In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the c...In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the correlation matrix. The eigenvalue normalized by M represents weight factor in the ensemble of the corresponding eigen microstate. In the limit M →∞, weight factors drop to zero in the ensemble without localization of the microstate. The finite limit of the weight factor when M →∞ indicates a condensation of the corresponding eigen microstate. This finding indicates a transition into a new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors are confirmed using Monte Carlo data of one-dimensional and two-dimensional Ising models.展开更多
The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAH...The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAHC),K-means clustering,Principal Component Analysis(PCA),and Independent Component Analysis(ICA)are limited by a fixed number of microstate maps and insufficient capability in cross-task feature extraction.Tackling these limitations,this study introduces a Global Map Dissimilarity(GMD)-driven density canopy K-means clustering algorithm.This innovative approach autonomously determines the optimal number of EEG microstate topographies and employs Gaussian kernel density estimation alongside the GMD index for dynamic modeling of EEG data.Utilizing this advanced algorithm,the study analyzes the Motor Imagery(MI)dataset from the GigaScience database,GigaDB.The findings reveal six distinct microstates during actual right-hand movement and five microstates across other task conditions,with microstate C showing superior performance in all task states.During imagined movement,microstate A was significantly enhanced.Comparison with existing algorithms indicates a significant improvement in clustering performance by the refined method,with an average Calinski-Harabasz Index(CHI)of 35517.29 and a Davis-Bouldin Index(DBI)average of 2.57.Furthermore,an information-theoretical analysis of the microstate sequences suggests that imagined movement exhibits higher complexity and disorder than actual movement.By utilizing the extracted microstate sequence parameters as features,the improved algorithm achieved a classification accuracy of 98.41%in EEG signal categorization for motor imagery.A performance of 78.183%accuracy was achieved in a four-class motor imagery task on the BCI-IV-2a dataset.These results demonstrate the potential of the advanced algorithm in microstate analysis,offering a more effective tool for a deeper understanding of the spatiotemporal features of EEG signals.展开更多
Emergence refers to the existence or formation of collective behaviors in complex systems.Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evol...Emergence refers to the existence or formation of collective behaviors in complex systems.Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system.In this framework,the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N×M matrix A,whose columns represent microstates and order of row is consist with the time.The ensemble matrix A can be decomposed as■,where r=min(N,M),eigenvalueσIbehaves as the probability amplitude of the eigen microstate U_I so that■and U_I evolves following V_I.In a disorder complex system,there is no dominant eigenvalue and eigen microstate.When a probability amplitudeσIbecomes finite in the thermodynamic limit,there is a condensation of the eigen microstate UIin analogy to the Bose–Einstein condensation of Bose gases.This indicates the emergence of U_I and a phase transition in complex system.Our framework has been applied successfully to equilibrium threedimensional Ising model,climate system and stock markets.We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown orderparameters,such as phase transitions of collective motion and tipping points in climate systems and ecosystems.展开更多
Macrostate and microstate characteristics of interregional nonlinear interdependence of brain dynamics are investigated for Zen-meditation and normal resting EEG. Evaluation of nonlinear interdependence based on nonli...Macrostate and microstate characteristics of interregional nonlinear interdependence of brain dynamics are investigated for Zen-meditation and normal resting EEG. Evaluation of nonlinear interdependence based on nonlinear dynamic theory and phase space reconstruction is employed in the 30-channel electroencephalographic (EEG) signals to characterize the functioning interactions among different local neuronal networks. This paper presents a new scheme for exploring the microstate and macrostate of interregional brain neural network interactivity. Nonlinear interdependence quantified by similarity index is applied to the phase trajectory reconstructed from multi-channel EEG. The microstate similarity-index matrix (miSIM) is evaluated every 5 millisecond. The miSIMs are classified by K-means clustering. The cluster center corresponds to the macrostate SIM (maSIM) evaluated by conventional scheme. Zen-meditation EEG exhibits rather stationary and stronger interconnectivity among frontal midline regional neural oscillators, whereas resting EEG appears to drift away more often from the midline and extend to the inferior brain regions.展开更多
Electroencephalography(EEG)is a powerful tool for investigating the brain bases of human psychological processes non-invasively.Some important mental functions could be encoded by resting-state EEG activity;that is,th...Electroencephalography(EEG)is a powerful tool for investigating the brain bases of human psychological processes non-invasively.Some important mental functions could be encoded by resting-state EEG activity;that is,the intrinsic neural activity not elicited by a specific task or stimulus.The extraction of informative features from resting-state EEG requires complex signal processing techniques.This review aims to demystify the widely used resting-state EEG signal processing techniques.To this end,we first offer a preprocessing pipeline and discuss how to apply it to resting-state EEG preprocessing.We then examine in detail spectral,connectivity,and microstate analysis,covering the oft-used EEG measures,practical issues involved,and data visualization.Finally,we briefly touch upon advanced techniques like nonlinear neural dynamics,complex networks,and machine learning.展开更多
利用微状态分析方法,在静息状态下的脑电图(EEG)尺度上探究自闭症谱系障碍(ASD)儿童与正常儿童(TD)在脑机制上的差异。根据Cartool中的准则和不同微状态类别的数目对于被试者EEG数据的解释程度,确定微状态类别的数目为4;使用原子化与凝...利用微状态分析方法,在静息状态下的脑电图(EEG)尺度上探究自闭症谱系障碍(ASD)儿童与正常儿童(TD)在脑机制上的差异。根据Cartool中的准则和不同微状态类别的数目对于被试者EEG数据的解释程度,确定微状态类别的数目为4;使用原子化与凝聚层次聚类算法,分割出个人水平和组水平上的微状态类别,分别标记为微状态A、B、C和D。然后根据这4类微状态的地形图和EEG数据各时间点的GEV相关性,将数据拟合回EEG数据,最终得到微状态时间序列,提取时域上的参数特征,比较ASD组和TD组的差异。选取的时间参数为平均持续时间、发生频率、时间覆盖率和转移概率,并通过计算马尔可夫模型的方法探究微状态序列的独立性。结果表明,在ASD组vs TD组中表现有统计差异(P<0.05)的微状态时间参数有:持续时间(A:0.110±0.013 vs 0.180±0.048,C:0.140±0.024 vs 0.220±0.067,D:0.130±0.050 vs 0.190±0.037,单位:s)、时间覆盖率(A:22.0±5.4 vs 27.0±7.2,B:27.0±4.7 vs 18.0±5.5,单位:%)、发生频率(A:1.93±0.52 vs 1.55±0.22,B:2.08±0.46 vs 1.39±0.32,C:2.10±0.49 vs 1.47±0.30,D:1.78±0.19 vs 1.27±0.27,单位:次/s),且卡方检验不支持微状态类别之间在时间序列上是独立的零假设(P<0.01),提示微状态类别之间存在依赖性以及信息共享性。本研究为自闭症的评估提供了客观指标和科学依据。展开更多
基金supported by the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZD-SSW-SYS019)supported by the HPC Cluster of ITP-CAS
文摘In a statistical ensemble with M microstates, we introduce an M × M correlation matrix with correlations among microstates as its elements. Eigen microstates of ensemble can be defined using eigenvectors of the correlation matrix. The eigenvalue normalized by M represents weight factor in the ensemble of the corresponding eigen microstate. In the limit M →∞, weight factors drop to zero in the ensemble without localization of the microstate. The finite limit of the weight factor when M →∞ indicates a condensation of the corresponding eigen microstate. This finding indicates a transition into a new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors are confirmed using Monte Carlo data of one-dimensional and two-dimensional Ising models.
基金funded by National Nature Science Foundation of China,Yunnan Funda-Mental Research Projects,Special Project of Guangdong Province in Key Fields of Ordinary Colleges and Universities and Chaozhou Science and Technology Plan Project of Funder Grant Numbers 82060329,202201AT070108,2023ZDZX2038 and 202201GY01.
文摘The analysis of microstates in EEG signals is a crucial technique for understanding the spatiotemporal dynamics of brain electrical activity.Traditional methods such as Atomic Agglomerative Hierarchical Clustering(AAHC),K-means clustering,Principal Component Analysis(PCA),and Independent Component Analysis(ICA)are limited by a fixed number of microstate maps and insufficient capability in cross-task feature extraction.Tackling these limitations,this study introduces a Global Map Dissimilarity(GMD)-driven density canopy K-means clustering algorithm.This innovative approach autonomously determines the optimal number of EEG microstate topographies and employs Gaussian kernel density estimation alongside the GMD index for dynamic modeling of EEG data.Utilizing this advanced algorithm,the study analyzes the Motor Imagery(MI)dataset from the GigaScience database,GigaDB.The findings reveal six distinct microstates during actual right-hand movement and five microstates across other task conditions,with microstate C showing superior performance in all task states.During imagined movement,microstate A was significantly enhanced.Comparison with existing algorithms indicates a significant improvement in clustering performance by the refined method,with an average Calinski-Harabasz Index(CHI)of 35517.29 and a Davis-Bouldin Index(DBI)average of 2.57.Furthermore,an information-theoretical analysis of the microstate sequences suggests that imagined movement exhibits higher complexity and disorder than actual movement.By utilizing the extracted microstate sequence parameters as features,the improved algorithm achieved a classification accuracy of 98.41%in EEG signal categorization for motor imagery.A performance of 78.183%accuracy was achieved in a four-class motor imagery task on the BCI-IV-2a dataset.These results demonstrate the potential of the advanced algorithm in microstate analysis,offering a more effective tool for a deeper understanding of the spatiotemporal features of EEG signals.
基金supported by the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZD-SSW-SYS019)。
文摘Emergence refers to the existence or formation of collective behaviors in complex systems.Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system.In this framework,the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N×M matrix A,whose columns represent microstates and order of row is consist with the time.The ensemble matrix A can be decomposed as■,where r=min(N,M),eigenvalueσIbehaves as the probability amplitude of the eigen microstate U_I so that■and U_I evolves following V_I.In a disorder complex system,there is no dominant eigenvalue and eigen microstate.When a probability amplitudeσIbecomes finite in the thermodynamic limit,there is a condensation of the eigen microstate UIin analogy to the Bose–Einstein condensation of Bose gases.This indicates the emergence of U_I and a phase transition in complex system.Our framework has been applied successfully to equilibrium threedimensional Ising model,climate system and stock markets.We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown orderparameters,such as phase transitions of collective motion and tipping points in climate systems and ecosystems.
文摘Macrostate and microstate characteristics of interregional nonlinear interdependence of brain dynamics are investigated for Zen-meditation and normal resting EEG. Evaluation of nonlinear interdependence based on nonlinear dynamic theory and phase space reconstruction is employed in the 30-channel electroencephalographic (EEG) signals to characterize the functioning interactions among different local neuronal networks. This paper presents a new scheme for exploring the microstate and macrostate of interregional brain neural network interactivity. Nonlinear interdependence quantified by similarity index is applied to the phase trajectory reconstructed from multi-channel EEG. The microstate similarity-index matrix (miSIM) is evaluated every 5 millisecond. The miSIMs are classified by K-means clustering. The cluster center corresponds to the macrostate SIM (maSIM) evaluated by conventional scheme. Zen-meditation EEG exhibits rather stationary and stronger interconnectivity among frontal midline regional neural oscillators, whereas resting EEG appears to drift away more often from the midline and extend to the inferior brain regions.
基金supported by the National Natural Science Foundation of China(Grant No.31822025,No.31671141)
文摘Electroencephalography(EEG)is a powerful tool for investigating the brain bases of human psychological processes non-invasively.Some important mental functions could be encoded by resting-state EEG activity;that is,the intrinsic neural activity not elicited by a specific task or stimulus.The extraction of informative features from resting-state EEG requires complex signal processing techniques.This review aims to demystify the widely used resting-state EEG signal processing techniques.To this end,we first offer a preprocessing pipeline and discuss how to apply it to resting-state EEG preprocessing.We then examine in detail spectral,connectivity,and microstate analysis,covering the oft-used EEG measures,practical issues involved,and data visualization.Finally,we briefly touch upon advanced techniques like nonlinear neural dynamics,complex networks,and machine learning.
文摘利用微状态分析方法,在静息状态下的脑电图(EEG)尺度上探究自闭症谱系障碍(ASD)儿童与正常儿童(TD)在脑机制上的差异。根据Cartool中的准则和不同微状态类别的数目对于被试者EEG数据的解释程度,确定微状态类别的数目为4;使用原子化与凝聚层次聚类算法,分割出个人水平和组水平上的微状态类别,分别标记为微状态A、B、C和D。然后根据这4类微状态的地形图和EEG数据各时间点的GEV相关性,将数据拟合回EEG数据,最终得到微状态时间序列,提取时域上的参数特征,比较ASD组和TD组的差异。选取的时间参数为平均持续时间、发生频率、时间覆盖率和转移概率,并通过计算马尔可夫模型的方法探究微状态序列的独立性。结果表明,在ASD组vs TD组中表现有统计差异(P<0.05)的微状态时间参数有:持续时间(A:0.110±0.013 vs 0.180±0.048,C:0.140±0.024 vs 0.220±0.067,D:0.130±0.050 vs 0.190±0.037,单位:s)、时间覆盖率(A:22.0±5.4 vs 27.0±7.2,B:27.0±4.7 vs 18.0±5.5,单位:%)、发生频率(A:1.93±0.52 vs 1.55±0.22,B:2.08±0.46 vs 1.39±0.32,C:2.10±0.49 vs 1.47±0.30,D:1.78±0.19 vs 1.27±0.27,单位:次/s),且卡方检验不支持微状态类别之间在时间序列上是独立的零假设(P<0.01),提示微状态类别之间存在依赖性以及信息共享性。本研究为自闭症的评估提供了客观指标和科学依据。
