase is utilized as a measure of brain signal complexity. After extracting this value from each trial and channel, we construct a feature space, which is subsequently fed into an SVM classifier to perform gender-based classification of the signals. In order to investigate the effectiveness of the proposed method, the classification accuracy obtained with the present method was compared with conventional methods of measuring signal complexity such as entropy, skewness, and Hurst exponent. The results show that this method significantly (more than 15%) increases the accuracy of gender-based classification and by filtering this enhancement increased to 30% relative to other measures of complexity. The data utilized in this study is derived from the SEED dataset, which was originally recorded to investigate the impact of emotions on brain activity. The results presented in various sections of the paper are based on trials conducted under neutral emotional conditions. At this stage, we hypothesized that emotional states might influence the feature space, potentially bringing it closer together or further apart in men and women, which could also be reflected in individual behavioral patterns. For instance, greater mutual understanding between men and women in positive emotional states might suggest that their brain activity patterns are more similar. To explore this, we compared the accuracy of gender classification across three emotional states: neutral, positive, and negative. The results revealed that classification accuracy remains unaffected by emotional state, with no significant differences observed across the three conditions. From these findings, two conclusions can be drawn. First, emotional states do not appear to influence the differences in brain activity between men and women. However, this is a general conclusion, as our analysis focused solely on the complexity of the signals. Therefore, a more precise conclusion would be that different emotional states do not affect the complexity of brain activity that accounts for gender-based differences. It is possible that if a different feature space were selected, the gender-dependent differences in brain activity across emotional states might vary, either diminishing or becoming more pronounced. Given the feature space employed in this study, which focuses on the level of signal complexity, several factors could potentially influence this complexity. For instance, if factor A is the primary differentiator between male and female brain activity, the observations in this study might merely reflect a secondary effect A. At a specific frequency, the signal-to-noise ratio (SNR) might be higher in one gender group than the other due to various reasons. It is also possible that the level of signal noise differs between the two groups in one frequency range, which could impact the observed differences in signal complexity. To ensure that the observed effects are indeed attributable to differences in signal complexity and not to other factors, we conducted a separate analysis. Specifically, we employed a signal filtering approach. If noise at a particular frequency were the primary cause of the complexity differences between genders, high classification accuracy would be expected only within that specific frequency band. We applied filtering in 5 Hz frequency windows ranging from 1 to 35 Hz and found that classification accuracy was significantly higher than chance across all frequency bands. Furthermore, we compared the accuracy of our method with conventional methods for measuring signal complexity across these frequency bands. This analysis revealed that the proposed method consistently achieved higher classification accuracy than traditional approaches in all frequency ranges. These results lead to several key findings. First, the high classification accuracy is likely due to genuine differences in signal complexity between men and women, rather than differences in SNR. Second, the observed differences in signal complexity and uncertainty are not confined to a specific frequency range; instead, significant differences between genders are evident across all defined frequencies. This suggests that the complexity-based feature space captures fundamental gender-related differences in brain activity that are broadly distributed across the frequency spectrum. The next analysis focuses on the localization of the observed effect in the brain. Figure 3 and Fig. 7 illustrates that when signals are grouped by gender, the most significant difference in complexity is located in the parietal and central lobe, and also observed in the frontal lobe. These regions have been previously documented in several studies for their sex-related differences in both activity and structure. For instance, some studies have reported an increase in gray matter volume in the parietal region in women compared to men, a finding that has been uniquely observed in this region and parts of the temporal lobe [ 30 – 32 ]. Furthermore, research has demonstrated that, in addition to structural differences, there are also functional and activity-related distinctions between male and female brains. For example, one study revealed that brain networks during activity in men exhibit more stable patterns compared to women, whereas women display more complex patterns of brain activity, particularly in the parietal lobe [ 33 ]. Another study highlighted that brain activity in the parietal lobe differs significantly between women and men, especially in areas associated with logical thinking and language processing [ 34 ]. There are also numerus evidences that frontal lobe is different between men and women structurally or physiologically and also in viewpoint of networking[ 35 – 37 ]. Numerous other studies align with our findings, emphasizing the differences in brain signal complexity between women and men, with women generally exhibiting higher complexity in brain activity than men, as discussed in the introduction section. Finally, based on these anatomical and physiological insights, we have developed a method capable of distinguishing between male and female brain signals with remarkable accuracy (86%). This level of performance accuracy surpasses what has been achieved using other methods of calculating signal complexity. Of course, after filtering this performance for lower frequencies increased even to 97%. Declarations Author Contribution This paper has only one author who is responsible for all aspects, including initial theorizing, analyses and calculations, generating the figures, as well as writing and reviewing the text. 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In 2013 6th international IEEE/EMBS conference on neural engineering (NER) (pp. 81–84). IEEE Im K, Lee JM, Lee J, Shin YW, Kim IY, Kwon JS, Kim SI (2006) Gender difference analysis of cortical thickness in healthy young adults with surface-based methods. NeuroImage 31(1):31–38 Sowell, E. R., Peterson, B. S., Kan, E., Woods, R. P., Yoshii, J., Bansal, R., …Toga, A. W. (2007). Sex differences in cortical thickness mapped in 176 healthy individuals between 7 and 87 years of age. Cerebral cortex, 17(7), 1550–1560 Salinas J, Mills ED, Conrad AL, Koscik T, Andreasen NC, Nopoulos P (2012) Sex differences in parietal lobe structure and development. Gend Med 9(1):44–55 Feng T, Mi M, Li D, Wang B, Liu X (2 024). Exploring neural mechanisms of gender differences in bodily emotion recognition: a time-frequency analysis and network analysis study. Front NeuroSci, 18, 1499084 Pradeep HBAC, Meegama RGN (2020) Age and gender related variations in human EEG signals. Int J Digit Signals Smart Syst 4(1–3):87–99 Gur RC, Gunning-Dixon F, Bilker WB, Gur RE (2002) Sex differences in temporo-limbic and frontal brain volumes of healthy adults. Cereb Cortex 12(9):998–1003 Szeszko, P. R., Vogel, J., Ashtari, M., Malhotra, A. K., Bates, J., Kane, J. M.,… Lim, K. (2003). Sex differences in frontal lobe white matter microstructure: a DTI study. Neuroreport , 14 (18), 2469–2473 Grabowska A (2017) Sex on the brain: are gender-dependent structural and functional differences associated with behavior? J Neurosci Res 95(1–2):200–212 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 09 Jun, 2025 Read the published version in Cognitive Neurodynamics → Version 1 posted Editorial decision: Revision requested 19 Apr, 2025 Reviews received at journal 12 Apr, 2025 Reviewers agreed at journal 09 Apr, 2025 Reviews received at journal 05 Apr, 2025 Reviewers agreed at journal 04 Apr, 2025 Reviewers invited by journal 03 Apr, 2025 Editor assigned by journal 02 Apr, 2025 Submission checks completed at journal 02 Apr, 2025 First submitted to journal 29 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6332401","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":445038475,"identity":"860fabe9-0392-4b2c-82ab-d16d9edf36e9","order_by":0,"name":"Fatemeh Zareayan Jahromy","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIiWNgGAWjYBAC9gY4qxHGZGzAphIOeA7AWQeBKhNI0iIBUp5AhMN4+A8/+/Ch5rC8ueTjNsmfPxjk+RuY2z7g1cJwzHjmjGOHDXfOTmyT5klgMJxxgLF5Bj4t9owNxsw8bIcZN9wGagE6jHEDA2Mzfocxs39m/vPvsP2GmwfbJH8kMNgT1sLGY8zM2HY4ccMNxjYJoMMSCWvh4Slm7O1LT95wJrHZmidNInnGYUJa+I9vZvjxzdp2w/HjD2/+sLGx7W9vf4xXCxTAzZVgYGAmRgMDQx1xykbBKBgFo2BkAgDPsUXjOiKbRAAAAABJRU5ErkJggg==","orcid":"","institution":"Iran University of Science and Technology (IUST)","correspondingAuthor":true,"prefix":"","firstName":"Fatemeh","middleName":"Zareayan","lastName":"Jahromy","suffix":""}],"badges":[],"createdAt":"2025-03-29 06:53:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6332401/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6332401/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11571-025-10271-9","type":"published","date":"2025-06-09T15:57:19+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":81449713,"identity":"5f9f52e3-d3f8-4283-90f0-f6cdea9efc1f","added_by":"auto","created_at":"2025-04-26 18:43:46","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":22267,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCalibration\u003c/strong\u003e: Determining the number of quantization levels of an EEG signal using the BIC criterion aims to find the number of clusters in which this criterion reaches its minimum value.\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6332401/v1/3eef4bb7a9fc3a75a0fee3b4.jpg"},{"id":81449715,"identity":"73e1deaa-3fe7-449c-bbe7-ccddd29794a3","added_by":"auto","created_at":"2025-04-26 18:43:46","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":25863,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEmotion effect:\u003c/strong\u003e Comparison between the classification accuracy of the proposed method in three emotional states. In this section, column 1 is related to the neutral emotional state, column 2 to the negative emotional state, and column 3 to the positive emotional state\u003c/p\u003e","description":"","filename":"Picture2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6332401/v1/5c791d1010c47e9b466abe6b.jpg"},{"id":81449716,"identity":"c2e0135a-4bb1-4fd3-836c-64d838880025","added_by":"auto","created_at":"2025-04-26 18:43:46","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":77481,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSpatial evaluation\u003c/strong\u003e: Locating the regions of the brain that have the most significant impact on improving the accuracy of gender classification based on signal complexity reveals that the largest differences in complexity between men and women are observed in the parietal, central and frontal lobes. This figure highlights that these areas exhibit the most distinct variations in signal complexity, which can be leveraged to enhance gender classification accuracy. Right figure represents the name of electrodes.\u003c/p\u003e","description":"","filename":"Picture3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6332401/v1/53252480a928213f441d70bf.jpg"},{"id":81449718,"identity":"6a285a09-a91a-40cc-868d-6fd3236730d0","added_by":"auto","created_at":"2025-04-26 18:43:46","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":53241,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe Effect of Frequency on Decoding Accuacy:\u003c/strong\u003e This figure illustrates whether filtering the EEG signal in different frequency bands affects classification accuracy. Each column in the figure represents the accuracy within a specific frequency window. \u0026nbsp;Here, seven non-overlapping 5 Hz frequency windows are used within the 0 to 35 Hz range.\u003c/p\u003e","description":"","filename":"Picture4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6332401/v1/5dd79da188793c10386e087f.jpg"},{"id":81450221,"identity":"98f3b01c-fc32-4623-83db-6e88ea5b02aa","added_by":"auto","created_at":"2025-04-26 18:59:47","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":44469,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eClassification Accuracy Across Different Frequency Bands\u003c/strong\u003e: A. This figure compares the classification accuracy achieved using various nonlinear features across different frequency bands. As shown, the proposed method achieves the highest classification accuracy in all frequency bands B. percentage of number of frequency bands with maximum decoding accuracy for each feature. C. Accuracy enhancement for best feature relative to second best feature.\u003c/p\u003e","description":"","filename":"Picture5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6332401/v1/51af9c9a7913a0d19d52d561.jpg"},{"id":81449736,"identity":"8163e8a7-2f31-44de-a4d1-637419d2f05c","added_by":"auto","created_at":"2025-04-26 18:43:47","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":161056,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTemporal Trends in Brain Maps\u003c/strong\u003e: In this figure, we aim to assess the temporal trends in brain maps to ensure that the electrodes identified as influential do not consistently exhibit higher SNR (Signal-to-Noise Ratio) throughout the entire time period. If this were the case, the observed effects in the parietal, central \u0026nbsp;and frontal regions could be attributed to higher SNR rather than genuine neural activity. This figure demonstrates that no specific brain region consistently maintains a higher SNR compared to other areas over time.\u003c/p\u003e","description":"","filename":"Picture6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6332401/v1/e77bc75b64df2a4bb71e8984.jpg"},{"id":81449720,"identity":"afff83ff-8a7b-4755-8722-3b273f353df3","added_by":"auto","created_at":"2025-04-26 18:43:47","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":17077,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAnalysis of Differences in Complexity and Unpredictability of EEG Signals Between Men and Women\u003c/strong\u003e: In this figure, the features extracted using the proposed method are calculated for both men and women and then subtracted, where positive values indicate higher values for men. According to the metric considered in this study, higher values reflect greater predictability and lower complexity of the signal.\u003c/p\u003e","description":"","filename":"Picture7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6332401/v1/e1d9ee0739df87176601125f.jpg"},{"id":84726771,"identity":"c407a3d0-aac2-4835-8954-02e165be2137","added_by":"auto","created_at":"2025-06-16 16:08:09","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":971212,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6332401/v1/36cae67e-143b-4f3a-a37d-b7e3ba1e4d02.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eComplexity and Non-Predictability in Neurodynamic: Gender-Specific EEG Dynamics Uncovered via Hidden Markov Models\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eOne intriguing application of electroencephalograph (EEG) signal analysis is classification of individuals based on their gender according to their brain activity. Understanding this difference is critical in neuroscience studies [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] because Many aspects of mind abilities are demonstrated to be different between genders which is related to either structural [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], and networking[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] of brain\u0026rsquo;s circuit and also some epigenetic mechanisms[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Given these well-documented differences between male and female, predicting this difference in many neuroscience studies can help us to improve the precision of signal analyzing algorithms. As we know, in neuroscience studies, EEG can serve as a non-invasive and precise tool for detecting mystery of brain function in different task. So detecting the aspects of gender difference in EEG signal is a beneficial finding either as a classification approach for gender-based classification of subjects or as a tool to enhance the accuracy of EEG studies by alignment of data from different genders. For instance, gender-specific brainwave patterns could help tailor medical treatments, improve BCI adaptability, and enhance diagnostic tools for neurological disorders.\u003c/p\u003e \u003cp\u003eAnalysis of EEG signals has been traditionally based on linear methods such as power, which, while useful, often fail to capture the nonlinearity of brain activity which is a main part of non-stationary nature of EEG signal. Recent advancements in introducing signal processing algorithms for measuring signal complexity have clarify the importance of nonlinear features and signal complexity in analyzing EEG data[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Complexity and nonlinear measures such commonly used entropy, fractal dimension, Lyapunov exponents and skewness provide a quantitative assessment of the irregularity and unpredictability of brain signals. By measuring the amount of complexity of EEG signals in each experiment, researchers can detect state-specific patterns that are hidden in the signal.\u003c/p\u003e \u003cp\u003eOne of the most widely used complexity measures is entropy, which quantifies the amount of randomness in a signal. Approximate Entropy (ApEn) and Sample Entropy (SampEn) have been extensively applied to EEG data to study various mental states such as different emotions, [\u003cspan additionalcitationids=\"CR10\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] or brain abnormalities such as epilepsy [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], Alzheimer's disease [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], autism [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] and sleep disorders [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFractal dimension (FD) is another prominent measure of signal complexity, reflecting the self-similarity and structural intricacy of EEG time series. Different methods including Higuchi\u0026rsquo;s fractal dimension and Katz's fractal dimension have been utilized to analyze EEG signals in various domain relating to brain activity [\u003cspan additionalcitationids=\"CR16 CR17\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. These studies have shown that fractal dimension can serve as a reliable indicator of the statues of brain activity.\u003c/p\u003e \u003cp\u003eLyapunov exponents, is a measure of complexity which quantifies the rate of divergence of nearby trajectories in a dynamical system. This measure can be applied to EEG signals to assess its chaotic behavior. Lyapunov exponent (LLE) can effectively characterize the stability and predictability of brain activity, introducing it as a method to distinguish between different mental and brain states [\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis paper aims to investigate the role of nonlinear features and signal complexity in the classification of EEG signals based on gender. There are some previous studies that have focused on finding the different of EEG complexity and nonlinearity between genders. In many of these papers, nonlinearity measures (as explained above) were extracted to indicate the degree of randomness and predictivity of signals. Research indicates that male and female brains exhibit distinct patterns in terms of signal complexity, entropy, and fractal dimensions and Hurst exponent [\u003cspan additionalcitationids=\"CR23 CR24\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], which can be effectively captured using nonlinear metrics. For instance, entropy-based measures have revealed gender-specific differences in the regularity and predictability of EEG signals, with females often showing higher entropy values, suggesting greater complexity and randomness in their brain activity [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Similarly, fractal dimension analysis has demonstrated that male EEG signals tend to exhibit more structured and predictable patterns compared to females, and so women often display higher fractal complexity [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBecause of this gender-specific pattern of complexity, these features can be used as an effective input for gender classification with EEG signal in resting state or task state. In our dataset in this research, popular measures of EEG complexity in average lead to decoding accuracy of about 60% that while significant, but is not a high accuracy. We seek to find a measure to quantify EEG complexity and predictability that give us a higher gender-classification accuracy.\u003c/p\u003e \u003cp\u003eHidden Markov Models (HMMs) have emerged as a powerful algorithm for characterizing the dynamics of EEG signals by analyzing the probability of hidden states underlying observed data. By representing EEG signals as a sequence of states with probabilistic transitions, HMMs can capture the temporal structure and variability of brain activity, so that we can calculate the complexity and predictability of neural processes. This study investigates the application of HMMs to quantify the complexity of EEG signals and assess their predictability, offering a novel framework for understanding brain dynamics and its implications for cognitive research.\u003c/p\u003e \u003cp\u003eSo, we used HMM to measure the predictability of EEG based on the accuracy of its fitted model for its hidden state in each single trial and we could reach to about 84% performance which is significantly higher performance relative to other measures of complexity. We controlled the effect of noise on this finding and demonstrated that this is a genuine feature of brain activity that differentiate between genders, not a noise effect. Although this is consistent with previous findings on the dependency between gender and signal complexity, but shows this distinction with greater accuracy. In addition, the greater signal complexity in female was also confirmed by the proposed method.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eDataset and preprocessing\u003c/h2\u003e \u003cp\u003eThe SEED (SJTU Emotion EEG Dataset) is a publicly available dataset that is recorded for emotion recognition research using EEG signals. It was developed by the BCMI Laboratory at Shanghai Jiao Tong University. The dataset contains EEG recordings from 15 participants (7 males and 8 females, although we used 7 males and 7 females for balancing the number of participants in each category) who were watching film clips to arouse different emotional states. These clips were carefully selected to elicit three primary emotional states: positive, neutral, and negative. Each participant performed 15 trials, with each trial consisting of a video stimulus followed by a self-assessment of their emotional state.\u003c/p\u003e \u003cp\u003eThe EEG signals were recorded using a 62-channel ESI Neuroscan system at a sampling rate of 1000 Hz, ensuring high temporal resolution. Preprocessing steps, such as down sampling to 200 Hz and bandpass filtering (0.5 Hz to 75 Hz), were applied to enhance signal quality and reduce noise. Additionally, artifacts like eye movements and muscle were removed from signal manually (EOG has been recorded to identify blink artifacts) [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn addition to the initial preprocessing steps, some channels still contained high-amplitude noise. To examine these channels, each channel was labeled with the maximum signal amplitude. Then, for each channel, the number of trials where this label exceeded the mean plus two times the standard deviation of the labels in that same channel was counted. If more than 10% of the trials in a channel exceeded the threshold value, that channel was identified as noisy and removed from further calculations. To maintain a balance between the two datasets (male and female), common channels were removed from the total set of channels, resulting in the removal of 8 channels in total.\u003c/p\u003e \u003cp\u003eFollowing this stage, given the critical role of signal amplitude and its variations in data classification, we normalized the data using z-score standardization. This process aligned the mean of all trials across both genders to zero and their variance to one. The calculation was performed individually for each trial across all 54 remaining channels, resulting in a 54-dimensional feature space per trial. Subsequently, we applied Independent Component Analysis (ICA) to identify and remove noise components unrelated to neural activity. Through systematic evaluation of all components, artifactual elements were eliminated, yielding denoised signals for subsequent analysis stages.\u003c/p\u003e \u003cp\u003eFurthermore, as detailed in later sections, we validated our approach across multiple frequency bands. The consistent performance of our method across all bands not only demonstrates its robustness but also confirms the methodological integrity of our proposed framework, as it remains unaffected by noise or band-specific artifacts. This multi-band verification underscores the reliability and novelty of our technique in capturing genuine neurodynamic features.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eHMM method\u003c/h3\u003e\n\u003cp\u003eHidden Markov Models (HMMs) are probabilistic models used to describe systems that transition between a finite set of hidden states, where each state generates observable outputs according to a probability distribution. For EEG analysis, the hidden states represent underlying neural dynamics, while the observed outputs correspond to the recorded EEG signals. An HMM is characterized by three main components: (1) the transition probability matrix, which defines the likelihood of moving from one state to another; (2) the emission probability matrix, which describes the probability of observing a particular EEG pattern given the current state; and (3) the initial state distribution, which specifies the starting probabilities of the hidden states. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eBy training the HMM on EEG data using algorithms such as the Baum-Welch algorithm, the model learns the optimal parameters that best explain the observed signal dynamics.\u003c/p\u003e \u003cp\u003eAfter training the model, we tested the model by decoding each single trial. while testing the model for each trial, the probability of that trial to be consistent with the model by a trained transition matrix is evaluated. The log of this probability is in each trial for each channel separately, is selected as the feature space element, so the features are negative quantities because the probabilities are between 0 and 1. If the time series (signal of single trial) is so complex and non-predictable, the model will not be responsible for the trial that is used for decoding and so the probability will be more negative. So, this approach provides a robust framework for capturing the non-stationary and stochastic nature of brain activity.\u003c/p\u003e \u003cp\u003eOne of the critical steps in implementing the hidden Markov model (HMM) is signal quantization, which prepares the data for model training. Quantization assigns each signal level to a specific state, enabling the creation of a model that represents the input signal. This step significantly influences the model's accuracy, making it essential to carefully determine the quantization levels. In this study, we utilized the Bayesian Information Criterion (BIC) to identify the optimal number of quantization levels. BIC is a widely used statistical measure that balances model fit and complexity, penalizing excessive parameters to prevent overfitting. In the context of EEG signal quantization, BIC helps determine the most suitable number of clusters by minimizing the criterion, ensuring that the model captures the signal's essential features while maintaining computational efficiency. After applying BIC, we identified 10 clusters as the optimal number, leading us to quantize the EEG signal amplitude into 10 distinct levels. The result is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eNonlinear features\u003c/h3\u003e\n\u003cp\u003eAs we explained above, nonlinear feature captures the complex and dynamic nature of brain activity. Here we proposed that we can extract nonlinearity and complexity of EEG signal with HMM to use it as a feature for gender-based classification. To examine the advantages of proposed method, we compared its results with the results of classification using other common methods of nonlinear feature extraction. Several methods are commonly employed to quantify nonlinear characteristics. Skewness measures the asymmetry of the probability distribution of the signal, calculated as the third standardized moment. In EEG analysis, skewness helps identify deviations from a normal distribution, which may reflect asymmetrical neural activity or the presence of artifacts.\u003c/p\u003e \u003cp\u003eEntropy is another nonlinear measure which quantifies the irregularity or unpredictability of the signal. Mathematically, Shannon Entropy is defined as H(X)=\u0026minus;\u0026sum;p(x)log p(x)H(X)=\u0026minus;\u0026sum;p(x) log p(x), where p(x) is the probability distribution of the signal. In EEG, entropy reflects the complexity of neural processes, with higher entropy values often associated with more complex brain states. The Hurst Exponent evaluates the long-term memory or persistence in a signal, computed using rescaled range analysis or detrended fluctuation analysis. For EEG signals, H\u0026thinsp;\u0026gt;\u0026thinsp;0.5 indicates persistent behavior, H\u0026thinsp;\u0026lt;\u0026thinsp;0.5 suggests anti-persistence, and H\u0026thinsp;=\u0026thinsp;0.5 corresponds to random behavior, providing insights into the temporal organization of neural activity.\u003c/p\u003e \u003cp\u003ehe Lyapunov exponent is a nonlinear dynamic measure used to quantify the sensitivity of a system to initial conditions, often applied to chaotic systems. In the context of EEG signal analysis, the Lyapunov exponent can be utilized as a feature to characterize the complexity and stability of brain activity. Specifically, it measures the average exponential divergence or convergence of nearby trajectories in the phase space of the EEG signal. A positive Lyapunov exponent indicates chaotic behavior, reflecting higher complexity and unpredictability in the signal, while a negative value suggests stability and regularity.\u003c/p\u003e \u003cp\u003eTogether, these methods provide a comprehensive framework for analyzing the nonlinear dynamics of EEG signals, enabling deeper insights into brain function, cognitive states, and neurological disorders.\u003c/p\u003e\n\u003ch3\u003eClassification\u003c/h3\u003e\n\u003cp\u003eAfter producing feature space (62D space), we trained a SVM classifier for each nonlinear feature separately. We used 5-fold cross validation, the trials of two groups were balanced at the first step. We repeated classification 100 time, so we obtained 500 accuracies for each analysis, the reported accuracies are just on test data. Statistical analysis was performed using ttest(p\u0026thinsp;\u0026lt;\u0026thinsp;0.01).\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eCompare between emotion states\u003c/h2\u003e \u003cp\u003eThe algorithm proposed in this study, based on the Hidden Markov Model (HMM), was initially designed to enhance the accuracy of gender classification using brain signals. Similar to other methods for measuring signal complexity, the Hidden Markov Model can predict the degree of randomness in a signal. The prediction rate of signal occurrences in this method is estimated based on how well the HMM fits the target signal. It is claimed that the efficiency of this approach is superior to other signal complexity measurement methods, a claim that will be substantiated in the following sections.\u003c/p\u003e \u003cp\u003eAt first, to evaluate the effectiveness of the proposed model, we utilized seed data, which consists of data related to emotions. In this dataset, three emotional states\u0026mdash;neutral, positive, and negative\u0026mdash;were defined across various trials. A key question in gender classification is whether there are differences in brain activity between men and women across different emotional states. Specifically, can the same level of gender classification accuracy be achieved in one emotional state as in others? If the classification accuracy decreases in a particular emotional state, it suggests that brain activity between men and women becomes more similar in that state. For instance, in the method proposed in this article, a significant drop in classification accuracy in a specific emotional state would imply that the signal complexity levels between men and women are converging in that state. However, as shown in the results presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, changing the emotional state does not lead to a significant difference in gender classification accuracy based on signal complexity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTwo conclusions can be drawn from this finding. One is that emotions do not generally cause brain activity states to become closer or further apart between men and women, and the other is a more correct understanding that the complexity of brain signals measured by the method presented in this article is not a function of the individual's emotional state. Of course, this understanding requires more detailed examination in future studies.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eEffective brain regions\u003c/h3\u003e\n\u003cp\u003eIn this dataset, we used 62-channel data. In this section, we will examine the role of signal complexity in which part of the brain has the greatest effect on distinguishing between the sexes of individuals. To do this by using chi-square method we sorted the features for gender classification (62 features for 62 electrodes) and selected the 15 electrodes as the most effective ones. For each time of cross-validation procedure we sorted the features separately, so we repeated this for 500 times. At last, we counted the repetition of each electrodes in 500 iteration. Number of repetitions was used as a marker of its importance. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows that this effect is not a global effect, but a concentrated effect, which is more pronounced in the parietal and central region and also frontal region. We will discuss the relationship between these regions and gender differences in more detail in the Discussion section.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe accuracy of the results presented from this brain map will be examined in the control methods discussed in the following sections.\u003c/p\u003e\n\u003ch3\u003eControls:\u003c/h3\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eFiltering\u003c/h2\u003e \u003cp\u003eOne of the issues that may affect the accuracy of our results is the effect of noise on the signal. If the increase in noise in some data affects the predictability of the signal, it cannot be said with certainty that the accuracy obtained is due to a genuine difference in the complexity of the brain signal between men and women. To ensure this, we first used signal filtering. In this method, we filtered the data with a Butterworth band-pass filter in 5 Hz frequency windows. If there is noise in a specific frequency spectrum and the effect of this noise on increasing the classification accuracy, the classification accuracy should increase only in that frequency band and we should face a decrease in the classification accuracy in the remaining frequencies.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, after applying the filter, the classification accuracy is higher than chance in all frequency bands, although in some frequency band performance is significantly higher. This indicates that noise does not affect the increase in the classification accuracy with the proposed method based on the predictability of the signal. On the other hand, it can be said that the difference in signal complexity between men and women is not specific to a specific frequency band and is visible in all bands.\u003c/p\u003e \u003cp\u003eAfter investigating the impact of frequency on the decoding power of the proposed method, we decided to compare the results of this method with those of conventional approaches for extracting nonlinear features and measuring signal complexity. Here, the proposed method is evaluated alongside entropy, skewness, Hurst exponent, and Lyapunov exponent, which are among the most widely used methods for calculating signal complexity.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.A and 5.B, the HMM-based method demonstrates significantly higher classification accuracy in 43% of frequency bands (3 from 7) compared to other methods, but it is important that the summation of performance enhancement for best features relative to the second best feature in all frequency bands is significantly higher for HMM method. This finding demonstrates that the proposed method significantly and effectively improves the accuracy of gender-based classification compared to other methods. This effect is observed not only at low frequencies but also at high frequencies. Alongside the noise removal techniques explained earlier, this indicates that the obtained results reflect a genuine phenomenon in the brain, rather than being an outcome of noise. Furthermore, in the discussion section, we will elaborate on how our findings regarding the difference in signal predictability between males and females are entirely consistent with previous studies and in this paper, we have proposed a method that measures this difference with high precision and utilizes it to classify signals based on gender\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eSNR:\u003c/h2\u003e \u003cp\u003eIn the next control stage, we focus on examining the effective electrodes. Has the difference in SNR in this electrode compared to other electrodes caused the classification accuracy in this electrode to be higher than others? To investigate this issue, the time course of the signal amplitude distribution in consecutive time intervals is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. If there is a decrease or increase in SNR in the introduced effective area, this difference should be noticeable in all time intervals. While in this time course, we see that at each time point, a specific area of ​​the brain had the most positive or negative activity and in the next time step, the location of the maximum has changed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis figure shows that the introduced area does not have any special characteristics in terms of SNR compared to other areas, and as a result, its effect on signal classification based on gender is significant.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eComplexity different between male and female\u003c/h2\u003e \u003cp\u003eAs discussed in the review of previous studies in the introduction section, previous studies have shown that the complexity of brain signals is different between men and women, and if we measure this complexity with criteria such as entropy and fractal, we will see that the level of complexity in women's brain signals is higher than that of men. This issue can be examined and compared from a structural and mental characteristics perspective, which we will discuss in detail in the discussion section.\u003c/p\u003e \u003cp\u003eNow we want to know whether the signal complexity in women is still higher than that in men with the currently presented method, which had a much higher gender classification accuracy than other criteria. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the brain map of the difference in model output between men and women, so that positive values ​​indicate that this value is higher for men. As we can see, the model output, which indicates the level of signal predictability, is higher in men than in women, which indicates the greater complexity and unpredictability of brain activity in women.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs expected, this difference increased in electrodes with higher classification accuracy.\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe aim of this study is to explore the differences in brain function between men and women. Using machine learning techniques, we sought to classify single trials related to males and females by leveraging various features extracted from EEG-recorded brain activity. Our primary focus is on the complexity and predictability of EEG signals. Previous research has indicated that the complexity of brain signals in women tends to be higher than in men, as assessed through criteria that measure signal predictability or irregularity. For instance, entropy, a measure rooted in information theory, has been used to quantify the irregularity of brain signals. These studies suggest that utilizing nonlinear features of EEG signals to construct a feature space for classifier input can be an effective approach for gender-based classification of brain signals.\u003c/p\u003e \u003cp\u003eIn this context, we aimed to develop a method that enhances the accuracy of EEG-based gender classification by evaluating signal complexity and irregularity. Our proposed approach involves the use of a hidden Markov model (HMM). This model is trained to describe spatial signals based on their temporal changes, incorporating several hidden states that we hypothesize underlie the observed brain activities. The trained model is then employed to decode the signals. The model's responsiveness to the input signal during the decoding phase serves as an indicator of signal complexity: the more complex and unpredictable the signal, the lower the likelihood of the model being responsive. In this study, this probability during the decoding phase is utilized as a measure of brain signal complexity. After extracting this value from each trial and channel, we construct a feature space, which is subsequently fed into an SVM classifier to perform gender-based classification of the signals.\u003c/p\u003e \u003cp\u003eIn order to investigate the effectiveness of the proposed method, the classification accuracy obtained with the present method was compared with conventional methods of measuring signal complexity such as entropy, skewness, and Hurst exponent. The results show that this method significantly (more than 15%) increases the accuracy of gender-based classification and by filtering this enhancement increased to 30% relative to other measures of complexity.\u003c/p\u003e \u003cp\u003eThe data utilized in this study is derived from the SEED dataset, which was originally recorded to investigate the impact of emotions on brain activity. The results presented in various sections of the paper are based on trials conducted under neutral emotional conditions. At this stage, we hypothesized that emotional states might influence the feature space, potentially bringing it closer together or further apart in men and women, which could also be reflected in individual behavioral patterns. For instance, greater mutual understanding between men and women in positive emotional states might suggest that their brain activity patterns are more similar. To explore this, we compared the accuracy of gender classification across three emotional states: neutral, positive, and negative. The results revealed that classification accuracy remains unaffected by emotional state, with no significant differences observed across the three conditions.\u003c/p\u003e \u003cp\u003eFrom these findings, two conclusions can be drawn. First, emotional states do not appear to influence the differences in brain activity between men and women. However, this is a general conclusion, as our analysis focused solely on the complexity of the signals. Therefore, a more precise conclusion would be that different emotional states do not affect the complexity of brain activity that accounts for gender-based differences. It is possible that if a different feature space were selected, the gender-dependent differences in brain activity across emotional states might vary, either diminishing or becoming more pronounced.\u003c/p\u003e \u003cp\u003eGiven the feature space employed in this study, which focuses on the level of signal complexity, several factors could potentially influence this complexity. For instance, if factor A is the primary differentiator between male and female brain activity, the observations in this study might merely reflect a secondary effect A. At a specific frequency, the signal-to-noise ratio (SNR) might be higher in one gender group than the other due to various reasons. It is also possible that the level of signal noise differs between the two groups in one frequency range, which could impact the observed differences in signal complexity. To ensure that the observed effects are indeed attributable to differences in signal complexity and not to other factors, we conducted a separate analysis. Specifically, we employed a signal filtering approach. If noise at a particular frequency were the primary cause of the complexity differences between genders, high classification accuracy would be expected only within that specific frequency band.\u003c/p\u003e \u003cp\u003eWe applied filtering in 5 Hz frequency windows ranging from 1 to 35 Hz and found that classification accuracy was significantly higher than chance across all frequency bands. Furthermore, we compared the accuracy of our method with conventional methods for measuring signal complexity across these frequency bands. This analysis revealed that the proposed method consistently achieved higher classification accuracy than traditional approaches in all frequency ranges. These results lead to several key findings. First, the high classification accuracy is likely due to genuine differences in signal complexity between men and women, rather than differences in SNR. Second, the observed differences in signal complexity and uncertainty are not confined to a specific frequency range; instead, significant differences between genders are evident across all defined frequencies. This suggests that the complexity-based feature space captures fundamental gender-related differences in brain activity that are broadly distributed across the frequency spectrum.\u003c/p\u003e \u003cp\u003eThe next analysis focuses on the localization of the observed effect in the brain. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e illustrates that when signals are grouped by gender, the most significant difference in complexity is located in the parietal and central lobe, and also observed in the frontal lobe. These regions have been previously documented in several studies for their sex-related differences in both activity and structure. For instance, some studies have reported an increase in gray matter volume in the parietal region in women compared to men, a finding that has been uniquely observed in this region and parts of the temporal lobe [\u003cspan additionalcitationids=\"CR31\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Furthermore, research has demonstrated that, in addition to structural differences, there are also functional and activity-related distinctions between male and female brains. For example, one study revealed that brain networks during activity in men exhibit more stable patterns compared to women, whereas women display more complex patterns of brain activity, particularly in the parietal lobe [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Another study highlighted that brain activity in the parietal lobe differs significantly between women and men, especially in areas associated with logical thinking and language processing [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThere are also numerus evidences that frontal lobe is different between men and women structurally or physiologically and also in viewpoint of networking[\u003cspan additionalcitationids=\"CR36\" citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNumerous other studies align with our findings, emphasizing the differences in brain signal complexity between women and men, with women generally exhibiting higher complexity in brain activity than men, as discussed in the introduction section.\u003c/p\u003e \u003cp\u003eFinally, based on these anatomical and physiological insights, we have developed a method capable of distinguishing between male and female brain signals with remarkable accuracy (86%). This level of performance accuracy surpasses what has been achieved using other methods of calculating signal complexity. Of course, after filtering this performance for lower frequencies increased even to 97%.\u003c/p\u003e "},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eThis paper has only one author who is responsible for all aspects, including initial theorizing, analyses and calculations, generating the figures, as well as writing and reviewing the text.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data used in this study is sourced from the publicly available SEED dataset, provided by the BCMI Laboratory at Shanghai Jiao Tong University. The dataset can be accessed and downloaded at (https://bcmi.sjtu.edu.cn/home/seed/).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eCahill L (2006) Why sex matters for neuroscience. 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Sex differences in frontal lobe white matter microstructure: a DTI study. \u003cem\u003eNeuroreport\u003c/em\u003e, \u003cem\u003e14\u003c/em\u003e(18), 2469\u0026ndash;2473\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGrabowska A (2017) Sex on the brain: are gender-dependent structural and functional differences associated with behavior? J Neurosci Res 95(1\u0026ndash;2):200\u0026ndash;212\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"cognitive-neurodynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cody","sideBox":"Learn more about [Cognitive Neurodynamics](http://link.springer.com/journal/11571)","snPcode":"11571","submissionUrl":"https://submission.nature.com/new-submission/11571/3","title":"Cognitive Neurodynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"EEG, complexity, gender classification, hidden Markov model, emotion","lastPublishedDoi":"10.21203/rs.3.rs-6332401/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6332401/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOne area of interest in neuroscience is the study of differences between male and female brains, encompassing structural, physiological, and neural activity, as well as their implications for behavioral traits and functional capabilities. In this study, we investigate the differences in the complexity of EEG signals between men and women and propose hidden Markov model (HMM) method for measuring complexity which significantly improves the accuracy of gender-based classification compared to conventional signal complexity measures. Using this method to measure complexity of signal, we enhanced the results by reaching to 86% decoding accuracy. Additionally, we demonstrated that the observed effect is particularly dominant in the parietal, frontal and central regions of the brain. Through signal filtering, we observed that differences in signal complexity between men and women are present across most of frequency bins with high rate of enhancement. It is also noteworthy that the level of complexity in women's brain activity is higher than in men's. The results of HMM method showed higher classification accuracy across most frequency bins compared to conventional methods for measuring signal complexity and nonlinearity, such as entropy, Lyapunov and Hurst exponent. Importantly, the performance improvement rate was significantly higher than that of other conventional methods. Additionally, our finding of higher signal complexity in female was entirely consistent with previous studies. \u003cem\u003eOverall, the results demonstrated that using a Hidden Markov Model can more effectively extract signal complexity, significantly enhancing the accuracy of EEG-based gender classification.\u003c/em\u003e\u003c/p\u003e","manuscriptTitle":"Complexity and Non-Predictability in Neurodynamic: Gender-Specific EEG Dynamics Uncovered via Hidden Markov Models","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-26 18:43:42","doi":"10.21203/rs.3.rs-6332401/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-04-19T05:49:47+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-13T03:22:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"124097387125600610281635186959278688690","date":"2025-04-10T01:47:10+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-05T17:37:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"173177172403726899110619511743058184535","date":"2025-04-04T06:03:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-04T02:39:44+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-04-02T05:16:04+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-02T05:13:57+00:00","index":"","fulltext":""},{"type":"submitted","content":"Cognitive Neurodynamics","date":"2025-03-29T06:44:56+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"cognitive-neurodynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cody","sideBox":"Learn more about [Cognitive Neurodynamics](http://link.springer.com/journal/11571)","snPcode":"11571","submissionUrl":"https://submission.nature.com/new-submission/11571/3","title":"Cognitive Neurodynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d471ae8a-b19b-4ced-b6e3-1677d3cc0313","owner":[],"postedDate":"April 26th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-06-16T16:05:23+00:00","versionOfRecord":{"articleIdentity":"rs-6332401","link":"https://doi.org/10.1007/s11571-025-10271-9","journal":{"identity":"cognitive-neurodynamics","isVorOnly":false,"title":"Cognitive Neurodynamics"},"publishedOn":"2025-06-09 15:57:19","publishedOnDateReadable":"June 9th, 2025"},"versionCreatedAt":"2025-04-26 18:43:42","video":"","vorDoi":"10.1007/s11571-025-10271-9","vorDoiUrl":"https://doi.org/10.1007/s11571-025-10271-9","workflowStages":[]},"version":"v1","identity":"rs-6332401","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6332401","identity":"rs-6332401","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}